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80

100

20X

Y

40

120

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140

160

SET ISET ISET ISET I

Answer all the questions

Group 'A' [9 (2 + 2) = 36]

1. (a) Simplify :1

1 a

x y +1

1 a

y x [Ans: 1]

(b) Evaluate :5

1024 [Ans: 2]

2. (a) Solve :1

3

2x 3

= 2 [Ans:25

16]

(b) The product of the ages of a man 10 years before and

10 years hence is 300. Find his present age. [Ans: 20]

3. (a) x 1, 2x + 1, x + 5 and 3x + 1 are in ascending order. If

its median is 18, find the value of x. [Ans: 10]

(b) Construct a cumulative frequency table represented by

the given ogive.

[Ans:

C.I. f

0 20 0

20 40 10

40 60 20

60 80 30

80 100 50

100 120

10

4. (a) A number card is drawn at random from a group of

number cards numbered from 2 to 13. Find the

probability of getting a prime numbered or even

numbered card. [Ans: 11/22]

(b) Three children are born in a family. Calculate the

probability of getting exactly two sons by drawing a

tree diagram. [Ans:

3

8]

5. (a) The area of the given parallelogram is

14 cm2. If SR = 4 cm, QR = 7cm, find

the value of QRS. [Ans : 30]

(b) Find the lateral surface area of the

given prism [Ans: 140 cm2]

6. (a) The radius and height of a right circular cone are in the

ratio 5 : 12 and its volume is 2512 cm3. Find the radius

of its base. [Ans: 10cm]

(b) Find the circumference of the sphere whose volume is1375

21 cm

3.

Ans:110

7cm

7. (a) A milkman bought 100 l of milk for Rs. 1500. 51

2 lof

milk was lost by leakage. If he sold the remaining milkfor Rs. 18 per litre, what was his gain or loss

percentage? [Ans: 13.4 %]

(b) Find the compound interest on Rs. 11250 for 3 years if

the rates of interest for the first, second and third year

are 4%, 5% and 6% respectively. [Ans: Rs. 1772.10]

8. (a) In the given figure if the areaof PQT is 50 cm

2. Find the

area of PRS. [Ans: 50 cm2]

Q R

SP

10 cm

4 cm6 cm

P Q

TSR


2/35

3 4

(b) Find the value of x:

[Ans: 125]

9. (a) In the adjoining figure, O is the centre of

the circle. OPQ = 50. Calculate the

value of x and y. [Ans: x = 100, y =

130]

(b) In the adjoining figure, Aand B are the points of

contact of the tangents TA

and TB. O is the centre of

the circle and ATB =

50. Calculate the value of x. [Ans: 65]

Group 'B' [16 4 = 64]

10. In a survey of a group of 120 people, 90 use Everest

toothpaste, 72 use brighter toothpaste and 10 use neither of

the past.

(i) Construct a Venn-diagram to illustrate the above

information.(ii) How many people use both the toothpaste?

(iii) How many people use Everest toothpaste only?

(iv) How many people use exactly one toothpaste?

[Ans: 52, 38, 58]

11. Find the H.C.F. of

2x3 16, x

2 4x + 4, x

3 3x

2+ 2x [Ans: x 2]

12. Solve: 5x 5

+ 54 x

= 115 [Ans: 4,5]

13. Simplify :1

a b +

1

a + b +

2a

a2+ b

2 +4a

3

a4+ b

4 [Ans:8a

7

a8 b

8]

14. The sum of the digits of a two digit number is 6. If 18 issubtracted from the number, the digits in the number are

reversed, find the number.

[Ans: 42]

15. Calculate the lower quartile (Q1) from the following data

[Ans: 41.67]

Marks 20-40 40- 60-

80

80-100

No of

students

8 12 10 6

16. The angle of elevation from the roof of a house to the top of

a tree is found to be 45 . If the heights of the house and tree

are 12 m and 25m respectively, find the distance between

the house and the tree. [Ans:13m]

17. Find the total surface area and

volume of the given solidobject.

[Ans:6006cm2, 1950.67cm

3]

18. In the given figure, the total surface area

of the given square based pyramid is

384cm2

and the side of the square base is12 cm, find the slant height of the

pyramid . [Ans: 10 cm]

19. Santosh and Mandip can reap a field in 10 days . Mandip

and Roshan can reap a field in 12 days. Roshan and Santosh

can reap the same field in 15 days.

(i) In how many days will they complete to reap the field

if all of them reap together?

