brochure of study kit for ias pre (csat) aptitude paper-2

Contents of The Brochure

1. Contents Details of Study Kit Paper - II (I) Contents of Comprehension & English Language Comprehension

· Contents of Comprehension · Contents of English Language Comprehension

(II) Contents of Interpersonal & Communication Skills, Decision Making & Problem Solving

· Contents of Interpersonal & Communication Skills · Contents of Decision Making & Problem Solving

(III) Contents of General Mental Ability, Logical Reasoning& Analytical Ability

· Contents of General Mental Ability · Contents of Logical Reasoning & Analytical Ability

(IV) Contents of Basic Numeracy

· Contents of Basic Numeracy

(V) Contents of Data Interpretation & Data Sufficiency

· Contents of Data Interpretation & Data Sufficiency

2. Sample Study Materials of Our Study Kit (I) Comprehension

· Comprehension

(II) English Language & Comprehension

· Sentence · Sentence Correction · English Language Comprehension

(III) Interpersonal & Communication Skills

· Interpersonal & Communication Skills

(IV) Decision Making and Problem Solving

· Decision Making and Problem Solving

(V) General Mental Ability

· Blood Relations · Sitting Arrangements · Arithmetical Reasoning · Number, Ranking and Time Sequence Test

(VI) Logical Reasoning & Analytical Ability

· Syllogism · Statement and Courses of Action · Assertion and Reason · Situation Reaction Tests · Statement and Assumptions

(VII) Basic Numarcy

· Number System · Simplification · Average · Percentage · Time and Distance · Probability · Set Theory, Venn Diagrams, Functions & Relations · Sequences & Series

(VIII) Data Interpretation & Data Sufficiency

· Introduction to Data Interpretation · Pie Charts · Mix Diagrams · Data Sufficiency

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Contents of Study Kit Paper -2

Contents of Comprehension & English Language Comprehension

Contents of Comprehension i Comprehension

Contents of English Language Comprehension

i Narration (Direct and Indirect) i Sentencei Common Errori One-Word Substitution i Synonyms and Antonyms i Idioms and Phrasesi Sentence Correction i Sentence Arrangement i Analogyi Foreign Words and Phrases i English Language Comprehension

Contents of Interpersonal & Communication Skills, Decision Making & Problem Solving

Contents of Interpersonal & Communication Skills

i Interpersonal & Communication Skills

Contents of Decision Making & Problem Solving i Decision Making and Problem Solving

Contents of General Mental Ability, Logical Reasoning & Analytical Ability

Contents of General Mental Ability i Analogy i Classification i Series i Coding-Decoding

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i Blood Relations i Direction Sense Test i Logical Venn Diagrams i Alphabet Test i Sitting Arrangements i Mathematical Operations i Arithmetical Reasoning i Inserting the Missing Character i Number, Ranking and Time Sequence Test i Eligibility Test

Contents of Logical Reasoning & Analytical Ability i Syllogism i Statement and Arguments i Statement and Assumptions i Statement and and Courses of Action i Statement and Conclusions i Deriving Conclusion i Assertion and Reason i Punch lines i Situation Reaction Tests i Cause and Effect i Analytical Reasoning

Contents of Basic Numeracy

Contents of Basic Numeracy i Number System i Fractions i Indices and Surds i Square Root & Cube Root i Simplification i HCF & LCM i Orders of Magnitude i Unitary Method i Average i Percentage i Profit and Loss i Ratio & Proportioni Partnership i Alligation or Mixure i Time and Work i Time and Distance i Simple Interest i Compound Interest




i Area of Plane Figures i Volume and Surface Area of Solid Figures i Clocks and Calendar i Concepts of Geometry i Coordinate Geometry i Combinatorics i Probability i Basic Algebra i Set Theory, Venn Diagrams, Functions & Relations i Statistics i Sequences & Series

Contents of Data Interpretation & Data Sufficiency

Contents of Data Interpretation & Data Sufficiency i Introduction to Data Interpretation i Approaches to Data Interpretation i Table Chart i Pie Charts i Bar Charts i Line Graphs i Mix Diagrams i Data Sufficiency


SAMPLE MATERIAL

OF OUR

STUDY KIT PAPER 2

Basic Numeracy

WWW.UPSCPORTAL.COMFor Any Guidance Call our CSAT Paper - 2 Expert at:at +91 8800734161, 011- 65023618

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A Civil Servant should be well-versed in basics of Number System. In the Civil Services Aptitude Test Paper2, in Basic Numeracy, certainly there will be asked some questions based on types of, and operations on numbers.

In Indian system, numbers are expressed by means of symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, called digits. Here, 0is called insignificant digit whereas 1, 2, 3, 4, 5, 6, 7, 8, 9 are called significant digits. We can express a number intwo ways.

Notation: Representing a number in figures is known as notation as 350.Numeration: Representing a number in words is known as numeration as Five hundred and forty five .

Place Value (Indian)

Crore Lakh Thousand UnitTen Crore Crore Ten Lakhs Lakh Ten Thousands Thousand Hundred Tens One

100000000 10000000 1000000 100000 10000 1000 100 10 1108 107 106 105 104 103 102 101 100

Place Value (International)

Million Thousand UnitHundred Ten Millions One Million Hundred Ten Thousand Hundred Tens OneMillions Thousands Thousands

100000000 10000000 1000000 100000 10000 1000 100 10 1108 102 106 105 104 103 102 101 100

Face Value and Place Value of a DigitFace Value: It is the value of the digit itself eg, in 3452, face value of 4 is four , face value of 2 is two .Place Value: It is the face value of the digit multiplied by the place value at which it is situated eg, in 2586,

place value of 5 is 5 102 = 500.

Number CategoriesNatural Numbers (N): If N is the set of natural numbers, then we write N = {1, 2, 3, 4, 5, 6, }The smallest natural number is 1.Whole Numbers (W): If W is the set of whole numbers, then we write W = {0, 1, 2, 3, 4, 5, }The smallest whole number is 0.

Number System

CHAPTER 1

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Integers (I): If I is the set of integers, then we write I = { 3, 2, 1, 0, 1, 2, 3, }Rational Numbers: Any number which can be expressed in the form of p/q, where p and q are both integers

and q # 0 are called rational numbers.

eg,3 7, ,5, 22 9

-- ¼

There exists infinite number of rational numbers between any two rational numbers.Irrational Numbers Non-recurring and non-terminating decimals are called irrational numbers. These

numbers cannot be expressed in the form of pq .

eg, 3, 5, 29,¼Real Numbers: Real number includes both rational and irrational numbers.

Basic Rules on Natural Numbers1. One digit numbers are from 1 to 9. There are 9 one digit numbers. ie, 9 100.2. Two digit numbers are from 10 to 99. There, are 90 two digit numbers. ie, 9 10.3. Three digit numbers are from 100 to 199. There are 900 three digit numbers ie, 9 102.

In general the number of n digit numbers are 9 10(n 1)

4. Sum of the first n, natural numbers ie, 1 + 2 + 3 + 4 + + n = ( )12

n n +

5. Sum of the squares of the first n natural numbers ie. 12 + 23 + 32 + 42 + + n2 = ( )( )1 2 16

n n n+ +

6. Sum of the cubes of the first n natural ie, 12 + 23 + 32 + + n3 = ( )21

2n né ù+ê úê úë û

Example: What is the value of 51 + 52 + 53 + + 100 ?Solution. 51 + 52 + 33 + ... + 100 = (1 + 3 + + 100) (1 + 2 + 3 + ... + 50)

=100 101 50 51

2 2´ ´

- = 5050 1275 = 3775

Different Types of NumbersEven Numbers: Numbers which are exactly divisible by 2 are called even numbers.eg, 4, 2, 0, 2, 4Sum of first n even numbers = n (n + 1)Odd Numbers: Numbers which are not exactly divisible by 2 are called odd numbers.eg, 5, 3, 1, 0, 1, 3, 5Sum of first n odd numbers = n2

Prime Numbers: Numbers which are divisible by one and itself only are called prime numbers.eg, 2, 3, 5, 7, 112 is the only even prime number.





1 is not a prime number because it has two equal factors.Every prime number greater than 3 can be written in the form of (6K + 1) or (6K 1) where K is an integer.

There are 15 prime numbers between 1 and 50 and l0 prime numbers between 50 and 100.Relative Prime Numbers: Two numbers are said to be relatively prime if they do not have any common

factor other than 1.eg, (3, 5), (4, 7), (11, 15), (15, 4)Twin Primes: Two prime numbers which differ by 2 are called twin primes.eg, (3, 5), (5, 7), (11, 13),Composite Numbers Numbers which are not prime arc called composite numberseg, 4, 6, 9, 15,1 is neither prime nor composite.Perfect Number: A number is said to be a perfect number, if the sum of all its factors excluding itself is

equal to the number itself. eg, Factors of 6 are 1, 2, 3 and 6.Sum of factors excluding 6 = 1 + 2 + 3 = 6.\ 6 is a perfect number.Other examples of perfect numbers are 28, 496, 8128 etc.

Rules for DivisibilityDivisibility by 2: A number is divisible by 2 when the digit at ones place is 0, 2, 4, 6 or 8.eg, 3582, 460, 28, 352, ....Divisibility by 3: A number is divisible by 3 when sum of all digits of a number is a multiple of 3.eg, 453 = 4 + 5 + 3 = 12.12 is divisible by 3 so, 453 is also divisible by 3.Divisibility by 4: A number is divisible by 4, if the number formed with its last two digits is divisible by 4. eg,

if we take the number 45024, the last two digits form 24. Since, the number 24 is divisible by 4, the number 45024is also divisible by 4.

Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5.eg, 10, 25, 60Divisibility by 6: A number is divisible by 6, if it is divisible both by 2 and 3.eg, 48, 24, 108Divisibility by 7: A number is divisible by 7 when the difference between twice the digit at ones place and

the number formed by other digits is either zero or a multiple of 7.eg, 658

65 2 8 = 65 16 = 49As 49 is divisible by 7 the number 658 is also divisible by 7.Divisibility by 8: A number is divisible by 8, if the number formed by the last 3 digits of the number is

divisible by 8. eg, if we take the number 57832, the last three digits form 832. Since, the number 832 is divisibleby 8, the number 57832 is also divisible by 8..

Divisibility by 9: A number is divisible by 9, if the sum of all the digits of a number is a multiple of 9.eg, 684 = 6 + 8 + 4 = 18.18 is divisible by 9 so, 684 is also divisible by 9.Divisibility by 10: A number is divisible by 10, if its last digit is 0. eg, 20, 180, 350, .Divisibility by 11: When the difference between the sum of its digits in odd places and in even places is

either 0 or a multiple of 11.





eg, 304263 + 4 + 6 = 13

0 + 2 = 213 2 = 11

As the difference is a multiple of 11 the number 30426 is also divisible by 11.

‘Smart’ Facts• If p and q are co-primes and both are factors of a number K, then their product p x q will also be a factor of r. eg,

Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24 prime factors of 24 are 2 and 3, which are co-prime also. Product of2 × 3 = 6, 6 is also a factor of 24.

• If ‘p’ divides ‘q’ and ‘r’, then p’ also divides their sum or difference. eg, 4 divides 12 and 20. Sum of 12 and 20 is 32which is divisible by 4. Difference of 20 and 12 is 8 which is divisible by 4.

• If a number is divisible by another number, then it must be divisible by each of the factors of that number. 48 isdivisible by 12. Factors of 12 are 1, 2, 3, 4, 6, 12. So, 48 is divisible by 2, 3, 4 and 6 also.

Division on NumbersIn a sum of division, we have four quantities.They are (i) Dividend, (ii) Divisor, (iii) Quotient and (iv) Remainder. These quantities are connected by a

relation.(a) Dividend = Divisor Quotient + Remainder.(b) Divisor = (Dividend Remainder) Quotient.(c) Quotient = (Dividend Remainder) Divisor.

Example 2: In a sum of division, the quotient is 110, the remainder is 250, the divisor is equal to the sum ofthe quotient and remainder. What is the dividend ?

Solution. Divisor = (110 + 250) = 360Dividend = (360 110) + 250 = 39850

Hence, the dividend is 39850.

Example 3: Find the number of numbers upto 600 which are divisible by 14.Solution. Divide 600 by 13, the quotient obtained is 46. Thus, there are 46 numbers less than 600 which are

divisible by 14.

Factors and MultiplesFactor: A number which divides a given number exactly is called a factor of the given number,eg, 24 = 1 24, 2 12, 3 8, 4 6Thus, 1, 2, 3, 4, 6, 8, 12 and 24 are factors of 24.1 is a factor of every numberA number is a factor of itselfThe smallest factor of a given number is 1 and the greatest factor is the number itself.If a number is divided by any of its factors, the remainder is always zero.Every factor of a number is either less than or at the most equal to the given number.Number of factors of a number are finite.

Number of Factors of a Number: If N is a composite number such that N = am bn c ... where a, b, c ... areprime factors of N and m, n, o ... are positive integers, then the number of factors of N is given by the expression(m + 1) (n + 1) (o + 1)





1. Evaluate: ( )

9 3 5 5 4 103 5 2 4 2- -

- -

(a) 9/10 (b) 8/17(c) 16/19 (d) 4/7

2. The sum of three consecutive natural numberseach divisible by 3 is 72. What is the largestamong them?(a) 25 (b) 26(c) 27 (d) 30

3. 55% of a number is more than one-third of thatnumber by 52. What is two-fifth of that number?(a) 96 (b) 240(c) 144 (d) 142

4. The digits of a two-digit number are in the ratioof 2 : 3 and the number obtained by interchangingthe digits is bigger than the original number by27. What is the original number?(a) 63 (b) 48(c) 96 (d) 69

5. What least number would be subtracted from427398 so that the remaining number is divisibleby 15?(a) 13 (b) 3(c) 16 (d) 11

ANSWER

1. (c) 2. (c) 3. (a) 4. (d) 5. (b)

EXPLANATIONS

1.( )- - ¸

- - ´ ¸

9 3 5 5 4 103 5 2 4 2

= ( ) ( )

( )´ - ´ ¸

- ´ - ¸

9 2 5 4 103 5 8 2 =

-

- -

18 215 4 = -

1619

2. 3x + (3x + 3) + (3x + 6) = 72Þ 9x + 9 = 72 = 9x = 72 9

or x = 639

= 7\ The largest of them = 27.

3. Let the number be x.55100

x× = 1 523x +

Þ 1360

x× = 52 Þ x = 240

\ 25x = 2 240

5 = 96

4. Let the number be 10x yx : y = 2 : 3(10y + x) (10x + y) = 27 ...(i)Þ 9y 9x = 27 Þ y x = 3 Þ y = x + 3Putting this value of y, in (i)

3x

x + = 23 Þ x = 6 \ y = 9

Hence the number is 69.5. Apply the divisibility tears of 3 and 5.

Example 4: Find the number of factors that 224 has.Solution. 224 = 25 71

Hence, 224 has (5 + 1) (1 + 1) = 6 2 = 12 factors.Multiple: A multiple of a number is a number obtained by multiplying it by a natural number eg,Multiples of 5 are 5, 10, 15, 20Multiples of 12 are 12, 24, 36, 48Every number is a multiple of 1.The smallest multiple of a number is the number itself.We cannot find the greatest multiple of a number.Number of multiples of a number are infinite.

EXERCISE



PercentagePer cent means per hundred . It is given by % symbol. Here x% means x per hundred or .

100x

Thus, any

percentage can be converted into an equivalent fraction by dividing it by 100.

eg 20% = 20 1 ;

100 5= 150% =

150 3100 2

=

Also, any fraction or decimal can be converted into its equivalent percentage by multiplying with 100.

eg 1 1 1005 5

= ´ = 20%; 3 3 1002 2

= ´ = 150%.

Important Formulae

1. Percentage increase = Increase 100

Original value´

2. Percentage decrease = Decrease 100

Original value´

3. If the price of the commodity increases by r% then the reduction in consumption so as not to increase the

expenditure is 100 %100

rr

é ù´ê ú+ë û

4. If the price of the commodity decreases by r% then the reduction in consumption so as not to increase the

expenditure is 100 %100

rr

é ù´ê ú-ë û

5. If A s income is r% more than B s income then B s income is less than A s income by 100 %100

rr

é ù´ê ú+ë û

.

6. If A s income is r% less than B s income then B s income is more than A s income by 100 %100

rr

é ù´ê ú-ë û

.

PercentageCHAPTER 10



7. Let the population of a town be P and it increases at the rate of r% per annum, then

(a) Population after n years = 1100

nrP æ ö+ç ÷

è ø

(b) Population n years ago = 1100

nPræ ö

+ç ÷è ø

8. Let the present value of the machine be P and if it depreciates at the rate of r% per annum.

(a) Value of machine after n years = 1100

nrP æ ö-ç ÷

è ø

(b) Value of machine n years ago = 1 100

nn

rP æ ö-ç ÷

è øExample 1: Express 3/2 as rate per cent.

Solution. 32 =

3 100 %2

æ ö´ç ÷

è ø= 150%

Example 2: Find 25% of 1000.

Solution. 25% of 1000 = 25 1000

100´ = 250

Example 3. What per cent of 6 is 144?

Solution. Required percentage = 144 100 %

6æ ö

´ç ÷è ø

= 2400%

Example 4: What per cent of 2.5 kg is 15 g?

Solution. Required percentage = 15 100 %

2.5 1000æ ö

´ç ÷´è ø= 0.6%

Example 5. If the price of tea falls by 12%, by how much pr cent must a house holder increase its consumption,so as not to decrease its expenditure on tea?

Solution. (Short cut method)

Increase % in consumption = 100 %100

rr

ì ü´í ý

-î þ=

12 100 %100 12

ì ü´í ý

-î þ

= 12 100 %88

æ ö´ç ÷

è ø=

150 %11 =

713 %11

Example 6: The value of a machine depreciates at the rate of 10% per annum. If its present value is` 162000, what was the value of the machine 2 year ago?

Solution. Value of machine 2 year ago = ̀ 2162000

101 100

é ùê úê úê úæ öê ú-ç ÷ê úè øë û

= ̀ 10 101620009 9

æ ö´ ´ç ÷

è ø

= ` 200000





Example 7: Due to a reduction of 5% in prices of sugar, a man is able to buy 1 kg more for ` 95. Find theoriginal and reduced rate of sugar.

Solution. Let the original rate be ` x per kg.

Reduced rate = ` 1(100 5)

100x- ´ = `

95100

x \

95 95 195100

x x- =

Þ 5 1x

= Þ x = 5

\ Original rate = ` 5 per kg

Reduced rate = `19 5.20 1

æ ö´ç ÷

è øper kg = `

194 = 4.75 er kg

Example 8: If the price of 1 kg cornflakes is increased by 25%, the increase is ` 10. Find the new price ofcornflakes per kg.

Solution. Original price = Difference in price 100

Difference in per cent´ =

10 10025

´ = 400

\ New price = 12540100

´ = ` 50

EXERCISE1. The difference of two numbers is 20% of the larger

number. If the smaller number is 20, then thelarger number is:(a) 25 (b) 46(c) 27 (d) 82

2. When any number is divided by 12, then dividendbecomes 1/4th of the other number. By how muchpercent first number is greater than the secondnumber?(a) 165 (b) 200(c) 300 (d) 400

3. If one number is 80% of the other and 4 times thesum of their squares is 656, then the numbersare:(a) 6,8 (b) 8, 10(c) 16, 20 (d) 10, 15

4. Two numbers A and B are such that the sum of5% of A and 4% of B is two-third of the sum of 6%of A and 8% of B. Find the ratio of A : B.(a) 1 : 2 (b) 3 : 1(c) 3 : 4 (d) 4 : 3

5. Three candidates contested an election andreceived 1136, 7636 and 11628 votes respectively.

What percentage of the total votes did the winningcandidate get?(a) 57% (b) 77% (c) 80% (d) 90%

ANSWERS

1. (a) 2. (b) 3. (b) 4. (d) 5. (a)

EXPLANATIONS

1. Let the larger number be x.

Then, x 20 = 20 1 20100 5

x x xÛ - =

Û 45x = 20 Û x =

5204

ì ü´í ý

î þ = 25%

2. Let the numbers be x and y. Then,

3 .12 4x y x y= Û =

Required percentage =

100 %x yy

æ ö-´ç ÷

è ø =

2 100 %yy

æ ö´ç ÷

è ø = 200%

3. Let one number = x. Then, other number = 80%





of x =45

\

22 44

5x x

é ùæ ö+ê úç ÷

è øê úë û= 656

Û x = 2 21625

x x+ = 164

Û241

25x = 164

Û x2 = 164 25

41´æ ö

ç ÷è ø

= 100Û x = 100So, the numbers are 10 and 8.

4. 5% of A + 4% of B =23 (6% of A + 8% of B)

5 4 2 6 8100 100 3 100 100

A B A Bæ öÛ + = +ç ÷

è ø

1 1 1 420 25 25 75

A B A BÛ + = +

1 1 100 4100 75 75 3

AA BB

Û + Û = =

5. Total number of votes polled= (1136 + 7636 + 11628) = 20400.

Required percentage = 11628 100 %20400

æ ö´ç ÷

è ø= 57%.





ProbabilityProbability is used to indicate a possibility of an event to occur. It is often used synonymously with chance.

(i) In any experiment if the result of an experiment is unique or certain, then the experiment is said to bedeterministic in nature.

(ii) If the result of the experiment is not unique and can be one of the several possible outcomes then theexperiment is said to be probabilistic in nature.

Various Terms Used in Defining Probability(i) Random Experiment: Whenever an experiment is conducted any number of times under identical

conditions and if the result is not certain and is any one of the several possible outcomes, the experiment iscalled a trial or a random experiment, the outcomes are known as events.eg, When a die is thrown is a trial, getting a number 1 or 2 or 3 or 4 or 5 or 6 is an event.

(ii) Equally Likely Events: Events are said to be equally likely when there is no reason to expect any one ofthem rather than any one of the others.eg, When a die is thrown any number 1 or 2 or 3 or 4 or 5 or 6 may occur. In this trial, the six events areequally likely.

(iii) Exhaustive Events: All the possible events in any trial are known as exhaustive events. eg, When a dieis thrown, there are six exhaustive events.

(iv) Mutually Exclusive Events: If the occurrence of any one of the events in a trial prevents the occurrenceof any one of the others, then the events are said to be mutually exclusive events. eg, When a die is thrownthe event of getting faces numbered 1 to 6 are mutually exclusive.

Classical Definition of ProbabilityIf in a random experiment, there are n mutually exclusive and equally likely elementary events in which n

elementary events are favourable to a particular event E, then the probability of the event E is defined as P (E)

P(E) = Favourabel Events

Total number of Events = ( )( )

n E mn S n

=

If the probability of occurrence of an event E is P(E) and the probability of non-occurrence is P ( )E , then,

Probability

CHAPTER 25





P(E) + P ( )E = 1. Hence, P ( )E = 1 ,m n m ien n

-- = the sum of the probabilities of success and failure is 1.

Also, 0 £ P(E) £ 1 and 0 £ P ( )E £ 1.If P(E) = 1, the event E is called a certain event and if P(E) = 0, the event E is called an impossible event.If E is an event, then the odds in favour of E are defined as P(E) : P(E) and the odds against E are defined

as P(E): P ( )E . Hence, the odds in favour of E are ( ) ( ): : ,n mm m n m

n n-

= - the odds against E are

( ) :n m m

n n-

= (n m):m

Addition Theorem on ProbabilityIf El and E2 are two events in a sample space S, then P (El È E2) = P (El) + P (E2) P (El Ç E2). If E1 and E2 are

mutually exclusive events (disjoint), then P(El È E2) = P (El) + P (E2) . (Q P(El Ç E2) = q)

Independent and Dependent EventsTwo or more events are said to be independent if the happening or non-happening of any one does not

depend (or not affected) by the happening or non-happening of any other. Otherwise they are called dependentevents.

eg, Suppose a card is drawn from a pack of cards and replaced before a second card is drawn. The result of thesecond drawn is independent of the first drawn. If the first card drawn is not replaced, then the second drawn isdependent on the first drawn.

If El and E2 are independent events, thenP(El Ç E2) = P(El) P(E2)

Simple EventAn event which cannot be further split is called a simple event. The set of all simple events in a trial is called

a sample space.

Compound EventWhen two or more events occur in relation with each other, they are called compound events.

Conditional EventIf El and E2 are events of a sample space S and if E2 occurs after the occurrence of El, then the event of

occurrence of E2 after the event El is called conditional event of E2 given El. It is denoted by E2/El.

Conditional ProbabilityIf El and E2 are the events in a sample space S and P(El) ¹ 0, then the probability of E2 after the event El has

occurred is called conditional probability of E2 given El. It is denoted by 2

1

EPE

æ öç ÷è ø

and we define,

2 2 2 1 2

1 1 1

( ) ( )( ) ( )

E P E E n E EP

E P E n Eæ ö Ç Ç

= =ç ÷è ø





Smart FactsWhen a die is rolled six events occur. They are {1, 2, 3, 4, 5 and 6}When two dice are rolled 36 events occur. They are [(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2),(2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1),(5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)]When a coin is tossed 2 events occur. They are {H, T}When two coins are tossed 4 events occur. They are {HH, HT, TH, T T} When three coins are tossed 8 events occur. They are {HHH HHT, HTH, HT T, T HH, THT, T TH, TT T}In a pack of 52 cards there are 26 red cards and 26 black cards. The 26 red cards are divided into 13heart cards and 13 diamond cards. The 26 black cards are divided into 13 club cards and 13 spadecard. Each of the colours, hearts, diamonds, clubs and spades is called a suit. In a suit, we have 13cards (ie, A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3 and 2)

Example 1: In a toss of a coin, find the probability of getting a tail.

Solution. Here, S = [H, T] and E = [T] \ P(E) = ( )( )

n En S =

12

Example 2: Two unbiased coins are tossed, what is the probability of getting both heads.Solution. Here, S = [HH, HT, TH, TT] and E = [HH]

P(E) = ( )( )

n En S =

14

Example 3: In a simultaneous throw of a pair of dice, find the probability of getting a total more than 9.Solution. Here n(S) = 6 6 = 36Let E = Event of getting a total more than 9 = [(4, 6), (5, 5), (5, 6), (6, 5), (6, 4), (6, 6)]

P(E) = ( )( )

n En S =

636 =

16

Example 4: In a simultaneous throw of a pair of dice, find the probability that the sum of numbers shown onthe two faces is divisible by 5 or 6.

Solution. Here, n(S) = 6 6 = 36Let E = Event of getting a sum of numbers shown on the two faces divisible by 5 or 6.= [(1, 4), (1, 5), (2, 3), (2, 4), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1), (5, 5), (6, 4), (6, 6)]\ N(E) = 12

P(E) = ( )( )

n En S =

1236 =

13

Example 5: A card is drawn from a well shuffled pack of cards. Find the probability that it is a (i) queen (ii)a red card (iii) a space.

(i) Let E be event of drawing a queen card. Then, one queen card can be drawn from 4 queens in 4C1 ways.

\ P(E) = ( )( )

n En S =

41

521

CC =

4 152 13

=

(ii) Let E be the event of drawing a spade card. Then, one spade card can be drawn from 13 spade cards in 13C1ways.





\ P(E) = ( )( )

n En S =

261

521

CC =

13 152 4

=

(iii) Let E be the event of drawing a spade card. Then, one spade card can be drawn from 13 spade cards in13C1 ways.

