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2

Physics

1. A car weighing 150kg is on a slope that makes an angle 60o with the

horizontal. The component of car’s weight (in Newton) parallel to the

slope is (g = 10 )

A. 1299

B. 1000

C. 15000

D. 20000

2. If force, acceleration is taken as fundamental quantities, then the

dimensions of length will be:

A. FT2

B. F-1A2T-1

C. FA2T

D. AT2

3. A hall has the dimensions 10 m × 10 m × 10 m. A fly starting at one corner ends up at a diagonally opposite corner. The magnitude of its

displacement is nearly

A.

B.

C.

D.

General Instructions 1. The duration of the test will be 60 minutes. Use the time accordingly.

2. The test paper consists of 50 questions divided into four sections, Section A, Section B, Section C and Section D.

* Section A contains 15 questions of Physics. * Section B contains 15 questions of Chemistry. * Section C contains 15 questions of Mathematics.

* Section D contains 5 questions of Aptitude. 3. Each question will have 4 choices, with the only single choice being

correct. 4. You will get 2 marks for every correct answer. 5. There will be no negative marking for any wrong answer or

unanswered question.

GTSE Sample Papers

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4. If L, C and R represent inductance, capacitance and resistance respectively, then which of the following does not represent

dimensions of frequency

A.

B.

C.

D.

5. A car covers the first half of the distance between two places at 40

km/h and other 60 km/h. The average speed of car is.

A. 40

B. 45

C. 48

D. 60

6. A spring whose unstretched length is l has a force constant k. The

spring is cut into two pieces of unstretched lengths l1 and l2 where, l1

= nl2 and n is an integer. The ratio k1/k2 of the corresponding force

constants, k1 and k2 will be :

A.

B. n

C. n2

D.

7. A ring of radius r is given a velocity v0 in forward direction and angular

velocity = 3v0/r in anticlockwise direction as shown and kept on a rough plane. The curve representing the variation of velocity of center

of mass vcm as a function of time t is

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A.

B.

C.

D.

8. An object is placed at a distance of 20 cm from a concave mirror of focal length 10 cm. At what distance from the mirror, should a screen

be placed to get the sharp image?

A. 10 cm

B. 20 cm

C. 30 cm

D. 15 cm

9. The laws of reflection are valid for _________

A. plane surfaces

B. any reflecting surfaces

C. curved reflecting surfaces

D. irregular surfaces

10. Read the given statements and mark the correct option.

Assertion: A normal human eye can clearly see all the objects below

and above 25 cm.

Reason: The human eye has the capacity to suitably adjust the focal

length of its lens to a certain extent.

A. Both assertion and reason are true and the reason is the correct

explanation of the assertion.

B. Both assertion and reason are true but reason is not the correct

explanation of the assertion.

C. Assertion is true but the reason is false.

D. Assertion is false but reason is true.

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11. The resistivity of a conductor does not depend upon,

A. temperature

B. length of the conductor

C. both temperature and the material of the conductor.

D. material of the conductor

12. The strength of the magnetic field between the poles of an

electromagnet would be unchanged if:

A. current in the electromagnet winding were doubled

B. direction of current in electromagnet winding were reversed

C. distance between the poles of electromagnet were doubled

D. material of the core of electromagnet were changed

13. What is the minimum distance between an object and its real image

formed by a convex lens?

A. f

B. 2f

C. 3f

D. 4f

14. The sun is visible to us about 2 minutes earlier than the actual sunrise.

The reason behind the early sunrise is,

A. the sun rays during the sunrise reaches earth before the sun

actually crosses the horizon.

B. the reflection of the sun rays from the Earth’s atmosphere appears

as a mirage of the sun in the morning sky.