B

OxQ

A

T50

A

A'

O P24cm

12 cm

P

D

A B

C

x

35O

B

C

A

D

PQ

R

S

x yO

50


3/35

5 6

0

51015

2025

3035

1020 30 40 506070

Class Interval

Y

X

40

(ii) How many days will each of them take to reap the field

completely ?[Ans; (i) 8days, (ii) 24 days, 171

7days , (iii) 40 days]

20. A merchant sells his goods marketing them 25% above the

cost price.

If he allows a discount of 12% on selling the goods, whatpercent profit does he make? [Ans:10%]

21. A person borrows Rs.10,000 for 1 year and 6 months at

10% p.a. compound interest payable yearly. But he

immediately lends the sum for the same time and same rate

of compound interest payable half yearly, How much does

he gain in his transaction? [Ans: Rs.781.25]22 Prove that the triangles standing on the same base and

between the same parallels are equal in area.

23. In the given figure ABCD is a square and AE

= AF Prove that BD // EF

24. Verify experimentally that the angle in the same segment ofa circle are equal. ( Two different figures are necessary but

the radii of the circles must not be less than 3 cm)

25. Construct a triangle equal in area to the quadrilateral ABCDin which AB = 5cm, BC = 4.5cm, CD = 3.4cm, AD =

4.2cm, and diagonal AC = 6cm.

SET ISET ISET ISET IIIII


Group 'A' [9 (2 + 2) = 36]

1. (a) Simplify: {(x-y)-3

}-n

{(x+y)n}

3

[Ans: (x2

- y2

)3n

]

(b) Evaluate:3

a6b

2c

3

4a

-8b

-8c

4 [Ans: a

5b

4/3]

2. (a) x+5 = x +1 [Ans: 4]

(b) The product of two positive numbers which are in the

ratio 2:3 is 96. Find the numbers. [Ams: 8 & 12]

3 (a) If x=50 and fx = 750, find the value of f. [Ans:15]

(b) Write down the frequency table corresponding to thealong side of frequency curve.

[Ans:

c.f. f

20 40 5

30 40 5

40 50 10

50 60 7

60 70 8

4. (a) A coin is tossed and a dice is rolled. Find the

probability of getting a head on the coin and a number

less than 3 on the dice. [Ans:

1

6]

(b) A bag contains 1 red ball, 1 white ball and 1 blue ball.

Two balls are drawn one after the other without

replacement. Show all the possible outcomes and

corresponding probabilities in a tree diagram.

5. (a) Calculate the area of parallelogram PQRS if PS = 3 2

cm, SR = 8 cm and PQR = 45. [Ans: 24 cm2]

BE

C

F

DA


4/35

7 8

(b) The area of a parallelogram is 48 cm2. If the two

adjacent sides are 8cm and 6 cm, find the length of its

diagonal. [Ans: 10cm]

6. (a) The surface area of a marble is 2 cm2. What will be

the difference in the area if the radius is made

2

3 of its

original size? [Ans:10

9cm

2]

(b) The volume of a rectangular pyramid is 210 cm3. If the

area of its rectangular base is 105 cm2, find the height

of the pyramid.

[Ans: 6 cm]

7. (a) A fruit seller bought a basket containing 1 grossoranges for Rs. 432. But 14 oranges were rotten. He

then sold the good oranges for Rs. 3.50 per orange.

Find his profit or loss. [Ans: Rs. 23]

(b) In what time will the compound interest compounded

semi-annually on Rs. 4000 at 5% p.a. be Rs. 202.50?

[Ans: 1 year]

8. (a) ABCD is a square. If the diagonal BD = 3 3 cm, findthe area of ABCD. [Ans: 9 cm

2]

(b) Find the values of x and y [Ans: x = 35,

y = 55]

9. (a) In the adjoining figure, PQ is thediameter of the circle with centre O. If

ROS = 42, find the value of RTS.

[Ans:69]

(b) Find the values of x and y from the

given figure, where O is the centre ofthe circle and TAN is the tangent at

the point A. AP is the bisector of

OAN. [Ans: x = 90, y = 45]

Group 'B' [16 4 = 64]

10. In a class of 50 students, 25 students like to play football,

35 like to play cricket and 15 like to play both the games.

How many students donot like to play any games? Show the

above information in a Venn-diagram. [Ans: 5]

11. Find the L.C.M. of

8x3 + 1, 8x

4 x, 16x

4 + 4x

2+ 1 [Ans: x(8x

3 1) (8x

3 + 1)]

12. Solve: xx+

108

xx = 31 [Ans: 2,3]

13. Simplify :

1 + x

1 x +

1 x

1 + x +

4x

1 + x2 +

8x3

1 x4

Ans:

2(1 + x)

1 x

14. 6 years ago, Ram was six times his son, 4 years hence,

thrice his age will be equal to eight time his son's age. What

are their present ages?