\ P(E) = ( )( )

n En S =

131

521

CC =

13 152 4

=

Example 6: If three cards are drawn simultaneously from a pack of well shuffled cards, then find theprobability of them being (i) all queens (ii) all red cards (iii) all spades.

Solution. The total number of ways of selecting three cards from 52 cards is 53C3 ways.(i) Let E be event of drawing the queen cards. Then, three queen cards can be drawn from 4 queen cards in

4C3 ways.

\ P(E) = ( )( )

n En S =

43

523

CC =

4 122100 5525

=

(ii) Let E be event of drawing the red cards. Then, three red cards can be drawn from 26 red cards i 26C3 ways.

\ P(E) = ( )( )

n En S =

263

523

CC =

2600 2622100 221

=

(iii) Let E be event of drawing spade cards. Then, three spade cards can be drawn from 13 spade cards in13C3 ways.

\ P(E) = ( )( )

n En S =

133

523

CC =

28622100 =

14311050

Example 7: A card is drawn at random from a normal pack of cards. What is the probability that it is eithera diamond or a king?

Solution. Out of 52 cards one card can be drawn in 52C1 ways.Let E1 be the event that the card drawn is a diamond, E2 be the event that the card drawn is king and (E1 Ç

E2) be the event that the card drawn is both diamond the king and S be the sample space.

P(E1) = 1( )( )

n En S =

131

521

1352

CC

=

P(E2) = ( 2( )( )

n En S =

41

521

452

CC

=

P (E1 Ç E2) = 1

152

1

152

CC

=

\ P (E1 È E2) = P(E1) + P(E2) P (E1 Ç E2)= 13 4 152 52 52

+ - =16 452 13

=

Example 8: A bag contains 4 red balls and 5 white balls. a ball is drawn at random. Find the probability thatit is a red ball or a white ball.





P(E1) = 1( )( )

n En S =

41

91

CC =

49

P(E2) = 2( )( )

n En S =

51

91

CC =

59

P(E1) = 0

\ P(E1 È E2) = P(E1) + P(E2) = 4 59 9

+ =9 19

=

Example 9: A bag contains 4 red balls and 4 white balls. Two balls are drawn in succession from the bagwith replacement, what is the probability that the two balls are of different colours?

Solution. Let E1 and E2 denote the events of drawing balls of different colours in the first and the seconddraw with replacement and S be the sample space.

P(E1) = 1( )( )

n En S =

41

81

CC =

4 18 2

=

P(E2) = 2( )( )

n En S =

41

81

CC =

4 18 2

=

\ P(E1 Ç E2) = P(E1) P(E2) = 1 1 12 2 4

´ =

Example 10: A family has two children. What is the probability that both the children are boys given that atleast one of them is a boy?

Solution. Let b stand for boy and g for girl. The sample space of the experiement isS = {(b, b), (g, b), (b, g), (g, g)}

Let E and F denote the following events:E : both the children are boysF : at least one of the child is a boy

Then, E = {(b, b)} and F = {(b, b), (g, b), (b, g)}Now, E È F = {(b, b)}

Thus, P(F) = 3 and ( )4

P E FÇ =14

Therefore, P(E|F) = ( )

( )P E F

P FÇ

=

1434

= 13

Example 11: In a school, there are 1000 students, out of which 430 are girls. It is known that out of 430,10% of the girls study in class XII. What is the probability that a students choosen randomly studies in Class XIIgiven that the choosen student is a girl?

Solution. Let E denote the event that a student choosen randomly studies in Class XII and F be the eventthat the randomly choosen student is a girl. We have to find P(E|F).





Now, P(F) = 430

1000 = 0.43 and P(E Ç F) = 43 0.043

1000=

[Q no. of girls studying in XII 10% of 430 = 43]

Then, P(E|F) = ( )

( )P E F

P FÇ

=0.0430.43 = 0.1

Example 12: A person has undertaken a construction job. The probabilities are 0.65 that there will bestrike, 0.80 that the construction job will be completed on time if there is no strike, and 0.32 that the constructionjob will be completed on time if there is no strike, and 0.32 that the construction job will be completed on time ifthere is a strike. Determine that probability that the construction job will be completed on time.

Solution. Let a be the event that the construction job will be completed on time, and B be the event thatthere will be a strike. We have to find P(A).

We have P(B) = 0.65, P(no strike) = P(B¢) = 1 P(B) = 1 0.65 = 0.35P(A|B) = 0.32, P(A|B¢) = 0.80

Since events B and B¢ form a partition of the sample space S therefore, by theorem on total probability, wehave

P(A) = P(B) P(A|B) + P(B¢) P(A|B¢)= 0.65 0.32 + 0.35 0.8 = 0.208 + 0.28 = 0.488

Thus, the probability that the construction job will be completed in time is 0.488.

EXERCISE1. Which of the following cannot be the probability

of an event ?(a) 1/4 (b) 20% (c) 1.2 (d) 0.3

2. If P(E) = 0.03, what is the probability of not E ?(a) 0.90 (b) 0.97 (c) 0.07 (d) 0.70

3. A bag contains orange flavoured candies only. Agirl takes out one candy without looking into thebag. What is the probability that she takes outan orange flavoured candy ?(a) 1 (b) 0(c) 1/2 (d) 1/4

4. A bag contains orange flavoured candies only. Agirl takes out one candy at random from the bag.What is the probability that she takes out astrawberry flavoured candy ?

(a)13 (b) 1 (c) 0 (d)

12

5. An unbiased die is thrown once. What is theprobability of getting a prime number ?

(a)12 (b)

14 (c)

23 (d)

13

ANSWERS

1. (c) 2. (b) 3. (a) 4. (c) 5. (a)

EXPLANATIONS

1. 1.2 cannot be the probability of an event because0 £ P (E) £ 1

2. Probability of not EP (not E) = ( )p E = 1 P(E) = 1 0.03 = 0.97

3. Probability that the girl takes out an orangeflavoured candy is 1 because the bag containsorange flavoured candies only.

4. Probability that she takes out a strawberryflavoured candy is 0 because the bag contains onlyorange flavoured candies.

5. Here, n(S) = {1, 2, 3, 4, 5, 6} and E = Event ofgetting a prime number = {2, 3, 5)

\ P(E) = ( )( )

n En S =

36 =

12





SetsA set is a collection of well defined objects.The objects of the sets are called elements.

(i) Sets are usually denoted by capital letters A, B, C,..., X, Y, Z.(ii) The elements of the sets are denoted by small letters like a, b, c,..., x, y, z etc.

Representation of SetsSets are usually described into two ways.

(i) Tabular form or roster form, in this form, all the elements of the set are separated by commas and enclosedbetween the bracket { }.

For example(a) The set of vowels of English Alphabet as

A = {a, e, i, o, u)(b) The set of numbers on a clock face is written as

B = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}(ii) Set builder from: We define a set by stating properties which its elements must satisfy. For example the

set of all even integers. Then, we use the letters usually x, and we writeA = {x | x is an even integer}

This is to be read as A is a set of numbers x such that x is an even integer. The vertical line | to be read assuch that some times we use x in place of vertical line.

A = {x : x is an even integer}eg, C = {1,w, w2} = {x | x3 1 = 0}

If an object x is an element of a set A, we write x Î A which is read as x belong to A and if an object x is nota member of A we write x Ï A and read as x does not belong to A .

Some Important Terms(i) Empty or Null set The set which contains no elements is called the empty set or the null set. The empty

set is written as f.Thus, f = { } as there is no element in the empty set.For example; the set of odd numbers divisible by 2 is the null set.

SetTheory,Venn Diagrams,

Functions & Relations

CHAPTER 27





(ii) Singleton set A set containing only one element is called a singleton for example, {1}, {4} are singletonsets.

(iii) Equality of sets. The sets A and B are equal if they have same members that is if every elements of A isan element of B and every element of B is an element of A, then A = Beg, if A = { l, 3,5,7} and B = {7, 3, 1, 5}, then A = BIf the two sets are not equal we write A ¹ B

Important Formulae1. A set does not change if its elements, are repeated.2. A set does not change even if the order of its elements is different.

(iv) Finite and Infinite set. The set which contains a definite number of elements is called a finite set. The setwhich contains an infinite number of elements is called an infinite set.eg, (I) The set of days in a week.eg, (II) The set of natural numbers.

(v) Disjoint set. Two sets A and B are said to be disjoint, if they do not have any element in common.eg, A = { 1, 2, 3}, B = { 4, 5, 6} are disjoint sets.

(vi) Subset. If every element in set A is also an element of another set B. Then A is called a subset of B. Also Bis said to be super set of A.Symbolically, we writeA Í B (ie, A contained in B)B Í A (ie, B contains A)More specifically A Í B if x A Þ x Beg, (I) Let A = { 2, 4, 7}, B = { 1, 2, 3, 4, 7}Then, A Î B since every element of A is in B.eg, (II) A = {x | x a real number} and B = {x | x is an integer} Then, A Ê B

1. If there is at least one element of A which is not in B, then A is not a subset of B written as A Í B.2. Every set is a subset of itself ie, A Í A.3. If A Í B and B c Í A, then A = B.

(vii) The Null set f is a subset of every set A.(viii) Proper Subset: A is a proper subset of B. if A Í B and A ¹ B and is written as A Ì B ie, if B contains at least

one element more than A, then A is a proper subset of B(ix) Power set: Set of all the subsets of a set is called the power set

eg, A = {a, b, c} subsets of A are f, {a}, {b}, {c}, {a, b}, {b, c}, {c,a}, {a, b, c}Hence, P(A) = [f, {a}, {b}, {c}, {a, b}, {b, c}, {c, a}, {a, b, c}]If n is the number of elements of a set A, then the number of subset of A ie, the number of elements of P (A)= 2n.

(x) Universal set: If all the sets under consideration are the subsets of a fixed set U, then U is called theUniversal set.

Union of setsUnion of two sets A and B is the set of all elements which belongs to A or B (or to both) and is written as

A È B (ie, A union B)The same is defined in set builder form as

A È B = {x|x Î A or x Î B}





If A = {1, 3, 5, 7, 9} and B = {2, 4, 5, 6, 9}Then, A È B = { 1, 2, 3, 4, 5, 6, 7, 9}

1. From the definition of Union of sets A u B = B u A (Commutative Law)If A is any set, then A È A = A and A È f = A

2. If A and B are any two sets, then A Í (A È B) and B Í (A È B)If x Î A È B,then x Î A or x Î B and if x Ï A È B,then x Î A and x Ï B.

3. If A, B, C are three sets, then A È (B È C) = (A È B) È C

Intersection of SetsIf A and B are any two sets, then intersection of A and B is the set of all elements which are in A and also in

B. It is written as A Ç B and is read as A intersection BIf A = {2, 4, 6, 8} and B = {4, 5, 6, 9}Then A Ç B = {4, 6}

1. From the definition of the intersection, it follows A Ç B = B Ç A (Commutative Law)2. If A is any set, then A Ç A = A and A Ç f) = f3. For any two sets A and B.

A Ç B = A and A Ç B Í B4 If A and B have no elements in common ie, A and B are disjoint, then A Ç B = f

If x Î A Ç B = x Î A and x Î B

eg, (I) If A = { 2, 3, 6, 8, 9} and B = (1, 3, 5, 6, 7, 9}, then A Ç B = {3, 6, 9}eg,(II) If A = {x1|< x < 4 } and B = {x|2 < x < 5}, then A Ç B = {x|2 < x < 4}If A, B, C are three sets, then

(i) (A Ç B) Ç C = A Ç (B Ç C) Associative Law(ii) A Ç (B Ç C) = (A Ç B) È (A Ç C) Distributive Law

Difference of SetsThe difference of two sets A and B is set of elements which belongs to A but do not belong to B. This is written

as A BA B = {x| x Î A and x Î B}

1. Set A B subset of A ie, A B Í A2. Set (A B) and B are disjoint ie, (A B) Ç B = f3. A B = (A È B) (A Ç B)

Symmetric Difference of SetsThe symmetric difference of two sets A and B is (A B) È (B A) and is written as A D BThus, A D B = (A B) È (B A)In the set builder form A D B = {x | x Î A or x Î B, but x Ï A Ç B}

Demorgan LawsIf A, B, C are three sets, then

(i) A (B È C) = (A B) Ç (A C)(ii) A (B Ç C) = (A B) È (A C)





Complement of a SetLet A be a subset of universal set U, then the complement of A is denoted by AC is defined by

AC = {x Î U, x Ï A} \ x Î AC Û x Ï Aeg, (I) If U = {1, 2, 3, 4, 5, 6} and A = { 1, 3, 5}, then AC = {2, 4, 6}eg, (II) U be the set of all letters in English alphabet and A is a set of all vowels, then AC is the set of all

consonants.1. (A È B)C = AC Ç BC 2. (A Ç B)C = Ac È BC

Venn DiagramsA simple way of explaining the relation between sets is by a diagram which is called Venn diagram. In this a

set is generally represented by a circle and its elements by points in the circle.CaseI: A Ì U and B Ì U and A Ç B ¹ f

A B

U

Here A and B are represented by a circle.A B is the lined regionB A is dotted region and A Ç B is plane region.Case II: A = {a, c, e}, B = {b, d}

fg

a b c

d e A B

A Ç B = f and A B = A and B A = BCase III: When A Í B Í UIn adjoining figure, in Venn diagram

A

B

U

A È B = B, A Ç B = A and A B = f

Some results from the Venn diagram(i) n(A È B) = n (a) + n(B) n(A Ç B)

(ii) n(A È B) = n (a) + n(B), when A Ç B = f(iii) n(A B) + n (A Ç B) = n(A)(iv) n(B A) + n (A Ç B) = n(A)(v) n(A B) + n (A Ç B) + n (B A) = n (A Ç B)





Example 1: If in a factory of 30 workers, 10 take tea but not coffee and 14 take tea. Then how many takeonly coffee ?

Solution. Total number of workers = n (T È C) = 30Number of workers who take tea n(T) = 14

n(T)

10 4 x

n

U = 30

( )c

Who take tea but not coffee = n(T C) = 10Who drinks both coffee and tea = n (T) n (T C) = 14 10 = 4Who takes only coffee = n (C T) = xFrom the figure = x + 4 + 10 = 30 = x = 30 14 = 16The worker who drinks only coffee = 16Example 2: An elocution competition was held in English and Hindi. Out of 80 students, 45 took part in

English, 35 in Hindi, 15 in both English and Hindi, then for the number of students.(a) Who took part in English but not in Hindi.

n(E) = 45n(H) = 35

only E only H

(b) Who took part in Hindi but not in English.(c) Who took part in either English or Hindi.(d) Who took part in neither.

Solution. Suppose E is the set of students who took part in English, His the set of students who took part inHindi, then E n H gives the set of students who took part in both English and Hindi.

(a) The number of students who took part in English but not in Hindi= n(E) = n(E Ç H) = 45 15 = 30

(b) The number of students who took part in Hindi but not in English= n(H) n(E Ç H) = 35 15 = 20

(c) The number of students who took part either in English or in Hindi isn(E È H) = n(E) + n(H) n(E Ç H) = 45 + 35 15 = 65

(d) The number of students who took part neither in English nor in Hindi= n (S) n (T È H) = 80 65 = 15

Ordered PairIf a, b be any two objects, then the pair (a, b) is called the ordered pair. The object a is called the first

coordinate (or first number) and b is called the second coordinate (or second number) of the ordered pair (a, b).1. The ordered pair (a, b) ¹ (b, a)

Two ordered pairs (a, b) and (c, d) are said to be equal, if and only if a = c and b = d.





Cartesian Product of SetsIf A and B be any two sets, then cartesian product of A and B is the set of all ordered pair (a, b), where a Î

and b Î BCartesian product of A and B is written as A B (ie, A cross B)ie A B = {(a, b) | a Î A and b Î B}eg, If A = {a, b, c} and B = {1, 2}, then

A B = {(a, 1), (a, 2),(b, 1),(b, 2),(c, 1),(c, 2)}B A = {(1, a),(1, b),(1, c),(2, a),(2, b),(2, c)}

Thus, A B ¹ B AA A = {(a, a), (a, b), (a, c),(b, a),(b, b),(b, c) (c, a),(c, b),(c, c)}B B = {(1, 1), (1, 2),(2, 1),(2, 2))

1. A (B È C) = (A B) È (A C)2. A (B Ç C) = (A B) È (A C)

RelationsA relation is a set of ordered pairs. If (x, y) is a member of a relation R, we write it as x R y (ie relation R to y).eg, If R is the ordered pairs of positive integers where R = {(x, y)| x2 = y} The relation is y is a square of x and

the set is {(1, 1), (2, 4),(3, 9),(4, 16),...}

Types of Relations(i) Reflexive: A relation R on a set A is said to be reflexive for every x Î A

(x, x) Î R(ii) Symmetric Relation: A relation R on a set A is said to be symmetric if x R y Þ y R x

(x, y) Î R = (y,x) Î Reg, Let A = {1, 2, 3} and R = {(1, 1), (2, 2),(1, 3),(3,1)}Clearly, R is a symmetric relation.

(iii) Transitive Relation: A relation R in a set A is called transitive if x R y and y R z Þ x R zeg, Let R be a relation in the real number defined by x less than y then

x < y and y < z = x < z(iv) Equivalence Relation A relation which is reflexive, symmetric and transitive is a equivalence relation.

FunctionsIf each element of a set A is associated with exactly one element in the set B, then this association is called a

function from A to B.The set A is called the domain and the set B is called the co-domain of the function.Consider : A = {1, 2}, and B = (3, 4, 5, 6), then {(1, 4),(2, 5)) is a function{(1, 4),(2, 5),(2, 6)} is not a function since element 2 in the set A have two images 5 and 6 in the set B

1. Each element of A must be associated with exactly one element in the set B.2. All the elements of the set B need not have the association.3. The set of elements of B which are associated with the elements of the set A is called the range of the

function.4. The range is the subset of the co-domain.





Types of Functions(i) One-one Function (injection): A function f : A ® B is said to be a one-one function elements of A have

different images in B ie,f(x) = zx, x Î {1, 2, 3}

f = {(1, 2),(2, 4),(3, 6)}(ii) Many-one Function: A function f : A ® B is said to be a many-one function if two are n of A have the

same images in B.(iii) Onto Function: A function f : A ® B is called an onto function if every element of B is an image of some

elements of A ie, if co-domain = range.eg, Let A = {a, b, c, d} and B = {1, 2, 3}f = {(a, 3),(b, 2),(c, 2),(d, 1))

(iv) Into Function: A function f: A B is called an into function if co-domain ¹ range.Example 3: A is set of prime numbers less than 20, write A in Roster form.Solution. Prime numbers Less than 20 are 2, 3, 5, 7, 11; 13, 17, 19 set A in Roster form.A = {2, 3, 5, 7, 11, 13, 17, 19}Example 4: Let A = {4, 5, 6, 7} and B = {6, 4, 7, 5}, thenSolution. {4, 5, 6, 7} = {6, 4, 7, 5}, since each of the elements 4 , 5, 6, 7 belongs to Band each of the elements

6, 4, 7, 5 belongs to A, then A = B.The set does not change if its elements are rearranged.Example 5: A = {x2 = 16, x is odd}, thenSolution. A is a empty set.

x 2 = 16 Þ x = + 4 or x = 4, but x is not odd\ A does not contain any element, A = fExample 6: Rewrite the following statements using set notations.(a) x does not belongs to A (b) A is not a subset of B(c) H does not include D (d) d is a member of E.

Solution.(a) x Ï A (b) A Ë B(c) H Ê D (d) d Î E

Example 7: Let A = {a, b, c}; ie, A contains the elements a, b, c, state whether each of the four statements iscorrect or incorrect tell why.

(a) a Î A (b) a Í A(c) {a} Î A (d) {a} Í A

Solution.(a) a Î A, correct.(b) Incorrect. The symbol Í must connect two set it indicates that one set a subset of other. Therefore,

a Í A is incorrect since a is a member of A, not a subset.(c) Incorrect. The symbol a connects an objects to a set. It indicates that object is a member of the set.

Therefore, {a} Î A is incorrect since {a} is a subset of A.(d) Correct.

Example 8: If S be the universal set of English alphabet and let A = {a, b, c}, then complement of A isSolution. AC = {d, e, f x, y, z}Example 9: If A = {1, 2, 3, 4} and B = {2, 4, 6, 8}, find A B, B A and A D B.Solution. A B = {1, 3},





(A B) contains the elements of A but not the elements of B. Similarly, B A = 16,81(B A) contains the elements of B but not the elements of A.

A D B = (A B) È (B A) = {1, 3, 6, 8}Example 10: If S = {1, 2, 3, 4, 5}, A= {1, 2, 4}, B= {2, 4, 5}Find

(a) A È B (b) A Ç B (c) BC (d) B A(e) AC È B (f) A È BC (g) AC Ç BC (h) BC AC

(i) (A Ç B)C (j) (A Ç B)C

Solution.(a) A Ç B = {1, 2, 4, 5}(b) A Ç B = {2, 4}(c) The complement of B consists of letters which are in S but not in B, therefore BC = {1, 3}(d) B A consisted of elements in B which are not in A ie, B A = {5}(e) AC = {3, 5} and B = {2, 4, 5}, therefore, AC È B = {2, 3, 4, 5}(f) A = {1, 2,4) and BC = {1, 3}, therefore, A È BC = {1, 2,3,4}(g) AC = {3, 5}, and BC = {1, 3} ; therefore, AC Ç BC = {3}(h) BC = {1, 3}, and AC = (3,5); therefore, BC AC = {1}(i) A Ç B = {2, 4}, therefore, (A Ç B)C = {1, 3,5}(j) A È B = {1, 2, 4, 5}; therefore, (A Ç B)C = {3}

Example 11: A = { 1, 2, 3} and B = {a, b}, then find A B and B ASolution. A B = {{1, a}, {1, b}, {2, a}, {2, b), {3, a}, {3, b}} and B A = {{a,1}, {a, 2}, {a, 3}, {b, l}, {b, 2}, {b, 3}}\ A B ¹ B A since the ordered pair (1, a) ¹ (a, 1)Example 12: If the set A contains 4 elements and set B contains 3 elements, then A B containsSolution. The set A B contains 12 elements.

EXERCISE1. The set in set builder form of vowels of English

alphabet is(a) {a, e, i, o, u}(b) A = {x | x is a vowel in English alphabet)(c) f(d) {a, b, c, d, e, f, g}

2. If A = {5} which of the following statement iscorrect?(a) A = 5 (b) 5 Ì A(c) {5} Î A (d) 5 Î A

3. If A = {a, (b, c), d)}, which of the following is asubset of A.(a) {a, b} (b) {b, c}(c) {c, d} (d) {a, d}

4. If A Ç B = f nd A and B are two sets, then(a) A Ì B (b) B Ì A(c) A ¹ B (d) A and B are disjoint

5. If n(A Ç B) = 13, n(A) = 20, n(B) = 44, then n(A ÈB) = ?(a) 27 (b) 13 (c) 75 (d) 51

ANSWERS

1. (b) 2. (d) 3. (d) 4. (d) 5. (d)

EXPLANATIONS

1. Set builder form of vowels of English alphabet isA = {x | x is a vowel in English alphabet}

2. The set A contains an element 5, therefore 5 Î A3. Clearly, {a, d} is a subset of {a, (b, c), d}4. If A and B are disjoint sets, then A and B have no

common elements A Ç B = f5. n (A È B)= n (A) + n (B) n (A Ç B)

= 20 + 44 13 = 51





Arithmetic Progression (AP)An arithmetic progression is a sequence in which terms increase or decrease by a constant number called the

common difference.(i) The sequence 2, 6, 10, 14, 18, 22 is an arithmetic progression whose first term is 2 and common difference

4.

(ii) The sequence 5 72, ,3, ,42 2 is an arithmetic progression whose first term is 2 and common

difference .An arithmetic progression is represented by a,(a + d), (a + 2d), (a + 3d) a + (n 1)dHere, a = first term

d = common differencen = number of terms in the progression

The general term of an arithmetic progression is given by Tn = a + (n - 1) d.

The sum of n terms of an arithmetic progression is given by S, = 2n

[2a + (n 1) d] or Sn = 2 [a + l]

where l is the last term of arithmetic progression.If three numbers are in arithmetic progression, the middle number is called the arithmetic mean of theother two terms.

If a, b, c are in arithmetic progression, then b = 2a c+

where b is the arithmetic mean.

Similarly, if n terms al, a2, a3 an are in AP, then the arithmetic mean of these n terms is given by

AM = 1 2 3 .na a a an

+ + +¼+

If the same quantity is added or multiplied to each term of an AP, then the resulting series is also an AP.If three terms are in AP, then they can be taken as (a d), a, (a + d).If four terms are in AP, then they can be taken as (a 3d), (a d), (a + d), (a + 3d).If five terms are in AP, then they can be taken as (a 2d), (a d), a, (a + d), (a + 2d).

Sequences & Series

CHAPTER 29





Geometric Progression (GP)A geometric progression is a sequence in which terms increase or decrease by a constant ratio called the

common ratio.(i) The sequence 1, 3, 9, 27, 81 is a geometric progression whose first term is 1 and common ratio 3.

(ii) The sequence 1 1 1 11, , , , ,3 9 27 81

¼ is a geometric progression whose first term is 1 and common ratio 1 .3

A geometric progression is represented by a, ar, ar2 arn 1.Here, a = first term

r = common ration = number of terms in the progression.

The general term of a geometric progression is given by Tn = an 1

The sum to n terms of a geometric progression is given by

( )1,

1

n

na r

Sr

-=

- when r < 1 ( )1

,1

na r

r

-

-when r > 1

If three numbers are in geometric progression, the middle number is called the geometric mean of the othertwo terms.

If a, b, c are in geometric progression, then b ac= where b is the geometric mean.Similarly, if n terms a1, a2, a3, a4, an are in geometric progression, then the geometric mean of 1 these n

terms is given by GM = ( )1

1 2 3 .nna a a a´ ´ ´¼´

For a decreasing geometric progression the sum to infinite number of terms is

,1

aSr¥ =

- where a = first term and | r | < 1.

If every term of a GP is multiplied by a fixed real number, then the resulting series is also a GP.If every term of a GP is raised to the same power, then the resulting series is also a GP.The reciprocals of the terms of a GP is also a GP.

If three numbers are in GP, then they can be taken as ,ar a, ar.

If four numbers are in GP, then they can be taken as 33 , , , .a a ar ar

rr

If five numbers are in GP, then they can be taken as 22 , , , , .a a a ar ar

rr

Harmonic Progression (HP)If the reciprocals of the terms of a series form an arithmetic progression, then the series is called a harmonic

progression.

(i) The sequence 4 3 12, , ,3 2 7

¼ is a harmonic progression as 3 2 7, ,4 3 12 is in arithmetic progression.

If a, b, c are in harmonic progression, then b = 2aca c+

where b is the harmonic mean.