C. the apparent position of the sun is slightly above the actual

position of the sun during the sunrise

D. the sun is nearer to the Earth during the sunrise.

15. The magnetic field at a point P due to a long straight conductor

carrying current is independent of

A. The current

B. Distance of conductor from the point

C. Length of conductor

D. None

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Chemistry

16. Calculate the number of molecules present in the following:

(i) in 34.20 g of cane sugar (C12H22O11)

(ii) in 1 L of water assuming that the density of water is 1 g/cm3

(iii) in one drop of water having a mass 0.05 g

A. (i) 1.673 ×1021 (ii) 3.346 ×1025 (iii) 6.022 ×1022

B. (i) 1.673 ×1021 (ii) 6.022 ×1022 (iii) 3.346 ×1025

C. (i) 6.022 ×1022 (ii) 1.673 ×1021 (iii) 3.346 ×1025

D. (i) 6.022 ×1022 (ii) 3.346 ×1025 (iii) 1.673 ×1021

17. The Bohr model can explain:

A. The spectrum of helium atom only

B. Spectrum of an atom or ion containing one electron only

C. Solar spectrum

D. None of the above

18. Half-filled and full-filled orbitals have _______ energy and hence

_______ stability.

A. higher, lower

B. lower, higher

C. higher, zero

D. zero, higher

19. The elements of the second and third period of the periodic table are

given below:

Which one element out of those given above is the most metallic?

A. Carbon

B. Sulphur

C. Magnesium

D. Sodium

20. Which of the following can undergo a chemical reaction?

A. MgSO4 + Fe

B. ZnSO4 + Fe

C. MgSO4 + Pb

D. CuSO4 + Fe

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21. The ratio of density of CO2 and N2O gases at same conditions is

A. 1 : 1

B. 1 : 3

C. 2 : 1

D. 3 : 2

22. The metal that reacts with hydrogen to form hydrides is:

A. Hg

B. Cu

C. Ag

D. Ca

23. Which of the following is the correct order of strength of H-bonding in

the given compound?

A. HF < NH3

B. H2O > H2O2

C. H2O2 > H2O

D. None of the above

24. Shyam and Hari have two identical pieces of marble chips with same mass. They take equal volumes of dil. HCl with the same concentration

in two different test tubes. Shyam puts the marble pieces directed into the acid whereas Hari powdered the marble piece and puts it into the

test tube. What will be the correct observation made.

A. Reaction in Shyam’s test tube will be faster

B. Reaction in Hari’s test tube will be faster

C. Both reactions will happen with the same speed

D. No reaction happens in both the test tube

25. An atom of an element A has three electrons in its outermost shell and

that of B has six electrons in the outermost shell. The formula of the

compound between these two will be

A.

B.

C.

D.

26. Diluting a substance

A. decreases the total number of moles per litre of solution

B. increases the total number of moles per litre of solution

C. does not change the number of moles of solute

D. increases its temperature

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27. Which of the following solutions will NOT have pH = 13 assuming

complete dissociation?

A. 2.0 g of NaOH in 500 cm3 solution

B. 100 cm3 solution of 0.05 M Ca(OH)2

C. 100 cm3 solution of 0.1 N Ca(OH)2

D. 4.0 g NaOH in 500 cm3 solution

28. The IUPAC name and symbol for element X (atomic number 119):

A. Ununennium and Uue

B. Ununennium and Ubn

C. Unnilennium and Uue

D. Unnilennium and Ubn

29. For the energy levels in an atom which one of the following

statement is correct?

A. The 4s sub-energy level is at a lower energy than the 3d sub-

energy level

B. The M-energy level can have maximum of 18 electrons

C. The second principal energy level can have three orbitals and

contain a maximum of 18 electrons

D. The 5th main energy level can have maximum of 49 electrons

30. When a 2 g mixture containing CaCO3 and Na2CO3 is heated

strongly,0.44 g of CO2 is produced. The mass percentage of the

Na2CO3 present in the mixture:

A. 75

B. 50

C. 40

D. 25

Maths

31. Let X = {1,2,3,4,5,6} be an universal set. Sets A,B,C in the universal set X be defined by A = {1,2,3},B = {2,4,5} & C = {3,4,5,6}. Then

which of the following is incorrect?