Sum of Natural Series

The sum of the first n natural numbers = ( )12

n n +

The sum of the square of the first n natural numbers = ( )( )1 2 16

n n n+ +

The sum of the cubes of the first n natural numbers = ( )22 14

n n +

The sum of first n even numbers = n(n + 1)The sum of first n odd numbers = n2

Example 1: Find the nth term and the fifteenth term of the arithmetic progression 3, 9, 15, 21Solution. In the given AP we have a = 3, d = (9 3) = 6

Tn = a + (n 1)d = 3 + (n 1)6 = 6n 3T15 = (6 15 3) = 87

Example 2: Find the 10th term of the AP 13, 8, 3, 2,Solution. In the given AP, we have a = 13, d = (8 13) = 5

Tn = a + (n 1)d = 13 + (n 1)( 5) = 18 5nT10 = 18 5 (10) = 32

Example 3: The first term of an AP is -1 and the common difference is -3, the 12th term isSolution. T1 = a = 1, d = 3

Tn = a + (n 1)d = 1 + (n 1)( 3) = 2 3nT12 = 2 3 12 = 34

Example 4: Which term of the AP 10, 8, 6, 4 is 28?Solution. We have, a = 10,d = (8 10) = 2, Tn = 28

Tn = a + (n 1)d 28 = 10 + (n 1)( 2) = n = 20Example 5: The 8th term of an AP is 17 and the 19th term is 39. Find the 20th term.Solution. T8 = a + 7d =17 ...(i)

T19 = a + 18d = 39 ... (ii)On subtracting Eq. (i) from Eq. (ii), we get 11d = 22 d = 2Putting d = 2 in Eq. (i), we get a + 7(2) = 17 = a = (17 14) = 3\ First term = 3, Common difference = 2

T20 = a + 19d = 3 + 19(2) = 41Example 6 Find the sum of the first 20 terms of the AP, 2, 1, 4, 7,Solution. Here, a = 5, d = ( 1 2) = 3 and n = 20

Sn = ( )2 12n a n dé ù+ -ë û Þ ( )( )20

20 20 5 20 1 3 4702

S é ù= ´ + - - = -ë û

Example 7: Find the sum of the series 5, 10, 15, 20, 125.Solution. Here, a = 5, Tn = 125, d = (10 5) = 5

Tn = a + (n 1)d 125 = 5 + (n 1) 5 n = 25

Sn = [ ] [ ]25 5 125 16252 2n a l+ = + =





Example 8: Find three numbers in AP whose sum is 36 and product is 1620.Solution. Let the numbers be (a d), a, (a + d). Then, (a d) + a + (a + d) = 36 Þ 3a = 36 Þ a = 12

(a d) a (a + d) = 1620 (12 d) l2 (12 + d) = 1620(144 d2) 135 Þ d2 9 Þ d = 3

\ Numbers are 9, 12, 15 or 15, 12, 9.Example 9: Find the nth term and 8th term of the GP 3, 6, 12, 24, 48,

Solution. In the given GP, we have a = 3, r = 6 23

=-

\ Tn = arn 1 = ( 3)( 2)n 1

T8 = ( 3)( 2)8 1 = ( 3)( 2)7= 384Example 10: The nth term of GP is 3/2n. Find the ratio of 5th to 10th term.

Solution. In the given GP, we have 32n nT =

55 10 5 105 10 5 10 5

3 3 3 3 1, , : : 1 : 2 :1 32 :12 2 2 2 2

T T T T= = = = = =

Example 11: Determine the 9th term of GP whose 8th term is 192 and common ratio 2.Solution. In the given GP, we have r = 2, T8 = ar7 = 192

Þ a(2)7 = 192 Þ a = 192 3128 2

= \ T9 = ar8 = ( ) ( )8 73 2 3 2 3842

= =

Example 12: The first term of a GP is 50 and the 4th term is 1350. Determine the 6th term.Solution. Let a be first term and r be the common ratio.Then, a = 50 ...(i)

T4 = ar3 = 1350 ...(ii)On dividing Eq. (ii) by Eq. (i), we get r3 = 27 Þ r = 3

Example 13: Find the sum to infinity for the GP1 1 1, , ,4 16 64

- - ¼

Solution. In the given GP, we have a = 1 1 /16 1, ,4 1 / 4 4

r -- = = - ¼

1 11 4 14 4

51 4 5 511 44

aSr¥

- -= = = = - ´ = -

- é ùæ ö- -ç ÷ê ú

è øë û

Example 14: In a certain colony of cancevous cells, each cell divides into two every minute. How many cellswill be produced from a single cell, if the rate of division continues for 12 min?

Solution. Total number of cells = 2 + (22 + 23 +24 +...+212)

= 21 + 22 + 23 +....+ 212 = ( )122 2 18190

2 1-

=-





1. If five times the fifth term of an AP is equal toseven times, the seventh term of the AP, thenwhat is the twelfth term?(a) 1 (b) 0(c) 1 (d) 2

2. Three terms are in AP such that their sum is 18.The sum of the first two terms is six more thanthe sum of the last two terms. Find the last term.(a) 6 (b) 9(c) 3 (d) 2

3. Determine k, so that (k + 2), (4k 6) and (3k 2)are three consecutive terms of an AP.(a) 3 (b) 2(c) 4 (d) 6

4. In an AP, the first term is 2 and the sum of thefirst five terms is one-fourth the sum of the nextfive terms. Find the second term.(a) 4 (b) 10(c) 16 (d) 12

5. The sum of four terms in an AP is 64. The productof the extreme terms is 220. Find the first andfourth term.(a) 14, 28 (b) 10, 22(c) 28, 14 (d) 6, 30

ANSWERS

1. (b) 2. (c) 3. (a) 4. (a) 5. (b)

EXPLANATIONS

1. T5 = a + 4d, t7 = a + 6d\ 5 (a + 4d) = 7 (a + 6d) Þ 5a + 20d = 7a + 42dÞ a = 11dT12 = a + 11d = 11d + 11d = 0\ The twelfth term is 0.

2. Let the three terms be a d, a, a + d.(a d) + a + (a + d) = 18

EXERCISEÞ 3a = 18Þ a = 6Also, [(a d) + a] [a + (a + d)] = 6 Þ d = 3So, the three terms are 9, 6, 3 respectively, lastterm = 3.

3. Since, (k + 2), (4k 6) and (3k 2) are in AP.(4k 6) (k + 2) = (3k 2) (4k 6)Þ 4k 6 k 2 = 3k 2 4k + 6 Þ k = 3

4. Given, a = 2, Sn = 2n

[2a + (n 1) d]

S5 = 52 [2 2 + (5 1) d] = 10 (d + 1) ...(i)

S10 = 102 [2 2 + (10 1) d] = 5 (9d + 4) ...(ii)

Sum of the sixth to tenth term isS10 S5 = (35d + 10) ...(iii)

Now, given S5 = 14 (S10 S5)

Þ 10(d + 1) = 14 (35d + 10)

Þ d = 6T2 = a + d = 2 + ( 6) = 4

5. Let the four terms be(a 3d), (a d), (a + d), (a + 3d)(a 3d) + (a d) + (a + d) + (a + 3d) = 644a = 64 Þ a = 16 ...(i)Also, (a 3d) (a + 3d) = 220Þ a2 9d2 = 220Þ (16)2 9d2 = 220 Þ d = 2First term = a 3d = (16 3 2) = 10Fourth term = a + 3d = (16 + 3 2) = 22





Relation between Time, Speed and DistanceDistance covered, time and speed are related by

Time = Distance

Speed ...(i)

Speed = Distance

Time ...(ii)

Distance = Speed Time ...(iii)Distance is measured in metres, kilometres and miles.Time in hours, minutes and seconds.Speed in km/h, miles/h and m/s.

1. To convert speed of an object from km/h to m/s multiply the speed by 5

18 .

2. To convert speed of an object from m/s to km/h, multiply the speed by 185 .

Average SpeedIt is the ratio of total distance covered to total time of journey.

\ Average speed = Total distance coveredTotal time of journey

General Rules for Solving Time & Distance ProblemsRule 1

If a certain distance is covered with a speed of x km/h and another equal distance with a speed of y km/h,then the average speed for the whole journey is the harmonic mean of the two speeds.

Average speed =2 km/h1 1

x y

æ öç ÷ç ÷ç ÷+ç ÷è ø

= 2 km/hxyx y

æ öç ÷

+è ø

Time and DistanceCHAPTER 16





Rule 2If three equal distances are covered by three different speeds x, y and z km/h, then average speed for the

whole journey is given by

Average speed = 3 km/h1 1 1

x y z

æ öç ÷ç ÷ç ÷+ +ç ÷è ø

= 3 km/h

xy yz zxæ öç ÷+ +è ø

Rule 3If a certain distance is covered with a speed of x km/h and another distance with a speed of y km/h but time

interval for both journeys being same, then average speed for the whole journey is given by

Average Speed = km/h2

x y+æ öç ÷è ø

Rule 4If a certain distance is covered with a speed of x, y and z km/h, but time inverval for the three journey being

equal, then average speed is given by

Average speed = km/h3

x y z+ +æ öç ÷è ø

Rule 5

If the ratio of speeds A and B is x : y, then the ratio of times taken by them to cover the same distance is 1 1: .x y

Relative Speed(i) If two bodies are moving in the same direction at x km/h and y km/h, where (x > y), then their relative speed

is given by (x y) km/h.(ii) If two bodies are moving in opposite direction at x km/h and y km/h, then the their relative speed is given

by (x + y) km/h.

General Rules for Solving Train ProblemsRule 1 Train Vs Stationary Object of no Length

Time taken by a train of length l metre to pass a stationary object such as a pole, standing man or a buildingis equal to the time taken by the train to cover l metre.

Speed of the train = Length of the train

Time taken to cross the stationary object

Rule 2 Train Vs Stationary Object of Certain LengthTime taken by a train of length l metre to pass a stationary object of length a metre such as another

standing train, bridge or railway platform is equal to the time taken by the train to cover (l + a) metre.

Speed of the train = Length of the train +Lengthof the stationary object

Time taken to cross the stationary object





Rule 3 Train Vs Moving Object of no LengthTime taken by the train of length l metre to pass a man moving is equal to the time taken by the train to

cover l metre(i) When the train and man move in the same direction with speeds of x m/s and y m/s. Then,

(x y) = Length of the train

Time taken to cross each other

(ii) When the train and man move in opposite directions with speeds of x m/s and y m/s. Then,

(x + y) = Length of the train


Rule 4 Train Vs Moving Object of Certain LengthTime taken by the train of length l metre to pass a moving object of length a metre such as another moving

train is equal to the time taken by the train to cover (l + a) metre.(i) When the two trains move in the same direction with speeds of x m/s and y m/s, (x > y), then

(x y) = Length of the train + Length of train two


(ii) When the two tains move in opposite directions with speeds of x m/s and y m/s. Then,

(x + y) = Length of the train one + Length of train two


Rule 5 Two Moving TrainIf two trains start at the same time from points A and B towards each other and after crossing they take a and

b second in reaching B and A respectively. Then, (A s speed) : (B s speed) = :b a .

General Rules for Solving Boats and Streams ProblemDownstream Motion

When an object is moving against (opposite) direction in which the water in the stream is flowing, then thebject is said to be moving upstream.

Upstream MotionWhen an object is moving against (opposite) direction in which the water in the stream is flowing, then the

object is said to be moving upstream.

Motion in Still WaterWhen an object is moving in water where there is no motion in water, the object can move in any direction

with a uniform speed, then the object is said to be moving in still water.Rule 1 Downstream and Upstream Speed

Let the speed of the boat in still water = x km/h and speed of the stream be y km/h, thenSpeed of the boat with stream downstream speed = (x + y) km/hSpeed of the boat against stream = upstream speed = (x y) km/hAs, when the boat is moving downstream, the speed of the water aids the speed of the boat and when the boat

is moving upstream, the speed of the water reduces the speed of the boat.





Rule 2 Speed of Boat in Still Water & Speed of StreamIf the downstream speed of boat is a km/h and the upstream speed of boat is b km/h, then

Speed of boat in still water = 1 ( )km/h2

a b+

Speed of stream = 1 ( )km/h2

a b-

General Rules for Solving Circular TracksRule 1

When two people are running around a Circular Track starting at the same point and at the same time, thenwhenever the two people meet the person moving with a greater speed covers one round more than the personmoving with lesser speed.Rule 2

When two people with speeds of x km/h and y km/h start at the same time and from the same point in thesame direction around a circular track of circumference c km, then

The time taken to meet for the first time anywhere on the track = hcx y-

The time taken to meet for the first time at the starting point = LCM of ,c c hx y

æ öç ÷è ø

Rule 3When two people with speeds of x km/h and y km/h respectively start at the same time and from the same

point but in opposite direction around a circular track of circumference c km, then

The time taken to meet for the first time anywhere on the track = hcx y+

The time taken to meet for the first time at the starting point = LCM of , hc cx y

æ öç ÷è ø

Example 1: Convert 90 km/h into m/s.

Solution. 90 km/h = 590 m/s

15æ ö

´ç ÷è ø

= 25 m/s

Example 2: Convert 10 m/s into km/h.

Solution. 10 m/s = 1810 m/s5

æ ö´ç ÷

è ø = 36 km

Example 3: A man can cover a certain distance in 1 h 30 min by covering one-third of the distance at 6 km/h and the rest at 15 km/h. Find the total distance.

Solution. Let the total distance be x km. Then,

23 36 15

x x+ =

32 Þ

218 45x x

+ =32 Þ

990x

=32 Þ10

x=

32





Þ x = (3 10)

2´

= 15

\ Total distance = 15 kmExample 4: An aeroplane started one hour later than the scheduled departure from a place 1200 km away

from its destination. To reach the distination on time, the pilot had to increase its speed by 200 km/h. What wasthe normal speed of the aeroplane?

Solution. Let the time taken by the aeroplane in second case be x hour. Then,1200

x = 1200 200

1x+

+Þ

6x =

6 11x

++

Þ 6x + 6 = 6x + x2 + x Þ x2 + x 6 = 0Þ (x + 3) (x 2) = x Þ x = 2h (Q = 3 is not possible)\ Time taken in second case = 2 h

So, Speed = 1200

2 = 600 km/h

Hence, normal speed = 600 200 = 400 km/hExample 5: The current of a stream runs at 1 km/h. A motor boat goes 35 km upstream and back again at

the starting point in 12 h. What is the speed of motor boat in still water?Solution. Let speed of boat in still water be x km/h. Then,

35 351 1x x

+- +

= 12 Þ 35 (x + 1 + x 1) = 12 (x2 1) Þ 6x2 35x 6 = 0

Þ (x 6) (6x + 1) = 0 Þ x = 6 (Q x = 1/6 is not possible)So, speed of boat in still water = 6 km/hExample 6: A train of length 100 m crosses a man who is coming to the train from opposite direction, in 6 s.

What is the speed of train?Solution. Let speed of train = x km/hThen, speed of tain relative to man = (x + 5) km/h

= 5( 5) m/s

18x + ´

\

1005( 5)

18x + ´ = 6 Þ

18005( 5)x + = 6

Þ x + 5 = 60 Þ x = 55 km/hExample 7: Speed of three cars are in the ratio 2 : 3 : 4. What is the ratio of time taken by them in covering

the same distance.Solution. Let speed of three cars be 2x, 3x and 4x km/h. If covered distance be d, then ratio of time taken by

them

= ; ;2 3 4d d dx x x =

1 1 1: :2 3 4 = 6 : 4 : 3

Example 8: A man can row 6 km/h in still waer. When the river is running at 4 km/h, it takes him 2 h 15 minto row to a place and back. How far is the place?

Solution. Speed downstream = (6 + 4) km/h = 10 km/h





Speed upstream = (6 4) km/h = 2 km/hLet the required distance be x km.

Then, 10 2x x

+ = 94 Þ x =

9 104 6´æ ö

ç ÷´è ø= 3.75 km

Example 9: Two men A and B start together from the same point to walk round a circular path 8 km long. Awalks 2 km and B walks 4 km an hour. When will they next meet at the starting point, if they walks in the samedirection?

Solution. Time to complete one revolution by A and B is 8 h2

æ öç ÷è ø

and 8 h4

æ öç ÷è ø

or 4 h and 2h.

\ The required time is the LCM of 4 and 2 which is 4 h.Thus, they will next time at the starting point after 4 h.

EXERCISE(c)

356

km (d)7158

km5. A, B and C are on a trip by a car. A drives during

the first hour at an average speed of 50 km/hr. Bdrives during the next 2 hours at an averagespeed of 48 km/hr. C drives for the next 3 hoursat an average speed of 52 km/hr. They reachedtheir destination after exactly 6 hours. Their meanspeed was:

(a) 50 km/hr (b)1503

km/hr

(c) 51 km/hr (d) 52 km/hr

ANSWERS

1. (d) 2. (c) 3. (d) 4. (a) 5. (b)

EXPLANATIONS

1. Speed from A to B = 2250

11æ ö

´ç ÷è ø mph =

50011

æ öç ÷è ø mph.

Speed from B to A = 2

2509

æ ö´ç ÷è ø

mph = 5009

æ öç ÷è ø

mph.

\ Average speed =

500 500211 9

500 50011 9

æ ö´ ´

ç ÷ç ÷

+ç ÷è ø

mph

1. Mac travels from A to B a distance of 250 miles in5 hours. He returns to A in 4 hours 30 minutes.His average speed is:(a) 42 mph (b) 49 mph(c) 48 mph (d) 50 mph

2. A boy goes to his school from his house at a speedof 3 km/hr and returns at a speed of 2 km/hr. Ifhe takes 5 hours in going and coming, the distancebetween his house and school is:(a) 8.5 km (b) 5.5 km(c) 6 km (d) 9 km

3. The average speed of a train in the onwardjourney is 25% more than that in the returnjourney. The train halts for one hour on reachingthe destination. The total time taken for thecomplete to and for journey is 17 hours, coveringa distance of 800 km. The speed of the train inthe onward journey is:(a) 50 km/hr (b) 53 km/hr(c) 52 km/hr (d) 56.25 km/hr

4. I started on my bicycle at 7 a.m. to reach a certainplace. After going a certain distance, my bicyclewent out of order. Consequently, I rested for 35minutes and came back to my house walking allthe way. I reached my house at 1 p.m. If mycycling speed is 10 kmph and my walking speedis 1 kmph, then on my bicycle I covered a distanceof:

(a)61

466

km (b)4

133

km





= 500000

4500 5500æ öç ÷è ø+

mph = 50 mph.

2. Average speed = 2 3 23 2´ ´æ ö

ç ÷è ø+km/hr =

125 km/hr.

Distance travelled = 12

55

æ ö´ç ÷è ø km = 12 km. \

Distance between house and school

= 122

æ öç ÷è ø = 6 km.

3. Let the speed in return journey be x km/hr.

Then, speed in onward journey = 125100 x

= 54xæ ö

ç ÷è økm/hr.

Average speed =

524

54

x x

x x

æ ö´ ´

ç ÷ç ÷

+ç ÷è ø

km/hr

= 109x

km/hr.

\ 9800

10xæ ö

´ç ÷è ø = 16

Û x = 800 916 10

´æ öç ÷è ø´ =

7200160 = 45.

So, speed in onward journey

= 5

454

æ ö´ç ÷è ø

km/hr.= 2254 = 56.25 km/hr.

4. Time taken = 5 hrs 25 min = 6512

hrs.Let the required distance be x km.

Then, 10 1x x

+ = 6512

Û 11x= 65012

Û x = 32566

= 61

466

km.5. Total distance traveled

= (50 1 + 48 2 + 52 3) km= (50 + 96 + 156) km = 302 km.Total time taken = 6 hrs.

\ Mean speed =3026

æ öç ÷è ø km/hr

= 5013 km/hr.



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Directions (Q.1 11): Read the following passagecarefully and answer the questions given belowit. Certain words are printed in bold in the passageto help you locate them while answering some ofthe questions.

What is immediately needed today is theestablishement of a Wrold Government or anInternational Federation of mankind. It is the utmostnecessity of the world today, and all those persons whowish to see all human beings happy and prosperousnaturally feel it keenly.

Of course, at times we feel that many of theproblem of our political, social, linguistic and culturallife would come to an end if there were one Govenmentall ovet the world. Travellers, businessmen, seekers ofknowledge and teachers of righteousness know very wellthat great impediments and obstructions are faced bythem when they pass from one country to another,exchange goods, get information, and make an effortsto spread their good gospel among their fellow-men. Inthe past, religious sects divided one set of people againstanother, colour of skin or shape of the body set oneagainst the other.

But today when philosophical light has explodedthe darkness that was created by religious differences,and when scientific knowledge has flasified thesuperstitions, they have enabled human beings of allreligious views and of all races and colours to come infrequent contact with one another . It is the governmentsof various countries that keep poeple of one countryapart from, those of another. They create artificial

barriers, unnatural distinctions, unhealthy isolation,unnecessary fears and dangers in the minds of commonmen who by their nature want to live in friendship withtheir fellow-men. But all these evils would cease to existif there were one Government all over the world.

1. What divides people of a country against another?(a) Different religions(b) Different language(c) Different social and political systems of

different people(d) Government of various countries

2. What is the urgent heed of the world today?(a) The establishment of an international

economic order.(b) The establishment of a world government.(c) The creation of a cultural international social

order.(d) The raising of an international spiritual army.

3. What will the world Government be expected todo?(a) it will arrange for interplanetary contacts(b) it will end all wars for all time to come(c) it will bring about a moral regeneration of

mankind(d) it will kill the evil spirit in man

4. Choose the word which is SIMILAR in meaningas the word "righteousness" as used in thepassage.(a) rectitude (b) religiosity(c) requirement (d) scrupulousness

EXERCISE 1

Comprehension





5. Which of the following problems has not beenmentioned in the passage as likely to be solvedwith the establishment of world Government?(a) Social Problems (b) Political Problems(c) Cultural Problems (d) Economic Problems

6. Choose the word which is most OPPOSITE inmeaning of the word 'implediments' as used inthe passage.(a) handicaps (b) furtherance(c) providence (d) hindrances

7. The most appropriate title of the above passagemay be ...........(a) The evils of the world order.(b) The man can make his destiny.(c) The need of world Government.(d) The role of Religion in the Modern Times.

8. What was the factor, according to the passage,that set one man against another?(a) Material prosperity of certain people in the

midst of grinding poverty.(b) Superior physical strength of some persons.(c) Colour of skin or shape of the body.(d) Some people being educated and other

illiterate.9. The theory of racial superiority stands falsified

today by ........(a) knowledge derived from scientific advances.(b) the ascendancy of people who were here to fore

considered of inferior racial stock.(c) the achievements of the so called backward

countries in every field of life.(d) the precedence given to the physical powers

of different races.10. In the part religious sects .............

(a) united the people with one another.(b) Interfered in political affairs.(c) did a good job by way of spreading message of

love and peace.(d) divided one set of people from another.

Directions (Q. 12-18): Read the following passagecarefully and answer the question given below it.Certain words are printed in bold to help you tolocate them while answering some of thequestions.

The window offered a view of the house opposite.The two families did not speak to each other because ofa property dispute. One day, Ruchira's textbooks layuntouched as the young girl's gaze was on the

happenings in the house opposite. There were two newfaces in the neighbouring household that of an elderlywidow and a girls aged sixteen. Some times the elderlylady would sit by the window, doing the young girl'shair. On other days she was absent.

The new young neighbour's daily routine could beseen through the window she cleaned the rice paddy;split nuts, put the cushions in the sun to air them. Inthe afternoons while the men were all at world some ofthe women slept and others played cards. The girl saton the terrace and read. Sometimes she wrote. One daythere was hindrance. She was writing when the elderlywoman snatched the unfinished letter from her hands.Thereafter the girl was not to be seen on the terrace.Sometimes during the day sounds came from the houseindicating that a massive argument was going on inside.

A few days passed. One evening Ruchira noticedthe girl standing on the terrace in tears. The eveningprayer was in progress. As she did daily, the girl bowedseveral times in prayer. Then she went downstairs. Thatnight Ruchira wrote a letter. She went out and postedit that very instant. But as she lay in bed that night,she prayed fervently that her offer of friendship wouldn'treach its destination. Ruchira then left for Madhupurand returned when it was time for college to start. Shefound the house opposite in darkness, locked. They hadleft.

When she stepped into her room she found the deskpiled with letters one had a local stamp on it with hername and address in unfamiliar handwriting. Shequickly read it. They continued to write to each otherfor the next twenty years.

11. Why did Ruchira write a letter to her newneighbour?(a) She wanted to offer her, her help.(b) She wanted to be friends with her.(c) To apologize for her family's behaviour

towards her family.(d) To encourage her to continue learning to read

and write.12. Which of the following can be said about Ruchira?

A. She used to spy on her neighbours becauseshe didn't trust them.

B. She was at home because she was studying.C. She did not speak to her neighbours because

they did not own property.(a) None (b) Only B(c) Both A & B (d) Only C





13. How did the new young neighbour spend herdays?(a) She was busy writing letters to Ruchira.(b) She used to daydream about her past

experiences.(c) She would attend to the needs of the widow.(d) She spent her time learning to read and write.

14. Why was the young neighbour prevented fromsitting on the terrace?(a) She used to while away her time instead of

working(b) The old woman could no longer keep an eye

on her.(c) She had not finished writing the letter she was

asked to.(d) She had been writing a letter which she wasn't

supposed to.15. What was the major argument in the house about?

(a) There were too many people living there,which resulted in arguments.

(b) The young girl was insisting on attendingcollege.

(c) The young girl had been wasting her timeinstead of working.

(d) The old woman did not guard the young girlclosely.

16. Which of the following is TRUE in the context ofthe passage?(a) The young girl was very devout and prayed

everyday.(b) Only two letters were exchanged between the

two girls.(c) The new young neighbour was a servant.(d) The afternoon was a time to relax for everyone.

17. Why did the young girl wish that the letter wouldnot reach its destination?A. She was going away and would not be able to

see if her neighbour was glad to receive it.B. She was afraid that it would lead to a quarrel

between the two families.C. She was afraid that her neighbour would be

angry when she received her letter.(a) None(b) Only A(c) Only C(d) Both B & C

Directions (Q.18-20): Choose the word which ismost nearly the SAME in meaning as the worldprinted in bold as used in the passage.

18. Hindrance(a) handicapped (b) delay(c) interruption (d) difficult

19. Offered(a) forward (b) willing(c) volunteered (d) provided

20. Choose the word which is most OPPOSITE inmeaning of the word piled as used in the passage.(a) low (b) empty(c) blank (d) nothing

Directions (Q. 21-27): Read the following passagecarefully and answer the questions given belowit. Certain words are printed in bold to help you tolocate them while answering some of thequestions.

The yearly festival was close at hand. The storeroom was packed with silk fabrics, gold ornaments, claybowls full of sweet curd and platefuls of sweetmeats.The orders had been placed with shops well in advance.The mother was sending out gifts to everyone.

The eldest son, a government servant, lived withhis wife and children in far off lands. The second sonhad left home at an early age. As a merchant he travelledall over the world. The other sons had split up over pettysquabbles, and they now lived in homes of their own.The relatives were spread all across the world. Theyrarely visited. The youngest son, left in the company ofa servant, was soon bored left her and stood at the doorall day long, waiting and watching. His mother, thrilledand excited, loaded the presents on trays and plates,covered them with colourful kerchiefs, and sent themoff with maids and servants. The neighbours looked on.

The day came to an end. All the presents had beensent off.

The child came back into the house and dejectedlysaid to his mother, "Maa, you gave present to everyone,but you didn't give me anything !"

His mother laughed, "I have given all the giftsaway to everyone, now see what's left for you." Shekissed him on the forehead.

The child said in a tearful voice, "Don't I get a gift?""You'll get it when you go far away.""But when I am close to you, don't I get something

from your own hands?"His mother reached out her arms and drew him to

her "This is all I have in my own hands. It is the mostprecious of all."