A. (A–B)– C = {1}

B. (A–B) (B–A) = {1,3,4,5}

C. A – B = {4,5}

D. A C' = {1,2}

32. ABC is a right-angled triangle right angled at B. A circle is inscribed in

it in the lengths of the two sides containing the right angle are 5 cm

and 12 cm. The radius of the circle is

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A. 1 cm

B. 1.5 cm

C. 2 cm

D. 2.5 cm

33. At present Asha’s age (in years) is 2 more than the square of her

daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of

Nisha. The present age of Nisha is:

A. 5 years

B. 7 years

C. 11 years

D. 15 years

34. If in a conference of total 900 people. 400 are experts in Maths. 200

are experts in both Maths and Computers. Then how many are experts

in computers only?

A. 500

B. 800

C. 200

D. 600

35. The degree of zero polynomial is

A. 0

B. 1

C. Not defined

D. Depends on the polynomial

36. (1 + tanθ + secθ) (1+ cotθ – cosecθ) is equal to

A. 1

B. –1

C. 0

D. 2

37. Find the domain of the function f(x)= log (x2 – 3x + 2)

A. R-{1,2}

B. R-I

C. R

D. I

38. A cylindrical pipe has inner diameter of 7 cm and water flows through it at the rate of 192.5 litres per minute. Find the rate of flow in

kilometres per hour.

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A. 2km/h

B. 3km/h

C. 3.5km/h

D. 4km/h

39. If the sum of first six terms of an AP is 42 and the ratio of its 10th and

its 30th term is 1:3. Then its thirteenth term is:

A. 13

B. 20

C. 26

D. 30

40. At t min past 2 pm, the time needed by the minute hand of a clock to

show 3pm was found to be 3 min less than min. The value of t is:

A. 11 minutes

B. 14 minutes

C. 16 minutes

D. 17 minutes

41. If sinθ + sin2θ = 1, then the value of cos2θ + cos4θ will be:

A. 0

B. 1

C. -1

D. 2

42.

=?

A. 1/2

B. 1

C. 2

D. -1

43. If the pth term of an AP is q and qth term is p, then its (p + q)th term

is

A. p

B. p + q

C. q

D. 0

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44. If both radius and height of a right circular cone are doubled then ratio

of its original CSA(curved surface area) to new CSA is

A. 1 : 1

B. 1 : 4

C. 2 : 1

D. 1 : 2

45. What is the value of

A. 2

B. 3

C. 1

D. 0

Aptitude

46. A is 40 m south-west of B. C is 40 m south-east of B. Then C is in

which direction of A?

A. West

B. East

C. North

D. South

47. Deepak and Amit are brothers. Deepak is the son of Suresh. Ramesh

is Suresh’s father.

How Amit is related to Ramesh?

A. Grandfather

B. Grandson

C. Father

D. Uncle

48. How many 0’s are there in the following series which are not

immediately followed by 3 but immediately preceded by 2?

72034042042070380203042047

A. Two

B. Four

C. Five

D. Three

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49. Pick the odd one out.

A. Listen

B. Walk

C. Swim

D. Climb

50. In a row of girls, If Sheetal who is 10th from the left and Hina who is 9th from the right, interchange their positions, Sheetal becomes

15th from the left. How many girls are there in the row?

A. 24

B. 23

C. 25

D. 26

***

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Physics

1. Ans. A.

Mass of car = 150 kg

Slope angle (θ) = 60o

g = 10 ms-2

Component of car will be given as,

2. Ans. D.

(A) F is given by [M1 L1 T-2 ], T is given by [M0 L0 T1 ]

FT2 = [M1 L1 T-2] × [ M0 L0 T2]= [M L ]

(B) F is given by [M1 L1 T-2 ], T is given by [M0 L0 T2 ] and A is

[ M0 L1 T-2 ]

F-1 A2 T-1 = [ M-1 L-1 T2 ] × [ L2 T-4] × [M0 L1 T-2]=[ M-1 L2 T-4]

(C) F is given by [M1 L1 T-2 ], T is given by [M0 L0 T2 ] and A is

[ M0 L1 T-2 ]

FA2T=[M1 L1 T-2 ] × [M0 L2 T-4] × [M0 L0 T1 ]=[ M1 L3 T-5]

(D) F is given by [M1 L1 T-2 ], T is given by [M0 L0 T2 ] and A is

[ M0 L1 T-2 ]

AT2 = [M0 L0 T-2] × [ M0 L0 T2] = [L]

Hence, the correct option is (D) has the same dimension as that of

length.

3. Ans. B.

Let us assume that the fly starting from point A at corner and ends

up at point B

Hints & Solutions

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Displacement = Length of body diagonal

d

d

d

Magnitude of displacement is

4. Ans. D.

Since, dimension of frequency is T-1

Dimensions of L = [ML2T-2A-2] , C = [M-1L-2T4A2] , R = ML2T-3A-2

satisfy the dimensions of frequency

∴ does not represent the dimension of frequency.

5. Ans. C.

Case 1: The car cover x/2 distance at speed of 40 km/h

Putting the values, We get

Case 2: The car cover x/2 distance at speed of 60 km/h

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Putting the values, We get

On solving for t, we get

Total time taken T= t1+t2

Putting the value in average speed formula, we get

Thus option C is the correct option.

6. Ans. D.

For the spring constant

as Δx ∝ l

For constant force

F = k Δx

Hence,

7. Ans. B.

By conservation of Angular momentum about an axis through any point on the ground, the final velocity of the COM when rolling

starts will be – V0. The change in velocity upto that instant will be a linear function of time (constant deceleration/acceleration due to

Kinetic Friction)

8. Ans. B.

Given:

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The object distance, u =-20 cm

The focal length of the concave mirror, f =-10 cm

The mirror formula is given as below:

Where,

f is the Focal length of the mirror

v is the image distance from the concave mirror

u is the object distance from the concave mirror

Putting the values in the equation, we get

Thus, the image is formed at a distance of 20 cm from the pole of

the concave mirror.

Hence, Option B is the correct option

9. Ans. B.

The laws of reflection are valid for any reflecting surface; regardless

of the fact that it is a curved surface or plane as long as the surface is a polished reflecting surface.

Thus option B is the correct answer.

10. Ans. D.

The range of vision for a normal eye is from 25 cm to infinity. The

eye is able to see clearly all objects in front of itself by adjusting its focal length suitably. The ability of the human eye to contract and

expand the ciliary muscles to adjust the focal length of the lens such that it can see an object which is nearby and faraway is called

accommodation.

11. Ans. B.

The resistivity of a conductor is a measure of the resistance of the conductor of given material and the physical condition such as

pressure and temperature. It does not depend on the dimensions of

the conductor. Therefore, option B is the correct answer.

12. Ans. B.

The strength of the magnetic field between the poles of an electromagnet would be unchanged if the direction of current in

electromagnet winding were reversed. The changing of the polarity

only reverses the direction of the magnetic field thus produced.

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Hence, option B is the correct answer.

13. Ans. D.

The minimum distance is 4f, i.e., when an object is placed at one of

the two centres of curvature and the image is formed at the other

centre of curvature, the image will be real.

Hence, D is the correct answer.

14. Ans. C.

The sun rays coming from the sun undergoes refraction causing the

light rays to bend. Therefore, the apparent position of the sun is

slightly above the actual position during the rise.

15. Ans. C.

The magnetic field due to a current carrying conductor depends on

the magnitude of the current flowing through it and the distance of

the point from the conductor,

B ∝ I and B ∝ r

Where I is the current flowing in the conductor; r is the distance of

the point from the conductor.