21. Why did the woman's second son travel?(a) He was restless by nature.(b) He did not want to stay at home.(c) He was rich and could afford to travel.(d) His job prevented him from taking leave

22. Why did the woman's eldest son not attend thefestival?(a) He was not on good terms with his youngest

brother who lived at home.(b) He had quarrelled with his mother.(c) His wife did not allow him to return home.(d) His job prevented him from taking leave

23. How did the woman prepare for the fesitval?A. She bought expensive gifts for her children

and neighbours.B. She ordered her servents to prepare sweets

and food well in advance.C. She made sure that her youngest child was

looked after so that he wouldn't be bored.(a) None (b) Only A(c) Only B (d) Both A & B

24. What did the youngest child do while his motherwas busy?(a) He waited for a chance to steal some

sweetmeats(b) He pestered his mother to give him a present.(c) He stood at the door with the servants.(a) Only A (b) Only B(c) Both A & C (d) Only C

25. Which of the following can be said about thewoman?(a) She was a widow who had brought up her

childern single handedly.(b) She was not a good mother since her childern

had left home at an early age.(c) She enjoyed sending her family gifts at festival

time.(d) She gave expensive presents to show that she

was wealthy.26. What did the boy receive from his mother?

(a) She taught him the value of patience(b) She encouraged him to grow up and live

independently like his brother.(c) She showed him the importance of giving

expensive gifts.(d) She gave him a hug to express her love.

27. Which of the following is TRUE in the context ofthe passage?(a) The woman usually ignored her youngest son.

(b) The woman's eldest son lived abroad.(c) The memers of the woman's family did not care

about her.(d) The woman made all the preparations herself

since she did not want to burden the servants.Directions (Q. 28 30): Choose the word which ismost nearly the SAME in meaning as the wordprinted in bold as used in the passage.

28. Left(a) gone (b) quit(c) remaining (d) disappeared

29. Packed(a) filled (b) squeezed(c) crowd (d) collected

30. Choose the word which is most OPPOSITE inmeaning of the word dejectedly as used in thepassage.(a) calmly (b) happily(c) willingly (d) fortunately

Direction (31-36): Read the following two passagescarefully and answer the questions given belowthem. Certain words/expressions are given in boldin Passage I to help you locate them whileanswering some of the questions.

Ghanshyam Das Birla was a great architect ofIndia's industrial growth. He started his career inKolkata at the beginning of 20th century. He set upmany industries. He entered the field of business duringthe days of the First World War and established himselfafter the war years. First, he established a cotton millin Sabzi Mandi, Delhi, followed by Keshoram CottonMills and Birla Jute Mills around 1920. The KeshoramMills were set up with the efforts of Andrew Yule. In1919, with an investment of Rs 50 lakhs, Birla BrothersLimited was formed and thereafter a mill was set up inGwalior.

Mr. Birla realised that political freedom from Britishrule was imperative for the industrial growth of India.In 1920, he came into contact with Gandhiji and becamehis disciple. In the decade of the 30's he set up sugarpaper mills. From 1943 to 1946, with the stock exchangegaining ground, Birla Brothers ventured into theareas of cars, cotton, machinery and man-made fabrics.United Commercial Bank was set up during this period.Prior to this, he had established Ruby, Asiatic InsuranceCo. and Inland Air Service.

After independence, the Birlas expanded theirbusiness and started production in many fields. Near





Mirzapur, he, in collaboration with Caesar, an Americanfriend, set up an aluminium plant Hindalco in recordtime. He bought the Century Mill from Sir ChunnilalV.Mehta, the cousin of Sir Purshottam Das Thakur. Healso bought tea estates and started cement and fertiliserfactories. He established a new style of management.In his birth place Pilani, and at many other places hestarted many educational institutions. To his credit gomany temples, planetariums and hospitals. In 1983, hedied while in London, but not before seeing his businessflourish as one of the topmost establishments in India.During the decades of 70's and 80's, Birla Brothers wasamong the topmost Industrial Houses in India.

Anna Saheb Karve's life was an simple and cleanas that of an ancient ascetic (Rishi Muni). He was liberalin his views and sympathetic in his attitude. He wasdeeply moved by the troubles and tribulations of womenflok.

What Anna Saheb did for the upliftment of womenin the last decade of the nineteenth century was beyondthe imagination of the people. He created an awakeningamong women through his writing in Kesari. He was astaunch supporter of widow remarriage. On March 11,1893, he set an example for society by taking the boldstep of marrying a widow. The couple dedicated theirlives to social work and reform. He established anorphanage in Pune.

Anna Saheb realised the importance of educationfor women. He spared no effort in starting the BharatiyaMahila Vidyapeeth, the first university for women. In1921, he travelled to Europe and America and metfamous people like Albert Einstein and formulated hisopinions regarding work. In 1958, he was awarded the'Bharat Ratna' in recognition of his services ineducational and social reforms.

31. Ghanshyam Das Birla was better known to Indiaas(a) a freedom fighter against British rule(b) an architect of temples in various cities(c) a pioneer of India's industrial growth(d) an architect of the textile industry in India

32. Ghanshyam Das Birla's first industrial venturewas(a) a textile related industry(b) a cotton mill, Gwalior(c) Keshoram Cotton Mills, Delhi(d) car manufacturing company

33. What was Andrew Yule's role in Ghanshyam DasBirla's career?

(a) He helped Ghanshyam Das Birla in settingup cotton mills in Sabzi Mandi, Delhi.

(b) He invested Rs. 50 lakhs in Keshoram CottonMills

(c) He extended a lot of help to Ghanshyam DasBirla in his second venture.

(d) He helped Ghanshyam Das Birla in the fieldof business before the First World War.

34. What was Ghanshyam Das Birla's view about theBritish rule in India?(a) The British rule was very atrocious.(b) The British rule was counter productive to

India's industrial growth.(c) The British rule was not a hindrance to India's

industrial growth.(d) The industrial growth of India had nothing to

do with gaining freedom from the British.35. Which of the following can be inferred from the

passage ?A. Ghanshyam Das Birla could set up a large

number of diverse industries due to British rulein India.

B. Ghanshyam Das Birla, with his familymembers, started various industries due toflourishing of the Stock Exchange.

C. Ghanshyam Das Birla was impressed byGandhiji's philosopy.

(a) Both A and B (b) Both A and C(c) All the three (d) Only B and C

36. Which of the following statements is FALSE inthe context of the passage?A. Ghanshyam Das Birla unfortunately died

before realising the progress his business hadmade.

B. Hindalco was set up in a very short time span.C. Ghanshyam Das Birla's management style

was different from the traditional one.(a) Only A (b) Only B(c) Only C (d) Both A and B

Directions (Q. 37-38): Choose the word/group ofwords which is/are most nearly the SAME inmeaning to the word/group of words given in boldas used in the passage.

37. Imperative(a) trial (b) dispensable(c) inadequate (d) unavoidable

38. Gaining Ground(a) obtaining land (b) making advances(c) losing heavily (d) grounding due to losses





Directions (Q.39-45): Choose the word which ismost OPPOSITE in the meaning of the wordprinted in bold as used in the passage.

39. Expanded(a) increased (b) extended(c) banned (d) curtailed

40. Flourish(a) flower (b) tarnish(c) gain (d) deteriorate

41. Which of the following makes Anna Saheb Karvecomparable to an ascetic?(a) His emphasis on the importance of education.(b) His efforts in founding Bharatiya Mahila

Vidyapeeth.(c) His liberal views and deep sympathy and

sensitivity for women and simple and cleanlife.

(d) His winning the 'Bharat Ratna' Award.42. What did Anna Saheb Karve do to prove that he

practised what he preached?(a) He wrote articles in 'Kesari' for creating

awareness among women(b) He established an orphanage in pune.(c) He expressed very strong views in support of

widow remarriage.(d) He married a widow.

43. What was Karve's ideology in starting BhartiyaMahila Vidyapeeth?A. Women must have greater access to and

opportunities for education.B. Widows and forsaken women should get

opportunities for being self reliant.C. Uplifting of women who had remained

underprivileged for years.(a) All the three (b) Both A and C(c) Both B and C (d) Only C

44. Anna Saheb Karve was felicitated with the'Bharat Ratna' award forA. His recognising that educational reform alone

was the solution to all the prolems that womenfaced.

B. His contribution to the education of womenand their social transformation.

C. His intellectual discussions with world famousscientists and social reformers.

(a) Only A (b) Only B(c) Only C (d) Only A and B

45. Which of the following statements is definitely.TRUE in the context of the passage?A. Before the last decade of 19th century, window

remarriages were socially unacceptable.B. Anna Saheb Karve thought that educating

women was one of the most effective ways oftheir upliftment.

C. Anna Saheb Karve's wife actively joined himin his social service.

(a) Both A and B (b) Both B and C(c) Both A and C (d) All of these

Direction (Q. 46 55): In the following passage,there are blanks, each of which has beennumbered. These numbers are printed below thepassage and against each, four words aresuggested. One of which fills the blankappropriately. Find out appropriate word in eachcase.

The Reserve Bank has taken a bold (46) in thedevelopment of money, the government securities andthe foreign exchange markets in (47) of their criticalrole in overall growth and development of the economyand (48) in the transmission mechanism of monetarypolicy. The approach has been one of simultaneousmovements on several fronts, graduated and callibrated,with an (49) on institutional and infrastructuraldevelopment and improvements in marketmicrostructure. The pace of reforms was contingent (50)putting in place appropriate systems and procedures,technologies and market practices. Initiatives taken bythe Reserve Bank have brought about a (51)transformation of various segments of the financialmarket. These developments by improving the depthand liquidity in domestic financial markets have (52) tobetter price discovery of interest rates and exchangerates, which, in turn, hae led to greater (53) in resourceallocation in the economy. The increase in size anddepth of financial market has (54) the way for (55) useof indirect instruments.

46. (a) interest (b) participation(c) step (d) role

47. (a) point (b) tune(c) view (d) pursuit

48. (a) decisively (b) reluctantly(c) visibly (d) particularly

49. (a) equilibrium (b) emphasis(c) appeasement (d) overload

50. (a) by (b) for(c) against (d) upon





ANSWERS

1. (d) 2. (d) 3. (c) 4. (a) 5. (d) 6. (b) 7. (c) 8. (c) 9. (a) 10. (d)11. (b) 12. (b) 13. (d) 14. (d) 15. (c) 16. (a) 17. (b) 18. (c) 19. (d) 20. (b)21. (d) 22. (d) 23. (a) 24. (a) 25. (c) 26. (d) 27. (a) 28. (c) 29. (a) 30. (b)31. (c) 32. (a) 33. (c) 34. (b) 35. (d) 36. (a) 37. (d) 38. (b) 39. (d) 40. (d)41. (c) 42. (d) 43. (b) 44. (b) 45. (d) 46. (c) 47. (d) 48. (d) 49. (b) 50. (d)





Language is the major means by which we communicate and interact with others. When we speak or write,we use words. These words are generally used in groups e.g.: A bad workman quarrels with his tools.

A group of words arrange din a manner which makes a complete sense is called a Sentence. Based on meaningand sense, the sentence can be classified as :

1. Declarative or assertive 2. Imperative3. Interrogative 4. Exclamatory

Parts of SpeechWords are classified into different kinds or groups called Parts of Speech according to their use and function

in a sentence. They are eight in number-Noun, Pronoun, Adjective, Verb, Adverb, Preposition, Conjunction andInterjection.

NounThe Noun is a word used as the name of a person, place or thing. The word thing includes (i) all objects that

we can see, touch, hear, smell or taste, and (ii) something we can think of but cannot perceive through our senses.There are five different kinds of noun.

They are :1. Proper Noun 2. Common Noun3. Collective Noun 4. Material Noun5. Abstract Noun.

Kinds of NounThe following chart will make you familiar with the different kinds of noun :

Noun Nature of Noun ExamplesProper Noun It denotes a particular person, place or thing. Chander, Kolkata, India, the Ganges, the Gita, etc.Common Noun It is the name given to any and Table, glass, town, king, book, river, country, etc.

every person or thing of the same class or kind.Collective Noun It denotes a group or collection of Army, class, host, jury, mob, crowd, team, parlia

similar individuals or things considered ment, committee, family, fleet etc.as one complete whole.

Material Noun It denotes the matter or substance of Wood, clay, rubber, iron, silver, gold, cloth, etc.Abstract Noun It expresses quality, state or action. Truth, love, soul, mind, greatness, life, poverty,

manhood, pleasure, pain, honesty, etc.

Sentence

CHAPTER 2





PronounThe repetition of a noun in a sentence or a set of sentences is really boring. So, Grammar prescribes that

instead of repeating the noun, we may use a word (for that noun) called pronoun. This leads us to a precisedefinition of Pronoun.

The Pronoun is a word that we use instead of a noun.Many people commit grammatical mistakes because they lack thorough knowledge regarding the use of

pronouns.The following facts can be stated on the basis of the above definition:

(a) A pronoun must itself be something equivalent to a noun.(b) As a rule, the pronoun should not be mentioned until the noun has been mentioned.(c) A pronoun must be of the same number, gender and person as the noun it stands for.

Pronouns have numerous subclasses. Though there are several features that pronouns have in common withnouns, yet there are some features which distinguish them from nouns. They are as follows:

(a) They do not admit determiners;(b) They often have an objective case;(c) They often have person distinction;(d) They often have overt gender contrast;(e) Singular and plural forms are often not morphologically related.

Kinds of PrnounsI. Personal Pronouns : A pronoun which is used instead of the name of a person is known as a Personal

Pronoun.Examples I, my, mine, me, we, our, ours, us.(First Person)

Thou, thine, thy, thee.You, your, yours. (Second Person)He, his, him, she, her, hers, it, its,they, their, theirs, them. (Third Person)

II. Reflexive or Emphatic Pronouns : When self is added to my, your, him, her, it and selves to our, your,them, we get Compound Personal Pronouns. When the action done by the subject turns back (reflects) uponthe subject, self is added to the pronoun and becomes a Reflexive or Emphatic pronoun.

Examples 1. I hurt myself2. He hurt himself.3. They hurt themselves.

III. Demonstrative Pronouns: The pronouns which are used to point out the objects which they refer to arecalled Demonstrative Pronouns.

Examples 1. This is a gift from my father.2. These are merely excuses.3. Mumbai mangoes are better than those of Bangalore.4. That is the fort of Allahabad.

IV. Indefinite Pronouns : All pronouns which refer to persons or things in a general way and do not refer toany particular person or thing are called Indefinite Pronouns.

Examples 1. Somebody has stolen my watch.2. Few escaped unhurt.3. Did you ask anybody to come? 4. Nobody was there to welcome her.





V. Distributive Pronouns: Each, either, neither are called Distributive Pronouns because they refer topersons or things-one at a time. For this reason, they are always singular and thus followed by the verb insingular.

Examples 1. Each of these men received a reward.2. Either of you can go.3. Neither of the accusations is true.

VI. Relative Pronouns: A Relative Pronoun refers or relates to some noun going before, which is called itsAntecedent.

Examples 1. I met Hari who used to live here.2. I have found the pen which I had lost.3. Here is the book that you lent me.

VII. Interrogative Pronouns: These pronouns are used to ask questions.Examples 1. Whose book is this?

2. What will all the neighbours say?3. What do you prefer, tea or coffee?

Note: Interrogative pronouns can also be used in asking indirect questions. Consider the following examples:1. I asked who was speaking.2. Tell me what you have done.3. Say which you would like best.

AdjectiveAn Adjective is a word that qualifies or adds something to the meaning of a noun.

1. Madan is a good boy. (Boy of what kind?)2. He gave me ten bananas. (How many bananas ?)3. We do not like that girl. (Which girl?)

In sentence 1, good tells what kind of boy Madan is.In sentence 2, ten shows how many bananas he gave me.In sentence 3, that points out which girl is meant.

Some Facts About Adjectives and their UsesAdjectives can be used in two ways-attributively and predicatively. When an adjective is placed just before the noun, itsuse is Attributive, but when it is used after the noun or pronoun, the use is called Predicative.Examples

(i) This is a sweet mango. (Attributive)(ii) This mango is sweet. (Predicative)(iii) Fame is the perfume of heroic deeds. (Attributive)(iv) The judge declared him guilty. (Predicative)(v) It is a beautiful painting. (Attributive)(vi) The painting is beautiful. (Predicative)(vii) Sita is a pretty girl. (Attributive)(viii) My daughter is pretty. (Predicative)(ix) Each boy of the class was punished yesterday.(x) There were only two poets. Each poet recited his poem.(xi) Every man is expected to do his duty. (xii) He comes to me every day.

(xiii) Every man in this world dies. (xiv) India wants peace in every corner ofthe world.





Directions: Each of the following question is in theform of a sentence with four underlined portionsmarked a, b, c and d, respectively. Choose themarked portion that carries errors. If no errorrequired then your answer is 5.

1. A tapestry consists of a foundation weave, acalled the wrap, which across are passed

bseveral coloured threads, called wefts,

cforming decorative patterns.

d2. The fossil remains of much extinct

amammals have been found in the tar pits

b cor Rancho Brea in Los Angles.

d3. Chemical engineering is based on the

aprinciples of physics, chemists, and

b cmathematics.

d4. The salesman refused to show the family

aaround the showroom, till they told him

b cwhat kind of a car they were looking for.

d5. Despite the manager's comprehensive and

aenthusiastic explanation of the scheme, we

bwere completely disinterested in the matter.

d6. I like both further and farther as I have

anever been been able to tell which is which

b cand why one is further or farther than the other.

d7. Some women acknowledge the fact that

atheir principal goal in life is to dress well,

b cbut such a principal is not guaranteed to

dlead to spiritual salvation.

8. Political pundits have been able to correctlya b

prophesy results of Election '98, but onec

wonders whether the outcome will holdgood for long.

d9. The doctor advised his young patient to

a

EXERCISE

Sentence Correction

CHAPTER 7





take two two capsful of the bitter medicine,b

but the latter stuck to the single-cup ritualc d

with no adverse effect.10. Radhika and Preeti were excited about the

aschool party, as they were alumni of the

bschool, and looked forward to meeting

c dtheir old friends.

11. Practising progressive muscular relaxation,a

like a contracting and relaxing the musclesb

of the different areas of the body strengthenc d

the neural connections too.12. Business magazines have been consistent

ain saying that unless Indian banks merged,

b cthey will lose market share.

d13. Wrapped as they were in layer of soft cotton

a bwool, neither of the two crystal goblets were

cbroken when the lady dropped the crate.

d14. Although my brother had been anxiously

a blooking forward to the prize-giving

cceremony for weeks, a bad-hair day prevented himtaking part in it.

d15. There reason for I refusing the gift was that

a bit was meant as a bribe to lure me away

c dfrom the case.

16. Charles Correa, the father of modern Indiaa

architecture, designed buildings that haveb c

earned him an international reputation and

dinflue need an entire generation of artists andarchitects.

17. In order to make bus journeys safer,a b

smoother and more enjoyable a number ofc

operators have hired consultants to suggestchanges.

d18. In the middle half of the nineteen hundreds,

athe political values taught in the public and

bprivate schools did not change substantially

cfrom those celebrated in the first fifty years of therepublic.

d19. After all, the informed voter's evaluation

aof a party depends on the extent of precise

binformation he has of its policies so that he shouldgauge the relationship between

cthose policies and his conception of his own

dwelfare.

20. While the BJP seeks a modification of thea

World Trade Organisation rules in concertb

with other developing nations, the Congress-Iwould prefer to work with

cindustry to smoothen the transition to an era offree trade.

d21. The adaptation of mammals to almost all

apossible modes of life parallels the reptiles

bin the Mesozoic time, and except for greater

cintelligence, the mammals do not seem to havedone much better than corresponding

dreptilian forms.

22. Sancho ran as fast as he could walk to help





a bhis master whom he found lying on the

cground and not able to stir, such a blow he

dand Rozinante had received.

23. As Caesar loved me, I wept for him, as hea b c

was fortunate I rejoice at it.d

24. The people of Orleans, when they first sawa b

her in their city thought she was an angel.c d

25. Chemical compounds with barium, cobalt a

and strontium are responsible to many of b c

the vivid colours in fireworks.d

26. Plants, which make up 90 percentage of a b

visible living organisms, get their food c d

energy from sunlight.27. In the company of human beings, parrots

ademonstrate a remarkable talent for

bmimicry, for which they never use in the forest.

c28. Conducting without a baton or score, the

aleader waved his and around in order that

b che would have knocked the music desk offthe podium if there had been a desk, which therewasn't

d29. Another outstanding characteristic of water

ais that water has a heat capacity which is

bthe highest in all liquids and solids exceptammonia

30. Like a number of her white friends ina

government, Bethune assumed that theb

preservation of democracy and black people's fullintegration into the benefits

c

and the responsiblities of American life wereinextricably tied.d

ANSWERS

1. (b) 2. (a) 3. (c) 4. (c) 5. (c) 6. (a) 7. (d) 8. (b) 9. (b) 10. (d)11. (d) 12. (c) 13. (d) 14. (d) 15. (a) 16. (c) 17. (c) 18. (a) 19. (c) 20. (a)21. (b) 22.(b) 23. (d) 24. (c) 25. (c) 26. (d) 27. (d) 28. (c) 29. (b) 30. (d)



SAMPLE MATERIAL OF


Data Interpretation &

Data Sufficiency



Data InterpretationBureaucrats and Government executives must face lots of facts and figures in everyday business. Normally

these facts are presented in more compact and precise forms such as1. Tables (known as data tables)2. Charts (Pie, Bar, Pert, etc.)3. Graphs (2D and 3D)4. Diagrams (Geometric or Venn diagram)

An Administrator must possess basic skills on deciphering the data from the above mentioned precise forms oftables, charts etc. which enhances his/her administrative efficiency. This ability is known as data interpretation.So IAS Prelim/CSAT exam test the candidates ability of data interpretation.Example 1

Question: These questions are based on following pie chart, which gives the details of percentage of energysource of India.

Nuclear, 2%Hydro, 2%

Gas, 9%

Coal, 51%

Oil, 36%

Q. The second largest energy source of India is(a) Coal (b) Oil(c) Gas (d) Hydro and Nuclear Ans: b

Note: Question may not be always direct. You may need to compute answers before arriving conclusion. Lookthe example below.Example 2

Question: These questions are based on following table, which gives the details of Distribution of paperindustry in India during 1997 especially state wise no of mills, its production capacity in thousand metric ton andPercentage of mills of all India it possess.

Introduction toData Interpretation

CHAPTER 1





State No. of Mills Production Capacity Percentage of(in ‘000 MT) all India

Maharashtra 63 624 16.52Andhra Pradesh 19 427 11.3Gujarat 55 369 9.77Uttar Pradesh 68 336 8.89All India (Total) 379 3778 100

Q. Which of the state has lowest productivity with respect to number of mills it possesses?(a) Maharashtra (10.19) (b) Andhra Pradesh (22.47)(c) Gujarat (6.71) (d) Uttar Pradesh (4.94) Ans: d

Note: Also there may be few questions unable to interpret using available chart or tables. It needs carefulattention however it is very easy.

Question Patterns of Data InterpretationThere are a multiple ways in which data can be shown to you. They are various forms of tables, charts, bars,

diagrams. For UPSC-CSAT, 2011, you can expect Data Interpretation questions on singular bar, multiple bars,tables, pie chart, line diagram etc. There you will be provided certain data and instructions. On the basis of theinstructions you have, you have to answer the questions asked to you, along with the data.

Ways to Prepare for Data InterpretationFor interpreting data, you should read a lot. Read lot of business reports and the analysis given with the

presentation of data. This will give you a fair idea on how data are presented and how to interpret or analyzethem. You must read articles, especially on business which are heavy on data and analyze them. This will keepyour DI cells on toes. In a similar note, Refer to the graphs and data provided in various business papers andmagazines. You need to identify techniques to solve questions which require big and time consuming calculations.

At this stage, when there are few months left for UPSC-CSAT, 2011 you should solve at least three to fourData Interpretation sets every day. Also, you need to be good with quick calculation of ratios, percentages, etc.With consistent practice, you will be able to achieve the same.

While Solving Data Interpretation QuestionsWhile solving the Data Interpretation questions, you must keep some points in mind. Experts suggest the

following points which you should keep in mind while you start attempting the Data Interpretation questions.Read the title carefullyTake your time and read both the questions and data set carefully. Understand what you are being asked todo before you begin figuring out the information.Check the data and types of information required. Be sure that you are looking at the right part of graph orchart, i.e., on paper columns or rows or proper lines.Read the parameters listed along with axes and the scale. This is the most important points as generally oneassumes standard scale as 1 unit = 100 or 1 unit = 10. Also the scales of two axes might be different.The footnotes give the additional information for particular data. This also explains the jargons and lists theformulae that might be needed to solve the questions asked.Check the units required. Be sure that your answer is in thousand, millions or whatever it is that thequestion specifies.





In this section the UPSC tests the ability of the candidate to identify whether the data given are sufficient toanswer the question or not. Although data sufficiency was given as a topic under Data Interpretation its scopealso extends from mathematical based quantitative ability questions to non-mathematical based simple reasoningunder Analytical Section.

Since these questions require candidates to identify the sufficiency of data, you must stop at the stage ofdetermining the sufficiency of data and you are not expected to solve the problem completely.

Like Assertion and Reason which all Civil service aspirants have prior knowledge from the old questionpattern, this data sufficiency questions also have set of directions?For example:

Raju is the tallest boy in the school. Is he the tallest student in the class?1. Priyanka is the tallest girl in the class2. Priyanka is shorter than Raju

Choose A: If statement 1 alone is sufficient and statement 2 alone is sufficient to answerChoose B: If statement 1 alone is sufficient and statement 2 alone is not sufficient to answerChoose C: If statement 1 alone is not sufficient and statement 2 alone is sufficient to answerChoose D: If both the statements are sufficient to answer

Ans: DHowever there are 3 different sets of Directions as they are appearing in different examinations.Note: If the UPSC did not mention the set of direction earlier in the oncoming notification, then we must

prepare for all sets of directions.

Some Typical Cases: Data SufficiencyThe questions can be broadly divided into the following categories:

1. Relationships2. Dates3. Comparison4. Critical Analysis5. Age6. Miscellaneous

Data Sufficiency

CHAPTER 8





1. RelationshipsThe wording goes like this: How is P related to Q? . In these questions one very prominent source of confusion

is the fact that students tend to conclude about relationship without knowing about the sex of the person involved.

2. DatesThe wording of the question goes like this: On which day of the week did P reach (say) Delhi? or What is

the date of birth of P? . In such questions, you have to determine a day or a date . Usually, the data will provideyou with some knowledge of some previous day or date and from this you can work out the required day or date.

3. ComparisonThe wording of the question is: Who is the tallest among P, Q and R? or Who is the heaviest among X, Y

and Z? or Who is sitting to the left of P when P, Q and R are sitting together? etc. Here you have to makecomparisons of the respective places of some persons in a fixed pattern or order.

4. Critical AnalysisSometimes questions asked in the examination are qualitative in nature, wherein you have to apply your

value-judgement in order to reach a conclusion.

5. AgeIn some questions of data sufficiency, problems are concerned with age. Again, we must emphasis that the

question does not ask you to actually calculate the age of the person. It only wants you to tell whether the givenstatements are sufficient (or not) to calculate the age of that person.

6. MiscellaneousAlthough the five categories mentioned above are standard categories and most of the questions asked will be

from these five categories, these are certain type which do not belong to any of them. We may sell them miscellaneousquestions.