It does not depend on the length of the conductor

Hence option C is the correct answer

Chemistry

16. Ans. D.

(i) 1 mole of C12H22O11 = 342 u

[∵ molecular mass of cane sugar (C12H22O11)]

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= 12 × 12 + 22 × 1 + 11 ×16 = 342 amu

= 6.022 × 1023 molecules

Now 342 g of cane sugar contains 6.022 × 1023 molecules.

∴ 34.2 g of cane sugar will contain

= 6.022 × 1022 molecules

(ii) 1 mole of water = 18 g = 6.022 ×1023 molecules.

Mass of 1 L of water = Volume × density

= 1000 × 1 = 1000 g

Now 18 g of water contains = 6.022 × 1023 molecules.

∴ 1000 g of water will contain =

= 3.346 ×1025 molecules

(iii) 1 mole of H2O = 18 g = 6.022 × 1023 molecules

Mass of 1 drop of water = 0.05 g

Now 18 g of H2O contains = 6.022 × 1023 molecules

∴ 0.05 g of H2O will contain

molecules

17. Ans. B.

• Bohr's model does not work for systems with more than one

electron.

• The Bohr model shows that the electrons in atoms are in orbits of

differing energy around the nucleus.

• The Bohr model works only for an atom or ion containing one electron only (eg: hydrogen) because it considers only the

interactions between one electron and the nucleus. The Bohr model is based on the energy levels of one electron orbiting a

nucleus at various energy levels. Any other electrons in the atom

will repel the one electron and change its energy level.

18. Ans. B.

Half filled and full filled orbitals have lower energy and hence higher

stability.

The extra stability of half-filled and completely filled subshell is due

to:

(i) relatively small shielding

(ii) smaller coulombic repulsion energy, and

(iii) larger exchange energy.

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The half-filled and fully-filled orbitals are more symmetrical than any other configuration and symmetry leads to greater stability. The

electrons present in the different orbitals of the same sub-shell can exchange their positions. Each such exchange leads to the decrease

in energy.

19. Ans. D.

Na is the most metallic element out of the given elements. This is

because on moving along a period from left to right, the metallic character decreases and on moving down a group the metallic

character increases. Thus Na is most metallic as it can easily lose its

valence electron.

20. Ans. D.

• CuSO4 + Fe can undergo a chemical reaction. As the iron metal is

more reactive than copper metal, iron displaces copper from copper sulphate solution and forms aqueous iron sulphate

(FeSO4) and solid copper (Cu).

Option D is correct.

21. Ans. A.

22. Ans. D.

• Most metals do not react with hydrogen.

• Metals form compounds by losing electrons and hydrogen also

loses the electrons to form compounds.

• Normally hydrogen atom does not accept electrons given by a

metal atom to form a compound.

• But there are few metals such as sodium, magnesium, calcium and potassium which force the hydrogen to accept the electrons

given by them and form a salt-like solid compound called metal

hydrides.

23. Ans. B.

The more are the partial charges generated, the more is the

strength of H-bonding.

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24. Ans. B.

As Hari took the powered marble piece, Hari’s test tube will react

faster. For a reaction involving a solid reactant, the smaller in the particle size, i.e., greater is the surface area, the faster is the

reaction.

25. Ans. B.

Valency of A will be 3

Valency of B will be 2

So,the formula of the compound will be A2B3

For e.g. Al2O3

26. Ans. C.

• The correct answer is C.

• Dilution is the process where more solvent is added to a solution

to decrease the concentration of the solute.

• In dilution, the amount of solute does not change and therefore,

the number of moles is the same before and after dilution.

27. Ans. D.

A. Number of moles of NaOH

B. n-factor is 2 in Ca(OH)2

C. For 0.1 N Ca(OH)2 = 0.1

28. Ans. A.

The IUPAC name and symbol for element X (atomic number 119):

Ununennium and Uue

29. Ans. B.

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The M-energy level can have maximum of 18 electrons. For M-energy level, the value of n is 3.

The number of electrons =2n2 = 2(3)2 =18

30. Ans. B.

Sodium carbonate is very stable and hence doesn't decompose

easily. Therefore, all the CO2 is produced by calcium carbonate.

CaCO3 → CaO + CO2

To produce 44 g of CO2, amount of CaCO3 required= 100 g

To produce 0.44 g of CO2, amount of CaCO3 required=1 g

Mass of Na2CO3= Total mass of the mixture – Mass of CaCO3 in the

mixture

= 2 – 1

= 1

Mass percentage of Na2CO3= 1/2×100

= 50%

Maths

31. Ans. C.

A–B = {1, 3}

32. Ans. C.

Given: AB = 12 cm and BC = 5 cm

To find: the value of r

Theorem Used:

Pythagoras theorem:

In a right-angled triangle, the squares of the hypotenuse is equal to

the sum of the squares of the other two sides.

Using the Pythagoras theorem stated above,

AC2 = AB2 + BC2

⇒ AC2 = 122 + 52

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⇒ AC2 = 144 + 25

⇒ AC2 = 169

⇒ AC = √169

⇒ AC = 13 cm

Now,

Area of ΔABC = Area of ΔOAB + Area of ΔOBC + Area of ΔOCA

As we know,

Area of triangle = 1/2 × base × height

⇒ 1/2 × BC × AB = (1/2 × AB × r) + (1/2 × BC × r) + (1/2 × AC ×

r)

⇒ 1/2 × 5 × 12 = (1/2 × 12 × r) + (1/2 × 5 × r) + (1/2 × 13 × r)

⇒ 30 = 6r + 2.5r + 6.5r

⇒ 30 = 6r + 2.5r + 6.5r

⇒ 30 = 15r

⇒ r = 2 cm

33. Ans. A.

Let Nisha’s age be x.

Then, Asha’s age = x2 + 2

When Nisha grows to Asha’s present age, Asha’s age be one year

less than 10 times that of Nisha’s present age i.e.,

(x2 + 2) + [(x2 + 2) – x] = 10x - 1

⇒ 2x2 - 11x + 5 = 0

By using quadratic formula,

Neglecting the fraction.

⸫ For ,

Nisha’s age is 5 years.

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34. Ans. A.

A = only maths B = only computers

N(AUB) = 900 N(A) = 400

N(A∩B) = 200

N(AUB) = N(A) + N(B) – N(A∩B) 900 = 400 + N(B) – 200

N(B) = 700

The required number of experts in computers only = N(B) – N(A∩B)

= 700 - 200 = 500

35. Ans. C.

Constant polynomial f(x) = 0 is termed as zero polynomial.

The degree of a zero polynomial is not defined.

36. Ans. D.

We have

(1 + tanθ + secθ)(1 + cotθ – cosecθ)

=

=

= [∵ (a + b)(a – b) = a2 – b2]

= [∵ sin2 θ + cos2 θ = 1]

=

Thus, (1 + tan θ + sec θ)(1 + cot θ – cosec θ) = 2

37. Ans. A.

Now the given function is f(x)=log (x2 - 3x + 2)

Now if we separate the functions then x2-3x+2 is valid everywhere being a polynomial function

But log(x) is invalid where x=0 Hence we need to check those values where x2-3x+2=0

x2-3x+2=0 (x-2)(x-1)=0

The function is invalid in {1,2}

So The function’s domain lies at R-{1,2}

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38. Ans. B.

Inner diameter = 7 cm

Rate of flow of water = 192.5 litres/min.

To find: Rate of flow of water.

Formula Used: Volume of cylinder = πr2h

The inner diameter of the pipe = 7 cm

The inner radius of the pipe = = 3.5 cm

We have,

Water flows at the rate 192.5 litres per minute,

⇒ The volume of water that flows in 1 min = 192.5L

⇒ Volume of water that flows in 60 min = (192.5 × 60)L

As 1L = 1000 cm3

⇒ (192.5 × 60) l = (192.5 × 60 × 1000) cm3

Let “h” cm be the length of column of water which flows in 1 hour.