EXERCISEDirection: Is the data given in two statements,labeled (1) and (2), sufficient for answering thequestion? All numbers used are real numbers.

Choose (a): If statement 1 alone is sufficient andstatement 2 alone is sufficient to answer

Choose (b): If statement 1 alone is sufficient andstatement 2 alone is not sufficient to answer

Choose (c): If statement 1 alone is not sufficientand statement 2 alone is sufficient to answer

Choose (d): If both the statements are sufficientto answer

1. If n is a positive integer greater than 1, is 3n(n2 -1) divisible by 12 ?(1) n is odd. (2) n is a multiple of 3.

2. Boxes A, B and C together contain a total of 8pencils. Each box contains at least 1 pencil. Box Acontains more than 1 pencil. How many pencilsclops each hox contain?

(1) The number of pencils in Box A is not a primenumber.

(2) Box B and Box C contain the same number ofpencils.

3. If 16x +y/2+1 = 4x + 2y what are the values of x andy?(1) 72x + 3y = 4938 (2) 5 4 = 25x y

4. How much did a family spend on their Alaskanvacation?(1) There were 4 members in the family.(2) Each family member spent ` 1799.

5. What is the value of m?(1) m = 81 (2) m2 = 81

6. Hemant s flower-vase contains only yellow astersand orange asters. What is the ratio of orangeasters to yellow asters in her flower-vase?(1) The number of yellow asters is 2 less than the

number of orange asters.





(2) The number of yellow asters is 3/4 the numberof orange asters.

7. What is the area of rectangle PQRS?(1) Its diagonal is 13 feet.(2) PS = 5 feet

S R

P Q

8. A rectangular photograph is to be placed in awooden frame. What is the area of the photograph?(1) The length of the photograph is 7 inches.(2) The area of the wooden frame is 55 square

inches.9. Is possitive integer a even?

(1) a is a multiple of 4.(2) a is a factor of 44 22.

10. What is the value of odd integer s?(1) 1 < s < 10.(2) s is also an odd integer.

ANSWERS

1. (a) 2. (c) 3. (a) 4. (c) 5. (a) 6. (b) 7. (c) 8. (c) 9. (a) 10. (c)

EXPLANATIONS

1. Now, 3n (n2 1) = 3n(n 1)(n + 1).For 3n(n2 1) to be divisible by 12, it is necessarythat n(n 1)(n + 1) be divisible by 4.Statement (1) specifies that n is odd, which impliesthat (n - 1) and (n + 1) are even numbers and areeach divisible by 2. So, (n - 1)(n + 1) is divisible by4. Thus, statement (1) ALONE is sufficient.Statement (2) specifies that n is a multiple of 3.Consider an even multiple of 3 [because an oddmultiple has been already considered in statement(1)]. If n is even, then (n 1) and (n + 1) are oddintegers. Since odd integers are not divisible by 2,n must be divisible by 4 for n(n 1)(n + 1) to bedivisible by 4. However, not all even multiples of3 are divisible by 4. Thus, statement (2) ALONEis not sufficient.Alternative Approach :Since statement (1) specifies that n is odd, letn = 2m + 1, where m is a positive integer. Then,3n(n2 1) = 3(2m + 1)(4m2 + 4m + 1 1) = 12(2m+ 1)(m2 + m), which is divisible by 12.

Thus, statement (1) ALONE is sufficient.Since statement (2) specifies that n is a multipleof 3, let n = 3m, where m is a positive integer.Then,3n(n2 1) = 9m(9m2 1), which is divisible by 9but not necessarily 12.Thus, statement (2) ALONE is not sufficient.

2. Let the pencil distribution be represented by (a,b, c), where Box A has a pencils, Box B has bpencils and Box C has c pencils.Each box has at least I pencil. So, out of a total of8 pencils, 5 pencils now need to be distributedamong 3 boxes.Given that 1, 2, 3, 5 and 7 are the only primenumbers less than 8, statement (1) gives rise tofour possibilities: (6, 1, 1), (4, 2, 2), (4, 3, 1) and(4, 1, 3).Thus, statement (1) ALONE is notsufficient. Statement (2) gives rise to threepossibilities: (6, 1, 1), (4, 2, 2) and (2, 3, 3). Thus,statement (2) ALONE is not sufficient.When both statements are considered together,two possibilities still exist: (6, 1, 1) and (4, 2, 2).Thus, statements (1) and (2) TOGETHER are notsufficient.

3. The question statement gives the followingequation, on converting to same base:

42x + y + 2 = 4x + 2y

\ 2x + y + 2 = x + 2y or y x = 2Statement (1) gives the following equation, onconverting to same base:

72x + 3y = 776

2x + 3y = 76The two equations (y x = 2 and 2x + 3y = 76) canbe simultaneously solved to obtain values of thetwo unknowns x and y. Thus, statement (1)ALONE is sufficient.Statement (2) gives the following equation, onconverting to same base:

5-4 = 52x - 2y

\ 2x 2y = 4 or y x = 2Note that this equation is the same as that obtainedfrom the question statement. Thus, statement (2)ALONE is not sufficient.

4. Statement (1) specifies the number of members,but not how much each member spent. Thus,statement (1) ALONE is not sufficient. Statement(2) specifies how much each member spent, but





not the number of members. Thus, statement (2)ALONE is not sufficient. Since the total expensesare obtained on multiplying the number ofmembers by the amount each member spent,BOTH statements TOGETHER are sufficient.

5. Statement (1) tells us that m = 9. Thus, statement(1) ALONE is sufficient.Statement (2) tells us that m = 19. Thus,statement (2) ALONE is not sufficient.

6. If o and y are the number of orange asters andyellow asters respectively, then o/y is the ratio thatis needed.Statement (1) gives the following equation:y = o 2, from which o/y cannot be determined.Thus, statement (1) ALONE is not sufficient.Statement (2) gives the following equation:y = 3/4o, which can be solved to obtain o/y = 4/3.Thus, statement (2) ALONE is sufficient.

7. To find the area of rectangle, its length and widthmust be known becauseArea of rectangle = Length Width.Statement (1) specifies the diagonal. To find therectangle s area using the Pythagorean theorem,either its length or its width must be known.Thus, statement (1) ALONE is not sufficient.Statement (2) specifies the width. To find therectangle s area, either its length or its diagonalmust be known. Thus, statement (2) ALONE isnot sufficient.Knowing the width as well as the diagonal of therectangle allows us to calculate its length by thePythagorean theorem, and subsequently its area.Thus, BOTH statements TOGETHER aresufficient.

8. To find the area of the photograph, its length andwidth must be known or some additional

information about the wooden frame must begiven.Statement (1) specifies the length of thephotograph, but not its width. Thus, statement(1) ALONE is not sufficient.Statement (2) specifies the area of the woodenframe, but nothing about the photograph. Thus,statement (2) ALONE is not sufficient. Combiningboth statements gives the following equation

(7 + 2wf)(wp + 2wf) 7wp = 55,where wp is the width of the photograph and wf isthe width of the wooden frame.Since there is one equation with two unknowns,it cannot be solved for wp unless the width of theframe is given. Thus, Statements (1) and (2)TOGETHER are NOT sufficient.

9. Statement (1) specifies that a is a multiple of 4,and all multiples of 4 are even. Thus, statement(1) ALONE is sufficient.Statement (2) specifies that a is a factor of 44 22,but a could be odd (1) or even (2, 4, ...). Thus,statement (2) ALONE is not sufficient.

10. Statement (1) tells us that s = 3, ors = 5, or s = 7, or s = 9. Thus, statement (1) ALONEis not sufficient.Statement (2) specifies that the square root of s isalso an odd integer, but there are manypossibilities of s (1, 9, 25, 49, ...) that satisfy thiscriterion. Thus, statement (2) ALONE is notsufficient.On combining both statements, the value of s isuniquely determined as 9 (since 9 = 3), because3 and 5 and 7 are not odd integers. Thus,

BOTH statements TOGETHER are sufficient.





You can compare several categories by a graph of the cumulative type. These are usually bar or line graphswhere the height of the bar or line is divided up proportionately among different quantities.

Q. In 1986, roughly what percent of the federal prisoners received from the courts were guilty in other offenses?(a) 10 (b) 15(c) 25 (d) 30

The total number of prisoners in 1986 was about 20,000, and guilty in other offences was about 5,000.

Since = =

5,000 1 25%,20, 000 4

the correct answer is (c).

In DI section of the question paper, the intention should be to attempt all questions as skipping them wouldamount to losing precious scoring opportunities. There are two approaches to arrive at the solution. One is to workon the data to arrive at the correct answer. The other one is the Elimination method which requires workingbackwards by eliminating the wrong choices. Though the elimation method is more time consuming, it may still bepreferred where direct solution involves enormous calculation of data.

At times, examiners pose rather difficult data sets at the beginning of the sections. These are intended to beSPEED BRAKERS which take away much of precious time. Therefore, as a rule, scan the whole section quicklybefore actually attempting the questions and start with easier part of the section.

In some exams, data are presented in more than one table or graph. The objective is to test not only quantitativeskills but also relational and analytical ability. Recently, in some exams the questions in this section are being

Mix Diagrams

CHAPTER 7





framed in caselet (paragraph) form, beginning with probability and reasoning questions. It is left to the reader tostudy the case, call out requisite data and arrange it in a suitable form for meaningful interpretation. It is best toarrange data with rough sketch to hasten comprehension.

Important Tips: These will help in saving time, reducing mistakes and finding solution easily.1. Get a general picture of the information by looking at the entire table or graph.2. Read the table title, nomenclatures of columns and rows.3. Simplify the questions being asked. Break down lengthy questions into smaller parts.4. Use only the information given for finding solutions. Select the appropriate data for answering a question.5. Eliminate impossible choices.6. Avoid lengthy calculations.7. Try to interpret through trends of the data in the graph. Whenever possible, try to answer the questions by

visualizing rather than by computing.8. Where calculation is required prefer approximate values at the first stage. Go for exact calculation where

values are close and require exact answer.9. Be careful to use proper units.

10. Make correct use of your knowledge of basic mathematical rules, principles and formulae.11. Don t confuse in decimals and percent ages. For example, 0.5% = 0.005.12. Use pencil or straight edge of the answer sheet to read the graph and find approximate values.13. Focus your answer on the question actually asked and not on what the question should be in your opinion.14. Never do anything that is unnecessary.15. Last, but not the least, make sure that the answer is sensible and reasonable.

EXERCISEDirections: Study the pie-chart given to answerthese questions.

Composition of Exports and Imports (per cent)Exports (1998–1999)

A Agriculture and Allied ProductsB Ores and MineralsC Manufactured GoodsD Crude and Petroleum ProductsE Capital Goods

Imports (1998–1999)

A Food and Allied ProductsB FuelC FertilisersD Paper Board Manuf.and NewsprintE OthersF Other Bulk ItemsG Others

1. India s trade balance during the year 1998 99was:(a) favourable (b) unfavourable(c) neutral (d) none of these

2. Maximum export contribution has been due to :(a) agriculture and allied products(b) ores and minerals(c) crude and petroleum products(d) manufactured goods.

3. The import of capital goods and other bulk itemsincurred more than of total import expenditure(a) 50% (b) 60%(c) 35% (d) 70%

4. The imports exceeded by about millions.(a) US$ 8000 (b) US$ 8200(c) US$ 8199.4 (d) US$ 8400





5. The export of agriculture and allied products wasto the tune of US$ :(a) 5700 millions (b) 6700 millions(c) 4700 millions (d) 1730 millions

ANSWERS

1. (b) 2. (d) 3. (a) 4. (c) 5. (a)

EXPLANATIONS

4. Import Export= (41857.9 33658.5) = 8199.4 million

5. % of Agriculture and allied products= 17.3%= 33658.5 17.3% = 5822 million» 5700 million





Circle graphs are used to show how various sectors share in the whole. Circle graphs are sometimes called piecharts. Circle graphs usually give the percentage that each sector receives.

Expenditure of Major Industries 2000 ($3,087 million)

Legal affairs, 12%

Research, 15%

Miscellaneous,5%

Materials, 18%Advertising,

12%Construction,2%

Taxes, 10%

Compensation,26%

2010 ($4,851 million)

Research, 14%

Materials, 22%

Construction, 5%

Advertising, 15%

Legal affairs, 4%

Taxes, 2%

Compensation,38%

Q. The amount spent on materials in 2000 was 120% of the amount spent on(a) research in 2000 (b) compensation in 2000

Pie Charts

CHAPTER 4





(c) advertising in 2010 (d) materials in 2010In 2000, 18% of the expenditures were for materials. We want x where 120% of x = 18%; so x = 15%. Any

category that received 15% of 2000 expenditures gives the correct answer, but only one of the five choices iscorrect. Here, the answer is (a) since research received 15% of the expenditure in 2000.Example

Directions : Study the following information to answer the given questions.Percentage of students in various courses (A, B, C, D, E, F) and Percentage of girals out of these.

Total Student: 1200 (800 girls + 400 boys) Percentage in Various Courses

A20%

B15%

C5%

D35%

E12%

F13%

Total Girls : 800Percentage of Girls in Couress

A, 30%

B, 10%

C, 2%

D, 30%

E, 14%

F, 14%

1. For which course is the number of boys the minimum?(a) E (b) F(c) C (d) A

2. How many girls are there in course C?(a) 44 (b) 16(c) 40 (d) 160

3. For course D what is the respective ratio of boys and girls?(a) 3 : 4 (b) 4 : 5(c) 3 : 5 (d) 5 : 6

4. For which pair of courses is the number of boys the same?(a) E and F (b) A and D(c) C and F (d) B and D

5. For course E, the number of girls is how much percent more than the boys for course E?(a) 250 (b) 350(c) 150 (d) 80





SolutionCalculations for questions (1 5)

Courses Boys Girls TotalA 0 240 240

B 100 80 180

C 44 16 60

D 180 240 420

E 32 112 144

F 44 112 156

1. (d) Number of boys in course A is minimum i.e., zero.2. (b) Number of girls in course C = 163. (a) Required ratio = 180 : 240 = 3 : 44. (c) Number of boys in each of courses C and F = 44

5. (a) Required percentage = -112 3232 100

= 1832 100

= 250

EXERCISEDirections: Study the following pie-diagramscarefully to answer these questions:

Number of students studyingin different faculties in the years 2001 and 2002 from

State XYear-2001

Total Students - 35000

Arts, 12%

Commerce, 22%

Science, 24%

Agriculture, 7%

Engmeering, 18%

Pharmacy, 6%

Medicine, 11%

Year - 2002Total Students - 40000





Arts, 11%

Commerce, 24%

Science, 22%

Agriculture, 5%

Engmeering, 19%

Pharmacy, 9%

Medicine, 10%

1. In which faculty there was decrease in the numberof students from 2001 to 2002?(a) None(b) Arts(c) Agriculture (d) Pharmacy

2. What is the ratio between the number of studentsstudying pharmacy in the years 2001 and 2002respectively?(a) 4 : 3 (b) 3 : 2(c) 2 : 3 (d) 7 : 12

3. What was the approximate percentage increasein the number of students of Engineering fromthe year 2001 to 2002?(a) 17 (b) 15(c) 25 (d) 20

4. In the year 2001, the number of students studyingArts and Commerce together is what percent ofthe number of students studying these subjects

together in 2002?(a) 76 (b) 85(c) 82 (d) 79

5. In which of the following faculties the percentincrease in the number of students was minimumfrom 2001 to 2002?(l) Arts(b) Science(c) Commerce(d) Medicine

ANSWERS

1. (c) 2. (d) 3. (d) 4. (b) 5. (d)

EXPLANATIONS

Calculation for questions (1 5):Number of students in different faculties

Subject Year 2001 Year 2002Arts 4200 4400Commerce 7700 9600Science 8400 8800Agriculture 2450 2000Engineering 6300 7600Pharmacy 2100 3600Medicine 3850 4000

1. The number of students decreased from 2450 to2000 in Agriculture

2. Number of students studying Pharmacy in 2001= 2100Number of students studying Pharmacy in 2002= 3600\ Required ratio = 2100 : 3600 = 7 : 12

3. Difference = 7600 6300 = 1300\ Required percentage increase

= 13006300

100 = 20.63 = 20

4. Total number of students in Arts and Commercefaculties in 2001

= 4200 + 7700 = 11900Total number of students in Arts and Commercefaculties in 2002 = 4400 + 9600 = 1400

\ Required percentage = 1190014000 100

= 85%5. Only on the basis of table, we can say, the

percentage increase in Medicine was minimum.



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SAMPLE MATERIAL OF


General Mental Ability, Logical

Reasoning &

Analytical Ability



What is Blood Relations ?Blood relation logical problems mainly deal with the hierarchical structure of a family i.e., grand-parents,

parents and children etc. Different relationships between the family members of different generations will begiven. To solve the questions related to blood relations, the entire family tree has to be drawn by putting thevarious relationships.

In such problems, the aptitude of candidate is shown by the knowledge of the various blood relations. Thetypical relationships that are commonly used in blood relation problems are summarized as followsv Father s or Mother s son = Brotherv Father s or Mother s daughter = Sisterv Father s or Mother s brother = Unclev Father s or Mother s sister = Auntv Father s or Mother s father = Grandfatherv Father s or Mother s mother = Grandmotherv Brother s or Sister s Son = Nephewv Brother s or Sister s Daughter = Niecev Uncle s or Aunt s son or daughter = Cousinv Sister s Husband = Brother-in-lawv Brother s wife = Sister-in-lawv Son s wife = Daughter-in-lawv Daughter s Husband = Son-in-lawv Husband s or wife s sister = Sister-in-lawv Husband s or wife s Brother = Brother-in-law

To develop a blood relation tree, some standard symbols are used in this chapter to indicate the relationshipsamong the family members. It is not compulsory to follow them, You can design your own symbols to draw thefamily tree quickly and accurately.v P is male = Pv P is female = Pv Gender of P is not known = Pv P and Q are married to each other P Û Qv P and Q are sibling = P « Q

Blood Relations

CHAPTER 5





v P and Q are R s children = R

v P is the Uncle/Aunt of Q = R

P Q

v P is the only child of q = Q

PTo draw a family tree, first of all identify the males and the females and then try to put each member at the

appropriate position in the tree.Example 1: Pointing to Lalit in the photograph, Rajan said, His mother has only one grandchild whose

mother is my sister. How is Rajan related to Lalit ?(a) Brother (b) Brother-in-law (c) Father-in-law (d) Data inadequate

Solution: (b)Sister

RajanBrother-in-law wife

Grandchild

MotherLalit

Mother

Example 2: Deepak said to Nitin, The boy playing with the football is the younger of the two brothers of thedaughter of my father s wife. How is the boy playing football related to Deepak?

(a) Cousin (b) Brother (c) Son (d) Brother-in-lawSolution: (b)

Father = Wife

Deepak

Daughter

Nitin

Example 3: B is the brother of A, S is the sister of B, E is the brother of D, D is the daughter of A, F is thefather of S. Then, the uncle of E is

(a) A (b) B (c) F (d) DSolution: (b)

Father

Sister Brother

Uncle Daughter

S B

E D

A

Brother

E and D are children of A and B is the brother of A.So, B is the uncle of E.





Example 4: Pointing to a man. On the stage Rita said He is the brother of daughter of the wife of myhusband . How is the man of stage related to Rita?

(a) Son (b) Husband(c) Cousin (d) Nephew

Solution: (a)

HusbandWife

Rita

Brother Daughter

So, that person is the son of Rita.Example 5: If P * Q indicates P is the father of Q ; P Q indicates `P is the sister of Q ; P o Q indicates

P is the brother of Q ; P f Q indicates P is the mother of Q ; which of the following would represent P is brother-in-law of Q ?

(a) PoRfQ (b) P *RfQ(c) P RfQ (d) None of these

Solution. (d) In order to represent the relationship of, brother-in-law , we need the symbol for eitherhusband or wife , which is not given in the question. Hence, the required relationship cannot be represented by

any of the combinations given. So, the answer is (d).Example 6: Introducing a boy, a girl said, He is the only son of my mother s mother . How is the girl related

to that boy ?(a) Aunt (b) Niece(c) Sister (d) Mother

Solution: (b)Mother

GirlNiece

Boy

Mother

Directions (Q. Nos. 7 to 8) Read the following inforamation and answer the questions given below. P +Q mean P is the daughter of Q, P Q means P is the son of Q and P Q means P is the wife of Q.

Example 7: If A B D, which of the following is true ?(a) D is wife of B (b) A is daughter of B(c) B is father of A (d) D is father of A

Solution: (d)

B D

A

Son

Example 8: If C D P O, which of the following is not true?(a) P is mother of D (b) D is daughter of P(c) C is wife of D (d) 0 is husband of P





Solution: (b)

D

Son

C

P O

Example 9: R is the brother of G. Q is the sister of R. 0 is the brother of N. N is the daughter of G. L is thefather of Q, who is the uncle of O ?

(a) R (b) L(c) G (d) Q

Solution. (a) O is the brother of N who is the daughter of G. So, 0 is the son of G. R is the brother of G. So,R is the uncle of O. Hence, the answer is (a) R.

L

R G Q(Sister or R)(Brother)

N (Sister)(Brother) O

Example 10: If R * S means R is the wife of S, RT S means R is the father of S, R # S means R is the daughterof S and R -S means R is the brother of S, if P 0 # H # D ® Q, then how is D related to P ?

(a) Father (b) Brother(c) Mother-in-law (d) Father-in-law

Solution. (d) P 0 # H # D ® Q means, P is the father of 0, 0 is the daughter of H, that means H is themother of 0. (So P is the husband of H) and H is the daughter of D and D is the brother of Q, this means D is thefather of H. So, D is the father-in-law of P .

Example 11: If Y says that his mother is the only daughter of X s mother, How is X related to Y?(a) Uncle (b) Brother(c) Cousin (d) Maternal uncle

Solution. (d) Assume Y s mother be S, and X s mother be T, As S is the only daughter of T. So, X is the sonof T. The family tree can be draw as following.

T

S X

Y

Brother

Mother

So, X is maternal uncle of Y.Example 12: Pointing to Sagar in a photograph, Manjula said, His brother s father is the only son of my

grandfather. How is Manjula related to Sagar ?(a) Aunt (b) Sister(c) Mother (d) None of these

Solution. (b) Only son of Manjula s grandfather. Manjula s father and Sagar s brother s father-Sagar sfather. So, Manjula is Sagar s sister.





Grandfather

Father

Majula Saga Brother of Sagar

Hence, the answer is (b) Sister.Example 13: Sia introduced Raghav as the son of the only daughter of the father of her uncle. How is

Raghav related to Sia ?(a) Brother (b) Cousin(c) Nephew (d) Can t be determined

Solution. (d) Only daughter of uncle s father-uncle s sister. But it is not clear that uncle s sister is Sia smother.

Father

(Son) Uccle Only Daughter

Sia Son (Raghav)

Hence, the answer is (d) cannot be determined.Example 14: If P @ Q means P is the brother of Q, P D Q means P is the mother of Q and P f Q means P is

the sister of Q, then which of the following would mean A is the uncle of B.(a) ADP@B (b) ADB@P(c) A@PDB (d) AfPDB

Solution. (c) A is the uncle of B means A is the brother of the mother of B. According to the given expressions.It must be A @PAB, so the answer is (c).

Example 15: Introducing a woman, Nisha said, She is the daughter-in-law of the grandmother of myfather s only son. How is the woman related to Nisha ?

(a) Grandmother (b) Sister-in-law(c) Sister (d) Mother

Solution. (d) My father s only son-my brother, grandmother of my brother-my grandmother and daughter-in-law of my grandmother-my mother.

Grand mother

Father

Nisha SonWoman

(Daughter-in-law)

Hence, Nisha is the daughter of the woman. So, the answer is (d) Mother.





1. Pointing to a woman, Naman said, "She is thedaughter of the only child of my grandmother."How is the woman related to Naman?(a) Sister (b) Niece(c) Cousin (d) Data inadequate

2. Pointing to a photograph, a person tells his friend,"She is the grand daughter of the elder brother ofmy father." How is the girl in the photographrelated to this man?(a) Niece (b) Sister(c) Aunt (d) Sister-in-law

3. A man said to a lady, "Your mother's husband'ssister is my aunt." How is the lady related to theman?(a) Daughter (b) Grand daughter(c) Mother (d) Sister

4. If Neena says, "Anita's father Raman is the onlyson of my father-in-law Mahipal", then how isBindu, who is the sister of Anita, related toMahipal?(a) Niece (b) Daughter(c) Wife (d) None of these

5. Pointing to the woman in the picture, Rajiv said,"Her mother has only one grandchild whosemother is my wife." How is the woman in thepicture related to Rajiv?(a) Cousin (b) Wife(c) Sister (d) Data inadequate

ANSWERS

1. (a) 2. (a) 3. (d) 4. (d) 5. (b)

EXPLANATIONS

1. Only child of Naman's grandmother Naman'sfather/mother.Daughter of Naman's father/mother Naman'ssister.

2. Brother of father Uncle; Uncle's granddaughter Daughter of Uncle's son Daughterof cousin Niece.

3. Lady's mother's husband Lady's father; Lady'sfather's sister Lady's aunt.So, Lady's aunt is man's aunt and thererfore ladyis man's sister.

4. Only son of Neena's father-in-law Mahipal Neena's husband.So, Raman is Neena's husband and Anita andBindu are his daughters.Thus, Bindu is the grand daughter of Mahipal.

5. Rajiv's wife's child Rajiv's child.The woman's mother is the grandmother of Rajiv'schild. So, the woman is Rajiv's wife.

BLOOD RELATIONS





When we see clouds in the sky. We take preassumption that it may be rain. Each action has an assumptionone in positive and another in negative. Let us suppose a baby born it may be a boy or a girl. So, here we take twoassumptions.

The candidate will be required to assess the given statement and decide which of the given assumptions isimplicit in the Statement. To understand the pattern of these questions, it is very essential to know what theterms Statement and Assumptions do stand for.

Hence, An assumption is something that can be supposed or assumed on the basis of a given statement.

Types of Questions Based on AssumptionType 1 Two-Assumptions Based

In this type of questions a statement: is given, followed by two assumptions. The candidate is required toassess the given statement: and then decide which of the given assumptions to implicit in the Statement: .Directions (Examples 1 to 3) In each of the illustrations below is given a Statement: followed byAssumptions numbered I and II. Consider the Statement: and decide which of the given Assumptionsis implicit? Give answer as

(a) if only assumption I is implicit(b) if only assumption II is implicit(c) if neither I nor II is implicit(d) if both I and II are implicit1. Statement: The Union Government has decided to withdraw existing tax relief on various small savings

schemes in a phased manner to augment its tax collection.Assumptions:

I. People may still continue to keep money in small savings schemes and also pay taxes.II. The total tax collection may increase substantially.

Solution. (d) Any measure is taken assuming that it would be accepted by the people. Therefore, both theassumptions are implicit in the statement .

2. Statement: The Government has decided to levy 2 per cent on the tax amount payable for funding droughtrelief programmes.

Statement and Assumptions

CHAPTER 3





Assumptions:I. The Government does not have sufficient money to fund drought relief programmes.

II. The amount collected by way of surcharge may be adequate to fund these drought relief programmes.Solution. (d) If there were sufficient money to fund drought relief programmes, why this measure shouldbe taken. Therefore, both the assumptions are implicit in the statement.

3. Statement: The Government has decided to allow the shopping complexes to remain open till mid night toreduce crowding of shoppers in these complexes during the weekends.Assumptions:

I. People may still prefer to shop during the weekends.II. Many people may now do their shopping illusively during the late evening hour.

Solution. (b) Only assumption II is implicit because the people may shopping illusively during the lateevening hours thinking, so the Government has decided to allow the shopping complexes to remain open tillmid night.

Type 2 Three-Assumptions BasedThis type also consists of similar type of questions as in Type I, with the difference that here three assumptions

are given and the candidate is required to choose that group which is implicit in context of the given statement.Directions: In each questions below is given a statement followed by three assumptions numbered I, IIand III. An assumption is something supposed or token for granted. You hove to consider the statementand the following assumptions and decide which of the assumptions is implicit in the statement.

4. Statement: If you desire to enjoy the best holidays to Europe join our exclusive EURO package , Anadvertisement of a travel agency in an Indian newspaper.Assumptions:

I. Many Indians travel of European countries to spend their holidays.II. These are other travel agencies in India which organize holiday tour to Europe.

III. Many people may still travel to Europe through other travel agencies.(a) All are implicit (b) Only I and II are implicit(c) Only I is implicit (d) Only I and III are implicitSolution. (a) All are implicit because on the basis of all the three assumptions this advertise is given.

5. Statement: Graduate with first class are eligible to apply for the admission to MBA courses in our institute .An advertisement by a management institute.Assumptions:

I. Only those who are first class graduates can be up with the studies for MBA courses.II. There are plenty of first class graduates who are likely to apply for admission to MBA.

III. Reputation of the institute may get affected, if students having less than first class are admitted.(a) Only I is implicit(b) Only II is implicit(c) Only III is implicit(d) Only I and II are implicitSolution. (b) The advertisement was issued assuming that sufficient number of first class graduates arelikely to apply for admission to MBA.





Directions: In each questions below is given aStatement: followed by two Assumptionsnumbered I and II. An assumption is somethingsupposed or taken for granted. You have toconsider the Statements and the followingAssumptions and decide which of theAssumptions is implicit in the Statements?

Give answer(a) If only assumption I is implicit(b) If only assumption II is implicit(c) If neither I nor II is implicit(d) If both I and II are implicit1. Statement: Invest in our regular scheme and

earn an interest of at least 10% . Advertisementby a financial institution.Assumptions:

I. 10% interest may attract a good number ofinvestors.

II. No other scheme offers interest as high as10%.

2. Statement: For easier and fastercommunication, use our broadcast connections .An advertisement.Assumptions:

I. Many people are looking up for bestcommunication facilities.

II. Broad band connections are preferred modeof communication.

3. Statement: You must refer to learn to dictionary,if you want to become a good writer -A advises B.Assumptions:

I. Only writers refer to the dictionary.

II. All writers, good or bad, refer to thedictionary.

4. Statement: If it does not rain throughout thismonth, most farmers would be in trouble this year.Assumptions:

I. Timely rain is essential for farming.II. Most of the farmers are generally dependent

on rains.5. Statement: A advises B- If you want to study

English, joint Institute Y.Assumptions:

I. B listens to A s advice.II. Institute Y provides good coaching for

English.

ANSWERS

1. (a) 2. (a) 3. (c) 4. (d) 5. (d)

EXEPLANATIONS

1. How can the advertisement be meaningful withoutI? Hence, I is implicit. II may or may not be anassumption. Hence, II is not implicit.

2. People are looking for best communication so thisadvertisement is introduced.

3. None of the Assumptions is implicit as nothing canbe said definitely.

4. (d) As the given Statement tells of the essentialityand requirement or rain for farmers, hence boththe Assumptions are implicit in the Statement .

5. Since, A advises B to join institute Y to studyEnglish, hence it is assumed that institute Yprovides good coaching for English. Secondly, itis also assumed that B listens to A s advice.

EXERCISE





1. If the positions of the first and the sixth digits ofthe number 2796543018 are interchanged,similarly the positions of the second and theseventh digits are interchanged and so on, whichof the following will be the third to the left ofseventh digit from the left end?(a) 0 (b) 1(c) 7 (d) 8

2. What will be the difference between the sum ofthe odd digits and the sum of the even digits inthe number 857423?(a) 0 (b) 1(c) 2 (d) None of these

3. If each of the odd digits in the number 54638 isdecreased by 1 and each of the even digits isincreased by 1, then which of the following willbe the sum of the digits of the new number?(a) 25 (b) 26(c) 28 (d) 29

4. How many times will you write even numerals ifyou write all the numbers from 291 to 300?(a) 11 (b) 13(c) 15 (d) 17

5. A number is greater than 3 but less than 8. Also,it is greater than 6 but less than 10. The numberis?

(a) 5 (b) 6(c) 7 (d) 8

ANSWERS

1. (b) 2. (b) 3. (d) 4. (b) 5. (c)

EXPLANATIONS

1. The new number formed after rearrangement is4 3 0 1 8 2 7 9 6 5.

2. Required difference = (5 + 7 + 3) (8 + 4 + 2) = 1514 = 1.

3. The new number formed is 45729.\ Required sum = (4 + 5 + 7 + 2 + 9) = 27.

4. The numbers are 291, 292, 293, 294, 295, 296,297, 298, 299 and 300.

5. According to first condition, the number is greaterthan 3 but less than 8. Such numbers are 4, 5, 6, 7.According to the second condition, the number isgreater than 6 but less than 10. Such numbersare 7, 8, 9.Clearly, the required number is the numbersatisfying both the above conditions, i.e.,7.

NUMBER, RANKING AND TIME SEQUENCE TEST





Here, we deal with the questions having information regarding arrangement. We are giving some objectsand then we have to arrange them according to information provided. Objects are arranged either in row or in acircle on the basis of such conditions. In some questions, we will also deal with other arrangements like square/pentagon/ hexagonal.

Different Types of Sitting ArrangementThere are two types of questions which are asked in various competitions

Type 1 Arrangement around a Closed PathIn such questions, we are giving some clues regarding arrangement. We have apply these clues on a circle

and using these information, we have to find the solutions of questions associated with them. In this arrangement,we also deal square/pentagon/ hexagon, questions.

Before solving type 1 questions, following facts are necessary to know.

For Circular ArrangementIn this arrangement some persons are sitting around a circle and they facing the centre.

LeftRight

1. Left movement also called clockwise rotation.2. Right movement also called anticlockwise rotation.

For Rectangular Arrangement

Right Left A B

C

DA « B (Fornt with each other) C « D (Front with wach other)

Sitting Arrangements

CHAPTER 9





For Hexagonal ArrangementA

B

C

D

E

F

Right Left

A « D (Front with each other) B « E (Front with each other)C « F (Front with each other)

Directions (Examples 1 to 5) Read the following information carefully and answer the questions basedon it:

P, Q, R, S, T, U, V and W are eight friends. They are sitting around a round table and taking coffee.(i) P is sitting between U and V (ii) Q is sitting between W and T(iii) R is sitting to the third left of V (iv) W is sitting to the third right of S

Example 1: What is the position of V with respect to S?(a) immediate left (b) immediate right(c) third to the left (d) fourth to the right

Example 2: How many persons are sitting between R and S?(a) 2 (b) 3(c) 4 (d) 5

Example 3: What is the position of T with respect to W?(a) immediate left (b) immediate right(c) third to the left (d) second to the left

Example 4: Which of the following is true?(a) U is sitting immediate right of R (b) U is sitting immediate left of P(c) There is only one friend between Wand T (d) All of the above

Example 5: Which of the following is false?(a) There are two friends between P and W (b) There is no friend between Wand Q(c) P is immediate right of V (d) S is to the second left of Q

Solutions. Given figure shows the correct sitting arrangement of all eight friends sitting around the circle.Q

T

S

V

P

U

R

W

1. (a) It is clear from the diagram, V is immediately left of S.2. (b) Clearly three members are sitting between R and S.3. (d) Clearly, T is sitting second to the left of W.4. (a) U is sitting immediately right of R (True)

(b) U is sitting immediately left of P (True) (c) There is only Q between W and T (True)





5. (a) There are two friends between P and W (True)(b) There is no friend between W and Q (True)(c) P is immediately right of V (False)(d) S is to the second left of Q (True)

Directions (Examples 6 to 7) Read the following information carefully and answer the questions basedon it.

Six persons M, N, 0, P, Q and R are playing cards sitting in a circle facing the centre. R is sitting between Mand N and Q is sitting between 0 and P. P is sitting immediate right of M.

Example 6: Who is sitting immediate left of 0?(a) R (b) M(c) Q (d) P

Example 7: Who are the neighbours of R?(a) M, N (b) P, Q(c) P, O (d) Q, O

Solution. Given figure shows the correct arrangement of these six persons.N

O

Q

P

M

R

6. (c) Clearly, Q is sitting immediately left of 0.7. (a) Clearly, M and N are the neighbours of R.

Type 2 Arrangement in a Line or OthersSometime, we deal with questions where arrangement is required to be done in a line orothers.Before solving type 2 questions, following facts are necessary to know.When A, B, C, D facing South direction and P, Q, R, S facing North direction in a line, then their position of

Right and Left will be

A B C D

P Q R S

Right

Left Right

Left

North

South

West East

When A, B in one line and P, Q in other line. then their diagonally opposite direction will be





A B

P QA is diagonally opposite to Q. B is diagonally opposite to P.

Directions (Example 8) Read the following information carefully and answer the question based on it.In a shop, the items were arranged in a shelf consisting of six rows. Biscuits are arranged above the tins of

chocolates but below the rows of packets of chips, cakes are at the bottom and the bottles of pepermints are belowthe chocolates. The topmost row had the display of jam bottles.

Example 8: The bottles of peppermints are below the chocolates. The topmost row hat the display of jambottles. Where exactly are the bottles of pepermints? Mention the place from the top?

(a) 2nd (b) 3rd

(c) 4th (d) 5th

Solution. (d) Jam s bottles are at the top. Now,

Chocolates

Biscuits

Chips Chocolates

Pepermints

Cakes

Finally

Jam Bottles

Chips

Biscuits

Chocolates

Pepermints

Cakes

5 from topth

Directions (Examples 9 to 12) Study the following information carefully and answer the questionsgiven below

Six friends A, B, C, D, E and F are sitting in a row facing towards North. C is sitting between A and E. E is notat the end. B is sitting immediate right of E. F is not at the right end. D is sitting second to the left.

Example 9: How many persons are there to the right of D?(a) One (b) Two(c) Three (d) Four

Example 10: Which of the following pairs is sitting to the left of D?(a) F (b) C(c) E (d) A

Example 11: Who is immediate left of C?(a) A (b) E(c) Either E or A (d) Cannot be determined





Directions (Q. Nos. 1 to 2) Read the informationgiven below and then answer the questions thatfollow

Eight friends A, B, C, D, E, F, G and H are sittingin a circle facing the centre. B is sitting between G andD. H is third to the left of B and second to the right of A.C is sitting between A and G and B and E are not sittingopposite to each other.

1. Who is third to the left of D?(a) F (b) E(c) A (d) None of these

2. Which of the following statements is not correct?(a) D and A are sitting opposite to each other(b) C is third to the right of D(c) E is sitting between F and D(d) A is sitting between C and F

Directions (Q. Nos. 3 to 5) Study the followinginformation to answer the given questions

(i) Eight friends A, B, C, D, E, F, G and H are seatedin a circle facing the centre.

(ii) D is between B and G and F is between A and H.(iii) E is second to the right of A.

3. Which of the following is A s position?(a) Left of F (b) Right of F(c) Between E and F (d) None of these

4. Which of the following information are notrequired to ascertain the position of C?(a) (i) (b) Either (ii) or (iii)(c) (iii) (d) All are required

5. Which of the following is C s position?(a) Between E and F (b) Between G and E

(c) Second to the left of B(d) None of these

ANSWERS

1. (a) 2. (c) 3. (b) 4. (d) 5. (d)

EXPLANATIONS

Explanation (Q. Nos. 1 to 2) Given figure showsthe correct position of persons sitting around thecircular table.

1. F is third to the left of D.2. E is sitting between H and D. Hence, alternative

is not correct.Explanation (Q. Nos. 3 to 5) Given figure showsthe correct position of persons sitting around thecircle.

B or G

E

C

A

F

H

B or G

D

3. A is sitting to the right of F.4. All information are necessary.5. It is clear from the diagram, C is sitting between

A and E.Explanation (Q. Nos. 6 to 10)Given figure shows the correctposition of persons sitting aroundthe circle.

Example 12: Who is at the right end?(a) A (b) B(c) E (d) Cannot be determined

Solution. The given figure, shows the correct arrangement of six friends.F D A C E B

Sitting Arrangement

9. (d) There are four persons to the right D-A, C, E, B.10. (a) Clearly, F is sitting to the left of D.11. (a) It is clear from the diagram that A is to the immediate left of C.12. (b) It is clear from the diagram that B is at the right end.

EXERCISE

B

E

F

C

G

D





First we should know some mathematical operations. They are add (+), subtraction ( ), multiply ( ) anddivision ( ), greater than (>), less than (<). This test is set up to test candidates skill in mathematical operations.The questions involving these operations are set using artificial symbols. You are required to substitute the realsigns and solve the questions accordingly, to get the answer.

Different Type of QuestionsThere are three types of questions based on mathematical operations which are asked in various competitive

examinations. They are,

Problem-Solving by SubstitutionIn such type of questions you have some substitutes for various mathematical symbols or numerals followed

by a question involving calculation of an expression or choosing the correct/incorrect equation.

Rule BODMASBracketsOfDivisionMultiplicationAdditionSubtractionWhile solving a mathematical operations proceed according to the BODMAS formula.Example 1: If + means minus means divided by means plus and means multiplied by then

which of the following will be the value of expression 7 3.5 2 4 + 5 ?(a) 4 (b) 5(c) 11 (d) None of these

Solution. (b) Using the proper notations in the given expression, we have= 7 3.5 2 4 + 5 = 7 + 3.5 + 2 4 5= 2 + 2 4 5 = 2 + 8 5 = 10 5 = 5

Arithmetical Reasoning

CHAPTER 11





Example 2: If means +, + means , means and means , then 6 4 5 + 2 1 =?(a) 10 (b) 11(c) 12 (d) 15

Solution. (d) Using the proper notations in the given expression, we have6 4 5 + 2 1 = 6 + 4 5 2 1

= 6 + 4 2.5 1= 6 + 10 1= 16 1 = 15

Example 3: If P denotes multiplied by T denotes subtracted from, M denotes added to and B denotesdivided by , then

12 P 6 M 15 T 16 B 4(a) 70 (b) 83(c) 75 (d) 110(e) None of these

Solution. (b) 12 P 6 M 15 T 16 B 4= 12 6 + 15 16 4 = 12 6 + 15 4= 72 + 15 4 = 87 4 = 83

Interchanging of Signs and NumbersThis type of question certain signs or numbers interchanging with each other. The candidate is required to

change the given signs or change the given numbers with each other and select which of the equation is correctof the given alternatives.

Example 4: If signs + and and numbers 4 and 8 interchanges with each other, which one of the followingfour equations would be correct?

(a) 4 8 + 12 = 0 (b) 8 4 12 = 8(c) 4 8 12 = 16 (d) 8 4 12 = 24

Solution. (a) On interchanging signs + and and numbers 4 and 8 in equation (a)8 + 4 12 = 0

Þ 12 12 = 0Þ 0 = 0Example 5: Which one of the four interchanges in signs and number would make the given equation correct?

6 4 + 2 = 16(a) + and , 2 and 4 (b) + and , 4 and 6(c) + and , 2 and 6 (d) None of the above

Solution. (b) On interchanging signs + and and 4 and 6,4 + 6 2 = 4 +12 = 16

Example 6: If 5 4= 15, 7 8 = 49 and 6 5 = 24, then 8 4= ?(a) 24 (b) 26(c) 28 (d) 30

Solution. (a) As, 5 4 = 5 (4 1) = 5 3 = 157 8 = 7 (8 1) = 7 7 = 49

and 6 5 = 6 (5 1) = 6 4 = 24Similarly, 8 4 = 8 (4 1) = 8 3= 24





Example 7: If 64 52 = 17, 48 56 = 23 and 74 35 = 19 then 84 37 = ?(a) 32 (b) 28(c) 22 (d) 20

Solution. (c) As,64 52 Þ (6 + 4) + (5 + 2) = 1748 56 Þ (4 + 8) + (5 + 6) = 23

and 74 35 Þ (7 + 4) + (3 + 5) = 19Similarly, 84 37 Þ (8 + 4) + (3 + 7) = 22

Deriving the Appropriate ConclusionsIn this type of questions certain relations between different sets of elements is given (in terms of less than ,

greater than , or equal to ), using either the real symbols or substituted symbols. The candidate is required tobriefly read the given statements and then choose which of the conclusions is/are definitely true.Directions (Examples 8 to 10) In the following questions, the symbols , @, , % and * are used with thefollowing means as illustrated below :

P Q means P is not smaller than QP % Q means P is neither smaller than nor equal to QP « Q means P is neither greater than nor equal to QP d Q means P is not greater than QP @ Q means P is neither greater than nor smaller than QNow in each of the following questions assuming the given statements to be true, find which of the three

conclusions I, II, III and IV given below them is/are definitely true and give your answer accordingly.Example 8: Statements D d T, T @ R, R M, M % K

Conclusions I. R @ D II. R % DIII. K « T IV. M d T

(a) Only either I or II is true (b) Only III and IV are true(c) Only either I or II and III are true (d) Only either I or II and III and IV are true

Example 9: Statements J @ F, F d N, N % H, H GConclusions I. G « N II. N J

III. F « J IV. J d G(a) Only I and II are true (b) Only I, II and III are true(c) Only I, III and IV are true (d) All I, II, III and IV are true

Example 10: Statements R « K, K % D, D @ V, V d MConclusions I. R « D II. V « R

III. D @ M IV. M % D(a) None is true (b) Only III is true(c) Only IV is true (d) Only either III or IV is true

Solutions (8 10)Finally Þ ³

% Þ >« Þ <d Þ £a Þ =





1. If stands for division , + for multiplication , for subtraction and for addition , then whichone of the following equations is correct?(a) 4 5 + 9 3 4 = 15(b) 4 5 9 + 3 4 = 11(c) 4 5 9 3 4 = 17(d) 4 5 + 9 3 + 4 =18

2. If stands for division , + for multiplication , for subtraction and for addition . Which

one of the following equation s is correct?(a) 6 + 20 12 7 1 = 38(b) 6 20 + 12 7 + 1 = 57(c) 6 + 20 12 7 1=62(d) 6 20 12 + 7 1 = 70

3. If + stands for division , stands formultiplication stands for subtraction and stands for addition .Which one of the following is correct?(a) 18 6 7 + 5 2 = 22(b) 18 6 + 7 5 2 = 16(c) 18 6 7 + 5 2 = 20(d) 18 + 6 7 5 2 = 18

4. If stands for addition , < for subtraction , +for division , > for multiplication for equal

8. (a) Here, D d T Þ D £ T; T @ R Þ T = R;R M Þ R ³ M; M % K Þ M > K

So, D £ T = R ³ M > KNow, R @ D Þ R = D (False); R % D Þ R > D (False)

K « T Þ K < T (True) M d T Þ M £ T (True)Hence, only either I or II and III and IV are true.

9. (a) Here, J @ F Þ J = F; F d N = F £ NN % H Þ N > H; H G = H ³ G

So, J = F £ N > H ³ GNow, G « N Þ G < N (True); N J Þ N ³ J (True)

F « J Þ F < J (False): J d G Þ J £ G (False)Hence, only I and II are true.

10. (d)Here, R « K Þ R < K; K % D Þ K > DD @ V Þ D = V; V d M = V £ M

So, R < K > D = V £ MNow, R « D Þ R < D (False); V « R Þ S V< R (False)

D @ M Þ D ?? M (False); M % D Þ M > D (False)But either III or IV is true.

EXERCISEto , for greater than and = for less than , thenstate which of the following is true?(a) 3 4 > 2 9 + 3 < 3(b) 5 3 < 7 8 + 4 1(c) 5 > 2 + 2 = 10 < 4 8(d) 3 2 < 4 16 > 2 + 4

5. If + stands for greater than , stands foraddition , + stands for division , stands forequal to , > stands for ,multiplication = standsfor less than and , stands for minus then whichof the following alternatives is correct?(a) 5 > 2 < 1 3 4 1(b) 5 < 2 1 + 3 > 4 1(c) 5 > 2 1 3 > 4 < 1(d) 5 + 2 1 = 3 + 4 > 1

ANSWERS

1. (a) 2. (d) 3. (d) 4. (c) 5. (c)

EXPLANATIONS

1. Using the proper notations in (a), we get thestatement as

4 + 5 9 3 4 = 4 + 5 3 4





= 4 + 15 4 = 152. Using the proper notations in (d), we get the

statement as6 20 + 12 7 1 = 6 20 + 84

= 90 20 = 703. Using the proper notation in (d), we get the

statement as18 6 7 5 + 2 = 3 7 5 + 2

= 21 5 + 2= 18

4. Using the proper notations in (c), we get thestatement as

5 2 2 < 10 4 + 8Þ 5 1 < 18 4Þ 5 < 14Which is true.





The word Syllogism is also referred to Logic . Syllogism is an important section of logical reasoning andhence, a working knowledge of its rules is required on the part of the candidate. Hence, it can be expressed as theScience of thought as expressed in language . The questions based on syllogism can be solved by using Venndiagrams and some rules devised with the help of analytical ability.

With this unique characteristic, this test becomes an instrument of teaching the candidates to follow the rulesand work as per the instructions without an error. Here, only the basic concept and rules, which have a bearingon reasoning faculty could alone help. There are some terminology which are used in syllogism.

PropositionIt is also referred to as Premises . It is a sentence which asserts that either a part of, or the whole of, one sets

of objects-the set identified by the subject term in the sentence expressing that sentence either is included in, or isexcluded from, another set-the set identified by the predicate term in that sentence.

Types of PropositionCategorical Proposition There is relationship between the subject and the predicate without any condition.Example : I. All beams are logs.

II. No rod is stick.Hypothetical Proposition: There is relationship between subject and predicate which is asserted

conditionally.Example : I. If it rains he will not come.

II. If he comes, I will accompany him.Disjunctive Proposition In a disjunctive proposition the assertion is of alteration.Example : I. Either he is brave or he is strong.

II. Either he is happy or he cannot take revenge.

Parts of PropositionIt consists of four parts.

1. Quantifier: In quantifier the words, all , no and some are used as they express quantity. All and no areuniversal quantifiers because they refer to every object in a certain set. And quantifier some is a particularquantifier because it refers to at least one existing object in a certain set.

2. Subject: It is the word about which something is said.

Syllogism

CHAPTER 1





3. Predicate: It is the part of proposition which denotes which is affirmed or denied about the subject.4. Copula: It is the part of proposition which denotes the relation between the subject and predicate.

Example : All boys are brilliant

Quantifier Subject Copula PredicateHence, the standard form of proposition isQuantifier + Subject + Copula + PredicateFour-fold classification of categorical proposition: On the basis of quality and quantity of proposition

we can classify them in four categories. To draw valid inferences it is necessary to have a clearunderstanding of the A, E, I, O relationship as given in the table.

Symbol Proposition Quantity Quality

A All A are B Universal AffirmativeE No A is B Universal NegativeI Some A are B Particular Affirmative

O Some A are not B Particular Negative

Rules for Deriving the Conclusions from Two Given Premises1. Universal affirmative or A-type proposition.

Dogs

Goats

Take an example : All goats are dogs This is A type proposition: We can see it by graphical representation ofthe above proposition we observe that goats are distributed in dogs. Hence. we can conclude that in A typeproposition only subject is distributed.

2. Universal negative or E-type proposition.

Boy Girl

Take an example : No girl is boy In this type of proposition both subject and predicate are denial of eachother. This can also be seen in the diagram representing boy Girl and girl. They have nothing in common.Hence, both subject and predicate are distributed.

3. Particular affirmative or I-type proposition.

Mobile Telephone

Take an example : Some mobiles are telephones. In this type of proposition subject and predicate havesomething in common. This implies that in I-type neither subject nor Mobiles Telephones predicate isdistributed. We can see it graphically as given in figure.





4. Particular negative or O-type proposition.

Boys Students

Take an example : Some boys are not students. In O-type propositions some of the category represented byboys subject is not students, which means that a section of boys is denied with the entire category of students.It is, therefore, deduced that in O-type proposition only predicate is distributed. On account of differentlogical approach required to be applied for drawing each type of inference, a clear understanding of thisdifference becomes more important.

Rules for Mediate InferenceFirst introduced by Aristotle, a syllogism is a deductive argument in which conclusion has to be drawn from

two propositions referred to as premises.Now consider an example.Statement: I. Vinay is a boy. II. All boys are honest.Conclusion I. Vinay is honest.

First two sentences I and II are called propositions and the sentence I is called conclusion. This conclusion isdrawn from above given two propositions.Types of Questions Asked in the Examination

There are mainly two types of questions which may be asked under this1. When premises are in specified form Here premise is in specified form. Here mainly two propositions are

given. Propositions may be particular to universal; universal to particular; particular to particular; universalto universal.

2. When premises are in jumbled/mixed form Here at least three or more than three proposition are given.Here pair of two propositions out of them follow as same as in specified form.

Type 1 Premises in Specified FormsCase 1: The conclusion does not contain the middle term Middle term is the term common to both the premises

and is denoted by M. Hence, for such case, conclusion does not contain any common term belong to both premises.Example 1

Statement: I. All men are girls.II. Some girls are students.

Conclusions I. All girls are men.II. Some girls are not students.

Solution. Since, both the conclusions I and II contain the middle term girls so neither of them can follow.Venn diagram Representation: All possible cases can be drawn by using Venn diagram.

Girls

men

Students

or,

Girls Men Students





By using both representation (a) and (b) it is clear all girls cannot be men as well as (a) shows some girls arestudents, here no man is included but at the same time (b) shows some girls are students have some men are alsostudents as all men are girls. Hence, we cannot deduce conclusion II.

So, neither of them can follow.Example 2

Statement: I. All mangoes are chairs.II. Some chairs are tables.

Conclusions I. All mangoes are tables.II. Some tables are mangoes.

III. No mango is a table.Solution. Here, the term chair is common to both the statement and hence, is the middle term. Statement

(I) is A type proposition and in A-type proposition, only subject is distributed, hence, chair being the predicate inthe statement (I) is not distributed in the second statement. Thus, none of the conclusions following statementis a valid inference.

Venn diagram representation: All possible cases can be drawn as

Chairs

MangoesTables

or,Chairs

Mangoes

Tables

(i) All mangoes are table-this inference is definitely false neither (a) nor (b) shows this conclusion.(ii) Some tables are mangoes, this inference is uncertain or doubtful.(iii) No mango is a table, this inference is also uncertain or doubtful. Though it can be concluded from the above

discussion that no valid inference can be drawn between mango and table.Case 2: No term can be distributed in the conclusion unless it is distributed in the premises.

If case 1 is compiled with by a pair of statement, it is confirmed that valid mediate inferences can be drawnfrom such pair of statement. But every mediate inference drawn cannot be valid. Therefore, case 2 is applied tocheck as to the conclusions drawn from a pair of statement in which middle term is distributed, is valid.Example 3

Statement: I. Some boys are students.II. All students are teenagers.

Conclusions I. All teenagers are students.II. Some boys are teenagers.

Solution. Statement I is an I-type proposition which distributes neither the subject nor the predicate.Statement II is an A type proposition which distributes the subject students . Conclusion I is an A-type propositionwhich distributes the subject teenagers only.