As water is flowing from cylindrical pipe,

So, Water column forms a cylinder of radius 3.5 cm and length “h”

cm.

Volume of water that flows in 1 hour = volume of the cylinder

⇒ h = 300000 cm

As

⇒ h = 300000 cm

= 3 km

Hence, the rate of flow of water is 3 km/h.

39. Ans. C.

If 'a' is the first term and 'd' is the common difference in an AP,

We know that,

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nth term of an AP, an = a + (n - 1)d

Sum of first 'n' terms of an AP,

Now, given

Sum of first six terms, S6 = 42

⇒ 3[2a + 5d] = 42

⇒ 2a + 5d = 14 …[1]

Also, given ratio of 10th and 30th term is 1 : 3

⇒ 3a + 27d = a + 29d

⇒ 2a = 2d

⇒ a = d

Putting d = a in [1]

⇒ 2a + 5a = 14

⇒ 7a = 14

⇒ a = 2

Now, a13 = a + 12d = 2 + 12(2) = 26

40. Ans. B.

Time (in minutes) taken by the minute hand to travel from 2 pm to

3 pm = 60 minutes

According to question,

⇒

⇒ 4(60 - t) = t2 - 12

⇒ 240 - 4t = t2 - 12

⸫ t2 + 4t – 252 = 0

Using the quadratic formula,

26

⸫ The required value of t is 14 mins. (⸪ Time cannot be negative)

41. Ans. B.

Given: sin θ + sin2 θ = 1

⇒ sin θ = 1 – sin2 θ

Taking LHS = cos2θ + cos4 θ = cos2 θ + (cos2 θ)2

= (1– sin2 θ) + (1– sin2 θ)2 …(i)

Putting sin θ = 1 – sin2 θ in Eq. (i), we get

= sin θ + (sin θ)2

= sin θ + sin2 θ

= 1 [Given: sinθ + sin2θ = 1]

42. Ans. A.

43. Ans. D.

We know that, nth term of an AP is

an = a + (n – 1)d, where

a= first term and d = common difference

Here, ap = q and aq = p

⇒ a + (p – 1)d = q [1] and

a + (q – 1)d = p [2]

ap + q = a + (p + q – 1)d [3]

Now, Subtracting [2] from [1], we get

(p – 1)d – (q – 1)d = q – p

⇒ d(p – 1 – q + 1) = q – p

⇒ d(p – q) = -(p – q)

⇒ d = -1

Putting this in [1], we get

a + (p – 1)(-1) = q

⇒ a – p + 1 = q

⇒ a = p + q – 1

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Putting values of ‘a’ and ‘d’ in [3], we have

⇒ ap + q = (p + q – 1) + (p + q – 1)(-1) = 0

Hence, Option D is correct.

44. Ans. B.

We know that,

Curved surface area of a cone = πrl

Where, r = base radius

l = slant height

When, Radius and height is doubled

r' = 2r and h’ = 2h

∴ New CSA = π(2r)(2l) = 4πrl

Hence, Ratio is πrl : 4πrl

= 1 : 4

Hence, Option B is correct.

45. Ans. C.

Given expression

Hence Option C is correct

Aptitude

46. Ans. B.

As is clear from the diagram below, C lies to the East of A.

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47. Ans. B.

As Deepak is Amit’s brother. Deepak is grandson of Ramesh

therefore, Amit is also grandson of Ramesh.

48. Ans. D.

Only 30s are not immediately followed by 3 i.e. the very next number is NOT 3 but preceded by 2, i.e. the number just before 0 must b

e 2.

49. Ans. A.

Except listening, all other require physical movement.

50. Ans. B.

Sheetal is 10th from left and Hina is 9th from Right. If they

interchanged their positioned Sheetal become 15th from left. So, Sheetal has gained its position from left. 15th Positions + 8th

positions = Total girls

Total Girls = 23.

***

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