Since. the term teenagers is distributed in conclusion I without being distributed in the premises. So, conclusionI cannot follow. In second conclusion, where it is asked that some boys are teenagers. But from statement I it isclear that some students are not students. These students may not be teenagers.

Venn diagram representation: All possible cases can be drawn as follows

Boys Students .





We have given that all students are teenagers so, its reverse cannot be possible. Hence, conclusion I is false.As we are also given that some boys are students and all students are teenagers. So, some boys which arestudents must be teenagers. Hence, conclusion II follows.

Case 3: If one premises is particular, conclusion is particular. Take an example which explains this caseExample 4

Statement: I. Some boys are thieves.II. All thieves are dacoits.

Conclusions I. Some boys are dacoits.II. All dacoits are boys.

Solution. Since, one premise is particular, the conclusion must be particular. So, conclusion II cannot follow.Venn diagram representation: All possible cases can be drawn as follows

Boys Thieves

Dacoits

Here conclusion I follows but the conclusion II cannot follow.Case 4 If the middle term is distributed twice, the conclusion cannot be universal Take an example which

explains such case.Example 5

Statement: I. All Lotus are flowers.II. No Lily is a Lotus.

Conclusions I. No Lily is flowers.II. Some Lilies are flowers.

Solution. Here, the first premise is an A proposition and so, the middle term Lotus forming the subject isdistributed.The second premise is an E proposition and so, the middle term Lotus forming the predicate isdistributed. Since, the middle term is distributed twice, so the conclusion cannot be universal.

Venn-diagram representation: All possible cases can be drawn as follows

Flowers

Lotus Lily

Lotus

Lotus

Flowers Flowers

Lily

It is clear from the given Venn-diagrams either conclusion I or II must be followed.Case 5 If both the premises are affirmative, the conclusions must be affirmative. Take an example which

follows such case:Example 6

Statement: I. All gardens are schools.II. All schools are colleges.

Conclusions I. All gardens are colleges.II. Some gardens are not colleges.





Solution. Since, both the premises are affirmative, the conclusion must be affirmative, so conclusion IIcannot follow.

Venn diagram representation: All possible cases can be drawn as follows.

Gardens

Schools

Colleges

Now, taking conclusion I, it is clear that all gardens are also colleges. But taking conclusion II, we cannot thatderive second conclusion is true. Hence, only the first conclusion must be true.

Case 6 No conclusion follows. There are three types of such cases.(a) If both the premises are particular

Example 7Statement: I. Some cups are spoons.

II. Some spoons are sauccers.Conclusions I. All cups are sauccers.

II. Some sauccers are cups.Solution.Since both the premises are particular, so no definite conclusion follows.Venn diagram representation

CupsSpoons

Sauccers

Cups Sacuccers Spoons

It is clear from both given Venn-diagrams that no conclusion is followed.(b) If both the premises are negative

Example 8Statement: I. No flower is mango.

II. No mango is cherry.Conclusions I. No flower is cherry.

II. Some cherries are mangoes.Solution. Since, both the premises are negative hence, neither conclusion follows.Venn diagram representation: It is clear from both Venn-diagrams that neither conclusion follows.(c) I f the major premise is particular and the minor premise is negativeMajor premise is the predicate of the conclusion and minor premise is the subject of the conclusion.

Example 9Statement: I. Some pubs are cows.

II. No kitten are pubs.





Conclusions I. No pubs are kitten.II. Some cows are kitten.

Solution. Here, the first premise containing the middle term Kitten as the subject is the major premise andthe second premise containing the middle term Kitten as the predicate is the minor premise. Since, the majorpremise is particular and the minor premise is negative. So, no conclusion follows.

Venn diagram representation: All possible cases are given

PutsCows

Kitten

Pubs Cows Kitten Pubs

Cows

Kitten

(a) (b) (c)

It is clear from the Venn-diagram representation that conclusion I follows.

Complementary pair of conclusionsIn drawing mediate inferences from given statement, students are required to be more attentive in selecting

complementary pair of conclusion where neither of the conclusions is definitely true but a combination of bothmakes a complementary pair. As we have already discussed in case number 1 that in the statement where middleterm is not distributed, no valid mediate inference can be drawn but there still exists a possibility that acomplementary pair of conclusions follows from the statement.

Example 10Statements I. Some cameras are radios.

II. Some statues are cameras.Conclusions I. Some ratios are statues.

II. No radio is statue.Solution. Either some radios are statues or No radio is statue follows, as I and E-type proposition form a

complementary pair.Venn diagram representation We can draw all possible cases as given below

Radios Cameras

Statues

Radios Cameras Statues

Hence, using both diagrammatical representation we can conclude either some radios are statues or no radiois statue. Hence, at least one of the conclusions must be true.





Special CasesFacts

Combinations (Conclusion) ConclusionA + E Either I or II followsE + I Either I or II followsI + O Either I or II followsE + O Either I or II follows

Example 11Statements I. All vegetables are green.

II. Some greens are fruits.Conclusions I. Some fruits are vegetables.

II. No fruit is vegetable.Solution. Here, conclusion I is particular affirmative and conclusion II is universal negative proposition.

Hence, either conclusion I or conclusion II follows.Alternatives

Green

Vegetables

Fruitor

Vegetables

Fruit

Green

Conclusion: If we follow Venn-diagram (a) then we can say no fruit is vegetable. Conclusion II but if wethat follow Venn diagram (b) then we can say some fruits are vegetables (conclusion I).

Here, either Venn diagram (a) or Venn-diagram (b) is possible. Hence, conclusion I or conclusion II must befollowed.

Minimal PossibilitiesWe can represent statements by keeping in mind our conclusions It we follow that our two conclusions

belong to special case, then either one of them is true.We can represent minimum possibilities as given directly in the statement, we don t need to think about

parameters.

Example 12 Statements I. Some fruits are vegetables.

II. Some vegetables are junk food.III. Some junk foods are snacks.

Conclusions I. Some junk foods are vegetables.II. Some junk foods are fruits.

Solution. Minimal possibilities

Fruit Vegetables Junk foods Snacks





It is clear from the above diagrams that only conclusion I follows.Type 2 Mixed/jumbled ProblemsIn such type of problem there is a constitution of mixed problems of universal and particular premises.

Directions (Q. Nos. 13 to 16) In each of the questions given below there are three statements followed bythree conclusions numbered I, II and III, you have to take the given statements to be true even if theyseem to be at variance from commonly known facts. Read all the conclusions and then decide which ofthe given conclusions logically follows from the given statements disregarding commonly known, facts.

Example 13Statements All halls are tyres.

Some tyres are wheels.All wheels are cars.

Conclusions I. Some cars are wheels.II. Some cars are tyres.

III. Some wheels are halls.(a) None follows (b) Only I follows(c) Only I and II follow (d) Only III follows

Solution. (c)Conclusions

Tyres

Halls

Cars

Wheels

I. Some cars are wheels. It can be seen from Venn-diagram.II. Also, some cars are tyres (as shown in Venn-diagram).

III. It is not clear from the Venn-diagram. Hence, only I and II follow.

Example 14Statements Some pictures are frames.

Some frames are idols.All idols are curtains.

Conclusions I. Some curtains are pictures.II. Some curtains are frames.

III. Some idols are frames.(a) Only I and II follow (b) Only II and III follow(c) Only I and III follow (d) All follow

Solution. (b)





Conclusions

Pictures

frames

idolsCurtains

I. Does not follow.II. Follows (clear from the Venn-diagram)

III. Follows (clear from the Venn-diagram)Hence, only II and III follow.

Example 15Statements Some ice are rings.

No ring is paint.Some rings are gold.

Conclusions I. No gold is paint.II. No ice is gold.

III. Some rings are paints.IV. All golds are rings.

(a) Only I and III follow (b) Only I and II follow(c) Only III and IV follow (d) None follows

Solution. (d) Hence, none of the conclusions follows.

Ice Rings

Gold

Paint

Example 16Statements No candle is bell.

Some shoes are bells.All tables are shoes.

Conclusions I. Some tables are bells.II. No table is bell.

III. Some shoes are candles.IV. No shoes are candles.

(a) Only I and IV follow (b) Only I and II follow(c) Only III and IV follow (d) None of these

Solution. (d)

Candles BellsTable

Shoes

Solution. (d) Here conclusion I is particular affirmative and conclusion II is its universal negative. Hence,either conclusion I or II follows. Also conclusion III is particular affirmative and conclusion IV is its universalnegative. Hence, either III or conclusion IV follows. Finally, either conclusion I or II follows and either conclusionIII or conclusion IV follows.





Directions (Q. Nos. 1 to 5) In each question givenbelow are two Statements followed by twoconclusions numbered I and II. You have to takethe two given Statements to be true even if theyseem to be at variance from commonly known factsand decide which of the given conclusions logicallyfollows from the the given two Statements,disregarding commonly known facts.

Give answer as(a) If only conclusion I follows(b) If only conclusion II follows(c) If neither I nor II follows(d) If both I and II follow1. Statement: I. All jungles are tigers.

II. Some tigers are horses.Conclusions I. Some tigers are jungles.

II. All horses are jungles.2. Statement: I. All birds are tall.

II. Some tall are hens.Conclusions I. Some birds are hens.

II. Some hens are tall.3. Statement: I. All artists are smokers.

II. Some smokers are drinkers.Conclusions I. All smokers are artists.

II. Some drinkers are notsmokers.

4. Statement: I. Some hens are cows.II. All cows are horses.

Conclusions I. Some horses are hens.II. Some hens are horses.

5. Statement: I. All buses are cars.II. Some cars are roads.

Conclusions I. Some cars are buses.II. Some buses are roads.

ANSWERS

1. (a) 2. (b) 3. (b) 4. (d) 5. (a)

EXPLANATIONS

1. Tigers

Jungles Horses

Hence, only I follows.2.

Tall

Birds Hens

Hence, from both Venn-diagram conclusion IIfollows.

3.Smokers

Aritist Drinkers

Hence, conclusion I follows.4.

Hens Cows

Horses

Hence, both conclusions are true.5.

Cars

Buses

Roads

Roads

Hence, only I follows.

EXERCISE





In such types of questions a situation would be presented and some courses of action are suggested in thecontext of those situations. These types of questions are designed to test candidate s decision making ability. Inother words a course of action is a step or administrative decision to be taken for improvement, follow up orfurther action with regard to the problem on the basis of data provided .

To solve these questions, the candidates are advised to keep in mind the following important points:1. Correct course of action should either lessen the problem or improve the situation created by the problem.2. Simple problem must have simple course of action and not a complex one which may create more problems

than to solve or reduce it.3. Course of action should be feasible and should relate with the practical aspect of life.

Type of Questions that could be Asked in CSATType 1 Two Courses of Action Based

In these type of questions a Statement is given followed by two courses of action numbered I and II.The candidate is required to grasp the Statement, analyse the problem or policy it mentions and then decide asto which of the courses of action logically follow(s).Directions (Examples 1 to 2) In each of the questions given below is a Statement followed by two coursesof action numbered I and II. A course of action is a step or administrative decision to be taken forimprovement, follow up or further action in regard to the problem, policy etc. On the basis of informationsgiven in the Statement you have to assume everything in the Statement to be true, then decide which ofthe two given courses of action logically follow.

Give your answer as(a) If only I follows (b) If only II follows(c) If neither I nor II follows (d) If both I and II follow

Example 1: Statement: A large number of engineering graduates in our country are not in a position tohave gainful employment at present and the number of such engineers are likely to grow in future.Courses of Action:

I. The government should launch attractive employment generating schemes and encourage these graduatesto opt for such schemes to effectively use their expertise and knowledge.

II. This happened due to poliferation of engineering colleges in the country and there by lowering the qualityof the engineering graduates. Those colleges, which are not equipped to impart quality education should beclosed down immediately.

Statement andCourses of Action

CHAPTER 4





Solution. (a) Only course of action I seems to be suitable for pursuing. The first line of course of action II isnot a course of action and second line does not properly address the problem.

Example 2: Statement: There have been many instances of dacoity and looting in many passenger trainsthis years.Courses of Action:

I. The railway authority should immediately deploy one policemen in each compartment in all thepassenger trains.

II. The passengers travelling by train should be given training on how to tackle the dacoits and looters.Solution. (c) Considering the insufficient number of security personnel the course of action I seems to be

untenable. Similarly, course of action II is not practically feasible. Thus, neither course of action I nor II follows.

Type 2 Three Courses of Action BasedIn such questions a Statement followed by three courses of action numbered I, II and III. A course of action

is a step or administrative decision to be taken for improvement follow - up or further action in regard to theproblem, policy etc. On the basis of the information given in the Statement, you have to assume everything inthe Statement to be true, then decide which of the suggested courses of action logically follow(s) for pursuing.

Example 3: Statement Many peoples in the locality have fallen sick and admitted in the local hospital afterconsuming sweets served during a community meal.Courses of Action:

I. The police should immediately arrest all the peoples responsible for making the sweets.II. The people admitted in the local hospital should immediately be shifted to bigger hospitals.

III. The local food and drug authority should investigate to find out the cause of the sickness and take necessaryaction.(a) Only I follows (b) Only I and II follow(c) Only III follows (d) Only II and III follow

Solutions. (c) Only III follows. After finding the cause of the sickness necessary action should be taken.Hence this authority should investigate to find out the cause of the sickness and take necessary action. As it is notpossible to shift local hospital of bigger hospital.

Example 4: Statement: Many management institutes in the city have enrolled a large number of studentsfor management courses which are not recognized either by the local university or by the department of technicaleducation.Courses of Action:

I. All these management institutes should immediately derecognized by the university and the department oftechnical education.

II. All these management institutes should be asked to refund fees to all such students and enroll them only forrecognized courses.

III. All such students should be advised to switch over to the recognized courses in other institutes.(a) Only I follows (b) Only II follows(c) Only III follows (d) Only II and III follow

Solution. (a) Such institutes should immediately be derecognized by the university. Hence I course of actionfollows. It is not possible to refund fees to all such students and enroll them only for recognized courses. Allstudents could not be advised to switch over to the recognized courses in other institutes.

Example 5: Statement: Higher disposal costs encourage those who produce waste to look for cheaper waysto get rid of it.Courses of Action:

I. The disposal costs should be made higher.





II. The disposal costs should be brought down.III. A committee should be set up study the details in this respect.

(a) Only I follows (b) Only II follows(c) Either I or II follows (d) Only II and III follow

Solution.(e) Action II and III are feasible and effective to combat the problem.

EXERCISETYPE 1 : TWO POSSIBLE COURSES OF ACTION

Directions (Q. Nos. 1 to 5) In each of the questionsbelow is given a Statement followed by two coursesof action. Course of action is a step foradministrative decision to be taken forimprovement, follow up or further action in regardto the problem, policy etc. On the basis of theinformation given in Statement, you have toassume everything in the Statement to be true,then decide which of the given suggested coursesof action is/are logically worth pursuing.

Give your answer as(a) If only I follows(b) If only lI follows(c) If neither I nor II follows(d) If both I and II follow1. Statement: A recent study show that children

below five die in the cities of the developingcountries mainly from diarrhoea and parasiticintestinal worms. Courses of Action

I. Government of the developing countriesshould take adequate measure to improvethe hygienic condition in the cities.

II. Children below five year in the of thedeveloping countries need to kept underconstant medication.

2. Statement: Air export volumes have increasesubstantially over the post decade causing be clogsand difficulties for air cargo agents because ofincreased demand for space and services. Coursesof Action

I. Airlines and air cargo agents should jointlywork out a solution a combat the problem.

II. The reasons for the increase in the volumeof air export should we found out.

3. Statement: There has been significant drop inthe water level of all the lakes supplying water tothe city.Courses of Action:

I. The water supply authority should amposea partial cut in supply to tackle the situation.

II. The government should appeal to allresidents through mass media for minimaluse of water.

4. Statement: On an average, about twenty peoplesare run over by trains and dies everyday whilecrossing the railway track through the levelcrossing.Courses and Action

I. The railway authorities should be instructedto close all the level crossings.

II. Those who are found crossing the trackswhen gates are closed should we finedheavily.

5. Statement: The state Government has decidedto declare Kala Azar as a notifiable disease underthe Epidemics Act, 1978. Family members orneighbours of the patient are liable to be punishedin case they do not inform the state authorities.Courses of Action:

I. Efforts should be made to effectivelyimplement the Act.

II. The cases of punishment should wepropagated through mass media so thatmore people become aware of the sternaction.

ANSWERS

1. (d) 2. (d) 3. (d) 4. (b) 5. (d)

EXPLANATIONS





1. If the Government concentrates to improve thehygienic condition in the cities, it may definitelyreduce the impact of problem and this course ofaction appears to be feasible also. Hence thiscourse of action appears to be correct Medicationis another practical feasible step which would helpminimize the cases of death due to diarrhoea andintestinal worms. Therefore, course of action II alsofollows.

2. The problem faced by airlines and cargo agents isthe non-availability of cargo space. Therefore,

right course of action is to combat the problem.3. The situation can be tackled by periodic cuts in

supply and urging people to conserve water. So,both the courses of action follow.

4. The accidents can clearly be prevented by barringpeople from crossing the tracks when the gatesare closed. So, only follow (II).

5. When the Government takes such an action it isnecessary that people are made aware of theconsequence they would face if they don t obeythe direct loss. Hence II follows, I is obvious.





According to the dictionary, Assertion refers to stating or claiming something forcefully and that of Reasonis fact. This test is meant to judge the candidate s knowledge and with it the aim is to determine his ability toreason out correctly.

Under, we shall deal with the combination of Assertion and Reason and relate with each other in order to findtheir correct coordination. Here, four alternative comments on these are given and the correct one is to be chosen.This is again an important feature of logical reasoning. Following illustrations will fully illustrate the type of suchquestionsDirections (Q. Nos. 1 to 3) In each of the illustrations questions, there are two statements labelled asAssertion (A) and Reason (R). Mark your answer as

(a) if both A and R are true and R is the correct explanation of A(b) if both A and R are true but R is not the correct explanation of A(c) if A is true but R is false(d) if A is false but R is true

Example 1Assertion (A): Most of ancient civilisations grew near the rivers.Reason (R): The main occupation of man was agriculture.Solution. The Assertion is correct because most of the ancient civilisations grew near the rivers as land overthere was fertile and water was easily available. But the Reason is not the correct explanation of the AssertionHence, option (b) is true.

Example 2Assertion (A): Seeds should be treated with fungicide solution.Reason (R): Seeds do not germinate, unless treated with fungicide solution.Solution: Seeds are treated with fungicide before sowing to avoid seed borne disease. But, it is not a truefact that unless seeds are treated with fungicide solution, they cannot germinate. Hence, option (c) is true.

Example 3Assertion (A): Appendix is a vestigial organ in the human body.Reason (R): It does not participate in digestion.

Assertion and Reason

CHAPTER 7





Solution: We know that, appendix is a vestigial organ in the human body and does not participate indigestion. Hence, both Assertion and Reason are correct and Reason fully explains Assertion. Hence, optionas (a) is our answer.

EXERCISEDirections (Q. Nos. 1 to 5) Choose the correctalternative from the following options as givenbelow for the Assertion (A) and Reason (R) givenin each of the questions.

(a) Both A and R are true and R is the correctexplanation of A

(b) Both A and R are true but R is not the correctexplanation of A

(c) A is true but R is false(d) A is false but R is true1. Assertion (A): Alcohol rather than mercury is

used in a thermometer to measure a temperatureof 60 C.Reason (R): Alcohol has a lower freezing pointthan mercury.

2. Assertion (A): Tides indicate the regular andperiodic rise and fall in sea level.Reason (R): Tides are caused by the gravitationalpull of the moon and sea level.

3. Assertion (A): Graphite is slippery and used asa lubricant.Reason (R): Graphite has free electrons.

4. Assertion (A): When common salt is kept open,it absorbs moisture from the air.Reason (R): Common salt contains magnesiumchloride.

5. Assertion (A): The steam engine was inventedby James Watt.Reason (R): There was a problem of taking outwater from flooded mines.

ANSWERS

1. (a) 2. (a) 3. (b) 4. (a) 5. (c)

EXPLANATIONS

1. We know that, mercury freezes at 39 C, whilealcohol freezes at a point far below -100 C. So,alcohol is used to measure lower temperatures.Similarly, mercury boils at 357 C, while alcoholboils at 78 C. So, mercury is used to measure hightemperature.

2. Reason is the main fact and given Assertion fullydescribes it.

3. In graphite, each carbon atom is linked to threeother carbon atoms, while one electron in thecarbon atom is delocalised. So, graphite has freeelectrons.

4. We know that, common salt contains magnesiumchloride, hence absorbs moisture from the air.

5. Assertion is correct but Reason is false.





This test is mainly to judge a candidate s ability to use his presence of mind to tackle a given situation, he maycome across anytime in life. For example, just think if you are going to appear in a test, and on the way you findan injured person. In this situation, what will you do?

So, at anytime we can face such problems. The candidate is, thus, expected to choose the best response whichshall present him/her as a good person or a sincere professional.

Types of QuestionsExample (Q. Nos. 1 to 5) Such questions consists four probable answers as an alternatives. You have toselect most appropriate alternative as the answer.

Example 1In a bus you realize that someone has left his/her wallet. You would

(a) give the money to the beggar(b) hand it over to the bus conductor(c) try to find his/her contact number and inform the owner(d) leave the wallet as it is

Solution. If you are an honest man then, you will try to find his/her contact number and inform the ownerof the wallet. In this way, that wallet will be reached in right hands. So option (c) is our answer.

Example 2Do you think that one should change his job often and face new situation?

(a) No, unless compelled one should not leave his old job(b) Yes, every new job is challenging and one should accept the challenge(c) No, as it takes time to get adjusted(d) No, as the new situation may not suit you

Solution. Most appropriate answer will be option (b). Because every new job is challenging and one shouldaccept the challenge. Unless you accept the challenges you can not get different views of life.

Example 3While travelling in a train, you observe some college students pulling the alarm chain simply to get down at

their desired point. You would

Situation Reaction Tests

CHAPTER 9





(a) with the help of some passengers, check them from doing so(b) let them pull the chain but check them from detraining(c) inform the guard of the train as soon as it stops(d) keep quiet and do nothing

Solution. Most appropriate option in this situation will be as in option (a). In this case, train will not be late.And others will not have to bear problems. As a good citizen, it is your duty to check such situations.

Example 4You want to get married to a person of your choice, but your family members give their own reasons, why you

should not marry that person which you do not find very convincing. What would you do?(a) Go by what your family says(b) Become throughly confused and still remain undecided(c) Marry the person of your choice(d) Try to convince your family about your choice

Solution. (d) Since, the person concerned does not find the views of the family members convincing, heshould try to convince them and mould their views to match his own. Just following his own choice shall hurt thefamily s sentiments and obeying the family members blindly shall be disloyalty towards the person he loves.

In this way the best way to settle a conflict is always to arrive at a consensus through peaceful talks andmutual discussions rather than stick to any one side and ignore the other.

Example 5You are a team leader and two of your colleagues are having a strained relationship with each other. As a

result, they are not contributing well in group activities. How will you handle such a situation?(a) How can I be bothered with such petty issues? At least the task is being done by others; so it is fine(b) You will make an explicit effort to help them shake hands(c) You will give them complementary tasks in which both have to work together(d) You will punish them for not contributing by keeping them out of the team

Solution. (b) As both your colleagues are having a strained relationship with each other, they are notcontributing well in group activities. But you are a team leader. So, it is your responsibility that work should bedone in good manner and in time. It can be possible if both your colleagues do works together. In this case, youshould make an explicit effort to help them shake hands.

EXERCISEDirections (Q. Nos. 1 to 5): In the followingquestions consist four portable answers as analternatives. You have to select most appropriatealternative as the answer.

1. No risk no gain , you(a) feel that risk means no gain(b) believe that this slogan is correct(c) feel it is foolish to accept unnecessary risk(d) feel that risk may be taken only after judging

the situation throughly.2. Your friends like smoking and influence you to do

the same. You will(a) smoke only because your friends are smoking(b) refuse to smoke(c) smoke but only in their presence(d) refuse and lie to them that you have asthma

3. You have a new boss. You(a) will be in different(b) welcome him warmly(c) go and flatter him as will help out in future(d) have problems adjusting as you are still loyal





to your old boss4. You are getting late for your college and bus is

not available. In such a situation(a) you start walking(b) you drop the idea of going to college that day

and return home(c) you think about other possible conveyance(d) you wait patiently for the bus though you are

late for the class5. If you are HR Manager of XYZ company and there

is only one vacancy. There are three candidatesto the post, one out of them is your nephew. Youwould(a) select your nephew though he is not eligible

for the post(b) select the candidate who is eligible for the post(c) consult with senior what needs to be done

(d) tell the candidate that vacancy is alreadyfulfilled

ANSWERS

1. (d) 2. (b) 3. (b) 4. (c) 5. (b)

EXPLANATIONS

1. In this case you feel that risk may be taken onlyafter judging the situation thoroughly.

2. Clearly, one should have a strong will power so asnot to yield to easy temptations and indulge inany activity that shall later prove harmful.

3. In such situation, you should welcome himwarmly as it is not your decision. This decision istaken by superiors.

4. As you are late for college, in such situation, youshould think about other possible conveyance. Asthe correct time of your bus is not known, it maybe further late.

5. You are HR Manager and it is your responsibilityto hire a quality person, you should givepreference for the one who is eligible for the post.



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SAMPLE MATERIAL OF


Interpersonal Skill &

Decision Making



Meaning of CommunicationTransmission of meaning from one person to another or to many people is communication, whether verbally

or non-verbally.Communication from one person to another is commonly depicted as a simple triangle consistingof the context, the sender, the massage, and the receiver.In the work area Communication skills have greatimportance just as they have in all areas of life.Communication skills such as being able to express one or tounderstand the others correctly are required for success and satisfaction at least in elementary level for most ofthe professions. Even though an organization performs its tasks more efficient than expected, one should knowthat this success will not continue so long if it lacks the same efficacy in communication. The success of communicationdepends on several factors. Transmission of message by the process of encoding and decoding the message, whichmay result in short-term perception, is not adequate for the success of communication. Communication should bein such a way that will give opportunity for the respondent or receiver to take decision with regard to the messagehe perceived.

Meaning of Interpersonal CommunicationThe concept of Inter Personal Communication (IPC) skills was introduced primarily in 1950s. Ability to work

well with people, and involve your acceptance of others, without prejudice is called IPC skills. Ability to respond tostaff s needs positively, fostering a non-discriminatory work environment where staff can develop to their fullpersonal potentials, and delegating authority Interpersonal communication competence consists of a set of skills,knowledge about communication, and self-evaluation is IPC skills. The skills involved in good interpersonalcommunication include

1. Demonstrating caring, concern and commitment2. Listening and Understanding3. Problem solving and Motivating.

You can demonstrate that you care by expressing your understanding of the feelings and concerns of theother person and by letting them know that you want to help them. You can reflect the other person s emotionsback to them with facial expressions that show you are concerned. You can also provide verbal feedback to themto show acknowledgement and recognition of their fears and concerns.Listening and understanding involve morethan simply being present while someone is speaking. Active listening means genuinely hearing the other person swords. Often, we think we are listening, but we actually do not pay close attention or do not really hear what theother person is trying to say.

Everybody has their own & unique Ability and strengths. Inspite of how bad you might think of yourself,you are special, unique and one of a kind.Trust in your abilities,recognise your strengths and succeed in life. On

Interpersonal &Communication Skills





the flip side, do recognise that even the weakest individual is better than you or me in some way or another. Itmay be intelligence or kindness or generosity or even grace.

Emerson once said: Every man is my superior in some way. In that case, I learn of him.Almost every man you meet feels himself superior to you in some way, and a sure way to win a person s heart

is to let him or her realize that in some subtle way, you recognize his importance in his little world, and recognizeit sincerely.

Salient features of IPC skillsv Think positively, and enter the mindset to work well with others and maintain good relationships. Do not

criticise others or yourself.v Be sensitive to others, this includes not gossiping.v Be patient.v Be cheerful and try to make others smile.v Treat others and their experience with respect.v Learn to listen, experts recommend listening 80% of the time and only talking 20%.v If you re not naturally confident or happy, fake it until you generally possess the desired characteristics.v Praise and compliment people when they deserve it,v When someone is telling a story, don t interrupt or try to upstage them with a story of your own.v Treat your team members and colleagues as friends and not as strangers or subordinates.v When you re unhappy, try your best to act happy anyway. You will end up feeling better and so will the

people around you, your mood is contagious.v Smile - even when you don t feel like smiling.v Look for solutions.v When someone compliments you, don t disagree or boast about it simply say thank-you with a smile and

move on.v Learn to appreciate, be helpful and not demotivate your team members. Work as a team, not as an individual.

This will achieve better results.

Behaviour PsychologyDeal with people as though they are your client or boss and convey the message you want in a proper

manner. (This includes rhythm of voice to make them comfortable with you.)Beatrice Vincent once said: The people with whom you work reflect your own attitude. If you are suspicious,

unfriendly and condescending, you will find these unlovely traits echoed all about you. But if you are on yourbest behaviour, you will bring out the best in the persons with whom you are going to spend most of your workinghours.

Robbins and Hunsaker (2003) reviewed a large number of studies and synthesized the IPC skills thatsurfaced on most lists Most of- these skills. belong to three categories - leadership, the process of communicationand motivation .Interpersonal skills under leadership relate to leadership style, handling conflicts, running meetings,team building and promoting change. The process of communication includes sending messages, listening andproviding feedback Similarly, motivating is broken down into goal setting, clarifying expectations, persuadingand empowering. Other interpersonal skill include negotiating. The dimensions and components of above modelare shown in the following table:

Concept Dimension ComponentInterpersonal communication skills (IPC) 1. Process of communication 1. Effective communication

2. Communication styles3. Building relationships





2. Motivation 1. Goal setting2. Clarifying expectations3. Self development4. Stress management5. Emotinal intelligence

3. Leadership 1. Leadership style2. Values and ethics3. Handling conflicts4. Promoting change

Steps to Develop Your IPC Skills?

1. NetworkingIn additionto strong communication Skills and Personal Skills, Networking uses the Background skills of

network building and motivating others. involves working with others ina group towards a common goal. Thisrequires cooperating with others, being responsive to others ideas, taking a collaborative approach to learning,and taking a responsibility for developing and acheving group goals.The ability to actively seek, identify andcreate effective contacts with others, and to maintain those contacts for mutual benefit.Teamwork uses theBackground skills of acollaboration, mentoring, decisionmaking and delegation.

2. LeadershipThe process of successfully influencing the activities of a group towards the achievement of a common goal is

called as leadership.As well as requiring strong communication Skills and Personal Skills, leadership uses theBackground skills of mentoring, decision making, delegation and motivating others.A leader has the ability ofinfluence others through qualities such as personal charisma, expertise, command of language, and the creationof mutual respect.

1. Leadership• Mentoring• Decision Making• Delegation• Motivating others

2. Networking• Self confidence• Network building• Effective

communication

3. Teamwork• Mentoring• Groupwork• Delegation• Collaboration

Interpersonal Skills





2. Background skills(i) Decision making

v Identifying appropriate evidence and weighing up that evidence to make a choice for example, gatheringand assessing information to find the best way to perform am experiment).

v Taking responsibility for a decision and its outcomes (for example, choosing a topic for a grouppresentation from a number of suggestions).

(ii) Mentoringv Being a trusted advisor and helper with experience in a particular field. Actively supporting and

guiding someone to develop knowledge and experience, or to achieve career or personal goals (forexample, a third-year student mentoring a first year student, helping to adjust tothe universityexperience).

v A mentoring relationship may be formal or informal, but must involve trust, mutual respect, andcommitment as both prties work together to achieve a goal (for example, mentoring a younger memberof a team to achieve better performance in the lead-up to a sporting event).

(iii) Group workv any activity inwhich sutdents work together;v any activity which has been specifically designed so that students work impairs or groups, and may be

assessed as a group (referred to as formal group work); orv when students come together naturally to help each other with their work (referred to as informal

group work).v peer group activity in lab classes, tutorials etc.

(iv) Group workv any activity inwhich sutdents work together;v any activity which has been specifically designed so that students work impairs or groups, and may be

assessed as a group (referred to as formal group work); orv when students come together naturally to help each other with their work (referred to as informal

group work).v peer group activity in lab classes, tutorials etc.

(iv) Motivating othersv Generating enthusiasm and energy by being positive, focussing on finding solutions and maintaining

a positive attitude even when things are not going well (for example, when something goes wrong,asking What can we try now instead of saying, That should have worked better. ).

v Encouraging others to come up with solutions, listening carefully to their ideas and offering constructivefeedback (for example, gathering suggestions for a group project, and giving each person s ideas fairdiscussion).

v Being prepared to support others in taking agreed, calculates risks, and not blaming others whenthings go wrong (for example, one group member s portion of a presentation receives a poor mark-make sure that this student isn t blamed by the group, and focus on learning from the mistakes).

(v) Delegationv Taking responsibility for determining when to ask someone else to make a decision or carry out a task

(for example, figuring out what is a fair distribution of the workload in a group project, and sharingresponsibility with others).

v Distributing responsibility and authority in a group by giving someone else the discretiontomakedecisions that you have the authority to make (for example, as the chosen leader of a lab experimentteam, you could assign tasks and decisions to different group members).





(vi) Collaborationv Working cooperatively and productively with other team members to contribute to the outcomes of the

team s work (for example, dividing the workload and sharing the results of your own work with othersin the group, or assisting members of the group who are having difficulty completing their tasks).

(vii) Network buildingv Creating contacts with other people and maintaining those contacts (for example, meeting someone at

a seminar with similar interests, and swapping email addresses with them).v Acquiring and maintaining information about people who might be useful contacts for specific purposes

(for example, seeking out people established in an industry you hope to work with one day).v Using a contact in an ethical manner to help each of you meet specific goals, (for example, collaborating

on projects of importance to both of you).

3. NetworkingThe ability to actively seek, identify and create effective contacts with others, and to maintain those contacts

for mutual benefit. In additionto strong communication Skills and Personal Skills, Networking uses the Backgroundskills of network building and motivating others. involves working with others ina group towards a common goal.This requires cooperating with others, being responsive to others ideas, taking a collaborative approach to learning,and taking a responsibility for developing and acheving group goals. Teamwork uses the Background skills ofacollaboration, mentoring, decisionmaking and delegation.

Types of LeadershipManagement experts have undergone a revolution in how they define leadership and what their attitudes

are toward it,in the past several decades. They have gone from a very classical autocratic approach to a verycreative, participative approach. Somewhere along the line, it was determined that not everything old was badand not everything new was good. Rather, different styles were needed for different situations and each leaderneeded to know when to exhibit a particular approach.

Four of the most basic types ofleadership are:A. DemocraticB. Laissez-faireC. AutocraticD. Bureaucratic

Although good leaders use all the styles, with one of them normally dominant, bad leaders tend to stick withone style.

A. Democratic Leadership TypeThe democratic leadership type encourages employees to be a part of the decision making therefore it is also

called the participative type. The democratic manager keeps his or her employees informed about everything thataffects their work and shares decision making and problem solving responsibilities. This style requires the leaderto be a coach who has the final say, but gathers information from staff members before making a decision.

Democratic leadership can produce high quality and high quantity work for long periods of time. Manyemployees like the trust they receive and respond with cooperation, team spirit, and high morale. Typically thedemocratic leader :

1. Develops plans to help employees evaluate their own performance2. Recognizes and encourages achievement.3. Encourages employees to grow on the job and be promoted4. Allows employees to establish goals





The democratic type is not always appropriate,like the other type. It is most successful when used withhighly skilled or experienced employees or when implementing operational changes or resolving individual orgroup problems. The democratic leadership type is most effective when :

1. The leader wants employees to share in decision-making and problem-solving duties.2. The leader wants to keep employees informed about matters that affect them.3. The leader wants to provide opportunities for employees to develop a high sense of personal growth and job

satisfaction.4. Changes must be made or problems solved that affect employees or groups of employees.5. There is a large or complex problem that requires lots of input to solve.

Democratic leadership should not be used when1. The manager feels threatened by this type of leadership.2. There is not enough time to get everyone s input.3. Employee safety is a critical concern.4. It s easier and more cost-effective for the manager to make the decision.

B.Laissez-Faire Leadership TypeLaissez-Faire type is one, in which the manager provides little or no direction and gives employees as much

freedom as possible. All authority or power is given to the employees and they must determine goals, makedecisions, and resolve problems on their own.This leadership type is also known as the hands-off type.

This is an effective type to use when :1. Employees are highly skilled, experienced, and educated.2. Employees have pride in their work and the drive to do it successfully on their own.3. Outside experts, such as staff specialists or consultants are being used4. Employees are experienced & trustworthy.

This style should not be used when1. Managers are unable to thank employees for their good work.2. It makes employees feel insecure at the unavailability of a manager.3. The manager doesn t understand his or her responsibilities and is hoping the employees can cover for him or

her.4. The manager cannot provide regular feedback to let employees know how well they are doing.

C. Autocratic Leadership TypeAutocratic Leadership type is one in which the manager retains as much power and decision-making authority

as possible. The manager does not consult employees, nor are they allowed to give any input.This is often consideredthe classical approach. Employees are expected to obey orders without receiving any explanations. The motivationenvironment is produced by creating a structured set of rewards and punishments.

This leadership type has been greatly criticized during the past 30 years. Some studies say that organizationswith many autocratic leaders have higher turnover and absenteeism than other organizations.These studies saythat autocratic leaders:

1. Rely on threats and punishment to influence employees.2. Do not trust employees.3. Do not allow for employee input.

Yet, autocratic leadership is not all bad. Sometimes it is the most effective type to use. These situations caninclude:





1. A manager s power is challenged by an employee.2. New, untrained employees who do not know which tasks to perform or which procedures to follow.3. Work needs to be coordinated with another department or organization.4. Effective supervision can be provided only through detailed orders and instructions.5. Employees do not respond to any other leadership type.6. There are high-volume production needs on a daily basis.

The autocratic leadership type should not be used when1. Employees begin depending on their manager to make all their decisions.2. Employees become tense, fearful, or resentful.3. There is low employee morale,absenteeism and work stoppage.4. Employees expect to have their opinions heard.

D.Bureaucratic Leadership TypeWhere the manager manages by the book and everything must be done according to procedure or policy is

Bureaucratic leadership.If it isn t covered by the book,the manager refers to the next level above him or her. Thismanager is really more of a policeofficer than a leader. He or she enforces the rules.

This type can be effective when :1. Employees are performing routine tasks over and over.2. Employees are performing tasks that require handling cash.3. Employees need to understand certain standards or procedures.4. Safety or securitytraining is being conducted.5. Employees are working with dangerous or delicate equipment that requires a definite set of procedures to

operate.This style is ineffective when

1. Work habits form that are hard to break, especially if they are no longer useful.2. Employees lose their interest in their jobs and in their fellow workers.3. Employees do only what is expected of them and no more.

Varying Leadership TypesWhile the proper leadership type depends on the situation, there are three other factors that also influence

which leadership style to use.1. The company, the traditions, values, philosophy, and concerns of the company will influence how a manager

acts.2. The manager s personal background.Employees are individuals with different personalities and backgrounds.3. The employees being supervised. The leadership type,managers may use will vary, depending upon the

individual employee and what he or she will respond best to.

VALUES AND ETHICSValues mostly remain predictable, they are consistent, even in volatile times. A clear set of values helps tell

people what their lives are for and what is worth working for. Values tell people what is good and important andvalues bind society. Social scientists believe that without values, a society could disintegrate, a risk often presentin India. Religious heads believe that without values, human life is meaningless and all the worldly pleasures willnot lead to any satisfaction. Yes, a lack of good values is why scams happen, nepotism exists and the governmentdoesn t care about its people.To any society and human being core values are vital.





Matters at StakeGood problem solving and decision making can avert tragedy and help the people recover from the event

more quickly. Conversely, poor decision making? or the absence of decisions? potentially can result in injury ordeath to victims or responders. (Clearly, in our case study, if the District Magistrate makes a poor decision-orsimply doesn t make any decision before it s too late-the consequences could be disastrous for the people of Murariganjand Dumdama.

But the repercussions don t stop there. Poor decisions in the early stages of an event can make the respondersjob more difficult and more dangerous. In addition, they can give rise to much more critical or complex decisionslater on? not to say the consequences on the lives of the local people. Good decision-making skills are one of yourmost critical assets as an Administrator, and CSAT will test on this account before you step to the next stage forthe selection to top administrative jobs in India. In this book , we shall familiarize you with what CSAT willactually attempt to test in you.We take here a case study to understand this aspect of making decisions in emergency.

Making Decisions in EmergencyCase Study* - Flood’s Fury and Koshi’s Wrath in North BiharInstructions: Read the following case study. As you read, try to identify what decisions must be made by the DistrictMagistrate or other emergency management officials. Mind your ideas as you read the situation.Background: Heavy rains have hit, and the entire area of the Koshi belt in the North Bihar bordering Nepal is inundateddue to change of course of Koshi. The district town of Sakri-located in the North Bihar—sits high and well away from thefury of Koshi, so the fear of floods is riot much of concern of the people in the Town. As the DM of Sakri district, last yearyou got a new chute(gutter, passageway) built to increase the capacity of the Reservoir in Sakri to 35 Crore litres ofwater. Two other subdivisional towns downstream-Murariganj and Dumdama are less than 15 minutes of drive from Sakri.Each Town has about 10,000 residents on both the sides of National Highway 77.

Events’ ChronologyLate afternoon Rains begins, and the Meteorological Office at Patna predicts it will be a strong, pachhuwa (Westerli(e),which will produce heavy rains.8:12 p.m. A flash flood watch is issued by the Meteorological Office.8:30 p.m. Heavy rains begin.10:15 p.m. The Executive Engineer of Sakri stations a Junior Engineer on the dam to watch for, and report any problems.The Junior Engineer sees water pouring a good 2 feet over the chute. (It was later estimated that the reservoir washolding 55 Crore litres of water during and after the storm )11:30 p.m. Six inches of rain have fallen over the last 3 hours.

Decision Making andProblem Solving





1:15 a.m. The Junior Engineer sees a section of dirt break away.1:30 a.m. When water recedes below the top of the dam, Junior Engineer and other workers discover that water haseaten around the drainage and is gradually carving away the side of the earthen dam. A first attempt at closing the holewith sandbags fails when the force of the water carries the bags right through.1:45 a.m. As the DM of Sakri , you are now in meeting with the Executive Engineer of Sakri, the PWD Engineer, the SP,the Chief Medical Officer of Sakri, and the District Disaster Cell Manager to discuss the situation.* The names of some of places and other recognized symbols could be fictitious and resemblances to events alreadyoccurred or occurring to the situations described here are only coincidental. This is just an academic reconstruction.

Decision PointsWhat decision points did we identify in the above situation? It is to be noted that the central problem is that

if the dam breaks, the people in the downstream towns will be flooded. Numerous decisions must be made toaddress this problem. Some of the key decisions that must be made are as follows, and we probably identifiedothers as well.

1. Should residents in the two downstream subdivisional towns of Murariganj and Dumdama be evacuated?2. If the decision is to evacuate, when should the evacuation take place?3. Who will notify the populace of the evacuation, and how?4. What additional resources will be necessary to accomplish the evacuation and provide any shelter needed?5. What is the most effective way to keep the dam from collapsing, and what resources will be needed to

accomplish that?

DECISION MAKING PROCESSWhether making ordinary day-to-day decisions or critical, time-sensitive decisions during an emergency,

using a standard problem-solving model will help ensure that your decisions are rational and logical.

Problem Solving VS Decision MakingLet’s first clarify what we mean by problem solving and decision making and how they go together:

• Problem solving is a set of activities designed to analyze a situation systematically and generate, implement, andevaluate solutions.

• Decision makings a mechanism for making choices at each step of the problem-solving process.Decision making is part of problem solving, and decision making occurs at the every step of the problem-solvingprocess.

Problem-Solving ModelThere are many different decision-making/problem-solving models that a decision making person can use.

Following is a five-step model which may be used in an emergency situation.Step 1 Identifying the problemStep 2 Exploring the alternativesStep 3 Selecting the best alternativeStep 4 Implementing the solutionStep 5 Evaluating the solution situation

When using this model, each step may be completed quickly, but every step must be considered. It is notnecessary to document each step, but it is important to think through every step.





Step 1 Identifying the ProblemProblem identification is undoubtedly the most important? and the most difficult? step in an situation. Whether

all subsequent steps are productive or not, will be based on how you define and assess the problem at hand.What is a Problem ?

Situation or condition of people or the organization that will exist in the future, and that is consideredundesirable by members of the organization is called a Problem.

Problem or Solution?We must distinguish between a problem and its solution in carrying out Step 1. Defining problems in terms

of their solutions is the most common error in problem solving. Sometimes people think that they are articulatingproblems when actually they are stating a potential solution.Marking Out the Problem Parametersv Identifying the problem also involves analyzing the situation to determine the complete extent of the problem.

Problem parameters include :v What is happening (and is not happening)?v Who is/are involved?v What the stakes are?

Checklist for Identifying, Defining, and Analyzing Problems1. Is this a new problem? (Answer in Yes or No)2. Is the problem clearly and precisely stated? (Answer in Yes or No)3. What assumptions are We making about the problem’? Are they true? (Answer in Yes or No)4. What would happen if nothing were done about this problem? (Answer in Yes or No)5. Can the problem be restated in other terms? If yes, how? (Answer in Yes or No)6. What data are Known that bear on the problem?7. Is the information accurate? (Answer in Yes or No)8. Are there any precedents or rules about other procedures that apply to the problem?

If so, what precedents or rules apply? (Answer in Yes or No)9. What additional facts are needed to analyze the problem? ( Make a List)

10. Is it possible to interpret the facts differently? How would that affect the problem’s solution? (Answer in Yes or No)11. Do I have to make this decision, or does someone else? If this decision is someone

else’s to make, whose is it? (Answer in Yes or No)

Step 2 Exploring the AlternativesTo explore alternative solutions to the problem identified in Step 1 is the second step in the decision-making

process. This step really consists of two partsv Generating alternativesv Evaluating alternatives

Methods of Generating AlternativesSo, what process should we use to generate the alternatives for the case study? There are three ways to

generate alternatives.v Brainstorming can be done individually or in a group. Brainstorming requires an environment in which the

participants (individuals or group members) are free to think out loud. Participants blurt out as manyideas as possible within a specified time period.





Surveys economically tap the ideas of a large group of respondents. Surveys present respondents with theproblem and a series of alternative solutions.Discussion groups should consist of those who are directly involved in decision making. In generatingalternatives, the group members should

1. Focus on the problem, not on the personalities of the people involved in the decision-making process.(But be sensitive to the impact of personalities on the process.)

2. Avoid initial judgments (as in brainstorming).3. Be comprehensive.

Criteria for Evaluating Alternatives:We must have some means of evaluating them,after we havegenerated alternative solutions. We should lists criteria by which we can evaluate alternatives. Another part ofevaluation is identifying contingencies-what could go wrong. Think in terms of Murphy s Law ( If anything cango wrong, it will. ) and identify what could get in the way of solving the problem you are facing.

Criteria for Evaluating AlternativesQuestions to Ask

1. Identify Constraints, Do any of the following factors serve as a limitation on this solution?• Human resources (limited ability of relevant people to understand or initiate certain actions)• Social (restrictions imposed by organized groups with special interests)

• Political (legal restrictions or ordinances)• Economic (cost or capital restrictions)

• Technical (limited equipment or technology)• Time (requirements that a solution be found within a prescribed time period, thereby eliminating consideration

of long-range solutions)2. Determine Appropriateness Does this solution fit the circumstances?3. Verify Adequacy Will this option make enough of a difference to be worth doing?4. Evaluate Effectiveness Will this option meet the objective?5. Evaluate Efficiency What is the cost/benefit ratio of this option?6. Determine Side Effects What are the ramifications of this option?

Step 3 Selecting the Best AlternativeTo select one of the alternatives explored in Step 2 for implementation is third step in the problem-solving

model. After you have evaluated each alternative, one should stand out as coming closest to solving the problemwith the most advantages and fewest disadvantages.

Implementing the solution may not be easy, however. There may be repercussions, and you should completea reality check to identify and evaluate the possible consequences of implementing the solution. Carefully considerhow the solution will be implemented before selecting an alternative.

Selecting an alternative is a critical step in the problem-solving process. When selecting an alternative, youwill encounter factors that affect your decision making. These factors may include:

Ethical factors. Financial factors. Political factors.

Environmental considerations.Safety factors.

All of these factors may not be readily recognizable. Be alert for these potential limits on the solutions thatyou can implement, as you examine the situation and apply the problem-solving model, .





Step 4 Implementing the SolutionThe fourth step involves five subparts.

1. Develop an action plan Implementation requires a series of steps to :Articulate who has to do what, with what resources, by what time, and toward what goal.Identify who must know about the decision.

2. Identify needed resources Resources include people, information (data), and things. Ask yourself:Are there any special requirements?

What resources do I need?How long will it take?

Where will I get them?What can others offer?

3. Determine objectives,Objectives are measurable targets that are:Used to monitor progress and establish priorities.Based on analysis of the situation and contingencies.

4. Build a plan Your plan should state :Who ...Will do what (and with whom) ...How

By whenWhere

Remember: Communicate the plan to all parties involved

5. Implement the plan Use the action plan to put the decision in place.The correct answers arePresents the best of the feasible solutions.Describes the activities required to implement the solution.Describes the resources needed to implement the solution.

Includes a timetable for implementing the solution.Addresses foreseeable side effects.Identifies who will take the action.

Remember that the plan must be disseminated to all who have responsibility for any part of implementing it.

Step 5 Evaluating the Solution SituationEvaluation involves two parts :Monitoring progress. Ask :

1. Has the situation changed?2. Are more (or fewer) resources required?3. Is a different alternative solution required?

Monitoring the success and results of a decision is an ongoing process that is critical to fine tuning a course ofaction.

Evaluating the results. Use the following checklist to help you evaluate the decision.





Checklists For Evaluating the Results1. Does the decision and action plan make use of existing channels of communication to generate feedback? 3. Will

the feedback test the effectiveness of the decision?2. Is the solution achieving its purpose?3. Will the feedback be sufficient to reflect changing circumstances and conditions that might occasion the need to

modify the plan?4. How will you know if the proposed decision has worked? Is it measurable? If yes, how?5. Is timely information generated so that it can be supplied to operational, administrative, and policy units in the

jurisdiction?For effective decision making, one needs to identify the various styles and attributes of Decision Making. One

must find one s psychological type , and the ways to relate it to one s personal preferences as well as factors andstyles that have an impact on one s ability to make rational and effective decisions. Also required is that you firstaccept whether the situation requires the individual decision or group decision.

Carl Jung s Psychological Type

TYPE AND COMPONENTS OF DECISION MAKINGThe psychiatrist Carl Jung categorized different personality patterns as psychological types. Based on his

observation of people s behavior, Jung concluded that people have inherent differences in how they use theirminds and where they derive and focus their energy.

Jung identified two mental processes:1. Taking in information (or perceiving).2. Organizing information and drawing conclusions (or judging).

Jung also identified two different ways in which people do each of these mental activities1. People take in information either through their senses or by intuition.2. People organize information either by thinking or by feeling.

People also differ in where they derive and focus their energy. They are either externally oriented (extroverts),energized by people and activity; or internally oriented (introverts), energized by ideas and thoughts. Thesedifferent ways of organizing and relating to the world obviously can be combined in different ways, thus creatingdifferent psychological types. For example, one person could be an extrovert who relies on thinking more thanfeeling and sensing over intuiting, while another individual could be an introvert who is intuitive and feeling-oriented.

Using Type Inventories to Determine PreferencesOne kind of personality test called a type inventory can help you to determine your preferred or dominant

ways of functioning, including your preferred decision-making style. Such tests ask you to answer a series ofquestions, and, based on your responses, assign you a type that is an aggregate of your preferences.

1. Extroversion vs. introversion (where energy is derived and focuse(d)2. Sensing vs. intuition (how information is obtaine(d)3. Thinking vs. feeling (how decisions are mad(e)4. Judging vs. perceiving (how the test taker is oriented toward the external worl(d)

Your Type What Does It Mean for Decision Making?The following are some generalizations about each dominant function:

1. Feeling: The bias is towards integrity. Decisions should consider people s values and needs. Ask, How doesthis affect those involved?





2. Sensing: The bias is toward stability. Decisions have to make sense based on past experience. Ask, Whatare the facts, costs, and benefits?

3. Thinking: The bias is toward effectiveness. Decisions must be objective and logical. Ask, What are the prosand cons, causes and effects?

4. Intuition: The bias is toward innovation. Decisions should creatively make use of new opportunities andinsights. Asks, What are the patterns and possible interpretations?

What Does It Mean to Flex?To flex means to ask yourself the questions of the other three functions, as well as the questions of your

dominant function that naturally occur to you.A key to good decision making is that it uses both sensing andintuition to gather all the pertinent information, and both thinking and feeling to weigh all the factors involved.When we rely only on our dominant function, we tend to miss things and make poorer decisions. Although thisprocess may feel awkward at first, it will lead to decisions that are more sound.

Who Decides?As you read through the four types, note that the amount of control that the leader has over the decision

drops from total to almost none.In addition to the four dominant functions explained above, there are also fourstyles of decision making based on who makes the decision.Yet, the leader retains ultimate responsibility.

As an emergency manager There are other times, however, when you must make a command decision alone.Several factors affect whether a decision should be made by an individual or a group. Use the questions in Job Aid3-1, on the following page, to determine whether the circumstances call for an individual or group decision.

Individual Decision MakingYou work often in situations that require a high degree of coordination in individual decision making. These

cases call for a group decision-making process. The leader must make the decision alone, and input from others islimited to collecting relevant information.

Group Decision MakingIn this case, the leaden and others work together until they reach a consensus decision. Each group member s

opinion and point of view is considered. As a result of helping to make the decision, group members buy into thefinal decision and commit to supporting its implementation.

Successful Group Decision MakingGroup decision making requires good leadership to be successful. There are special conditions necessary for

group decision making, such as adequate time. There are also particular pitfalls unique to group decision making,such as groupthink.

Decision Making Through ConsultationIn consultation, the leader shares the issue with one or more people-seeking ideas, opinions, and suggestions

and then makes a decision. The leader considers the input of others, but the final decision may or may not beinfluenced by it.

Delegating the DecisionWhen delegating a decision, the leader sets the parameters, then allows one on more others to make the final

decision. Although the leaden does not make the decision, he on she supports it.



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