[Ans: 36 yrs, 11 yrs]

15. Calculate the upper quartile (Q3) from the given data [Ans: 61.43]

Marks

obtained

20

30

50 60 30

40

60

70

40 -50 70

80

No. of

students

5 10 6 7 8 4

16. A tree of 14m height is broken by the wind so that its toptouches the ground and makes an angle of 60 with the

ground. Find the length of the broken part of the tree.[Ans: 7.50 m]

17. Find the slant height of the cone if the

volume of the given solid is660

7cm

3.

[Ans: 5 cm]

18. Given figure is a square pyramid is which

vertical height is 8 cm and length of base side

x

O

y70

A

B C

42

R T

S

Q

O

P

Ox y

AT N

P

B

C

O A3cm

12cm

12cm


5/35

9 10

is 12cm. Find its total surface area and volume. [Ans: 384

cm2, 1152 cm

3]

19. Deekshyanta can do2

5 part of a work in 9 days. He calls

Samir to finish the remaining work. They work together and

finish it in 6 days. How many days will be taken by Samirto finish the work alone? [Ans: 18 days]

20. The marked price of an article is 25% above its selling price

and the cost price is 30% less than its marked price. Find

the discount percent and gain percent. [Ans: 20%, 142

7%]

21. In what time will a sum of Rs. 1280 at 121

2 % p.a.

compounded annually amount to Rs. 1620? [Ans: 2 years]

22. In the given figure, P is the mid point of

RC. Prove that area of RBC = area of

//gm ABCD.

23. Prove that a parallelogram inscribed in a circle is a

rectangle.

24. Verify experimentally that the angles in the conjugatesegments are supplementary, (Two different figures are

necessary but the radii of the circles must not be less than3cm)

25. Construct a triangle ABC in which BC = 7 cm, ABC =

45 and AC = 8.5 cm. Also construct a triangle equal in

area to the given ABC.

SET IIISET IIISET IIISET III


Group 'A' [9 (2 + 2) = 36]

1. (a) Simplify :12

1

4

1

+ 3

1 [Ans: 1/7]

(b) Evaluate:(343)

2/3

5

(32)3

[Ans:1

112]

2. (a) Solve:4

6x + 5 =4

x + 30 [Ans: 5]

(b) The difference of the square of a number and 23 is 2.

FInd the number . [Ans: 5]

3. (a) The average temperature from Sunday to Friday is

28C and that of Sunday to Saturday is 30C. Find the

temperature on Saturday.

[Ans: 42 C]

(b) From the ogive given

alongside, find the median. [Ans: 55]

4. (a) The probability of solving a mathematical problem by

two students A and B is1

2 and

1

5 respectively. If the

problem is given to both the students find theprobability of the problem being solved.

[Ans:3

5]

(b) There are 30 students in a class of which2

3 are boys.

Three students are chosen from the class at random, one

after the other. Draw the probability tree diagram and

B C

DPA

R

0

510152025

3035

50 545862

Height (inch)

Y

X

40


6/35

11 12

find the probability that there will be at least two boys

selected. [Ans:152

203]

5. (a) Find the area of the given

quadrilateral ABCD in which AB =

BC, AD = DC = 3cm, BD = 5cm andADB = 30. [Ans: 7.5 cm

2]

(b) Find the area of ABC in which AB = 105cm, BC =91cm and AC = 98 cm. [Ans: 4116 cm

3]

6. (a) A solid metallic sphere of radius 7cm is out into two

halves. Find the total surface area of each hemisphere

so formed [Ans: 462 cm2

](b) If the volume and height of a right circular cone are

1887 cm3and 37 cm respectively. Find the area of its

base. [Ans: 153 cm2]

7. (a) An electrician bought 50 balls at Rs. 15 per bulb. If 7

bulbs were defective and he has to make a profit of Rs.

67 on the total outlay, find the selling price of one bulb.[Ans: Rs. 19]

(b) Find the rate of compound interest when Rs. 5120amounts to Rs. 7290 in 1 year 6 months, if the interest

is compounded half yearly?

[Ans: 25 %]

8. (a) In adjoining figure NMRP is a

quadrilateral in which MN // PR.

NMR = PRM = 90, MR = 8cm

and PN = 10cm. Find the area of

quadrilateral NMRP.

[Ans: 120 cm2]

(b) Find the values of x and y: [Ans: x =

130, y = 115]

9. (a) If O is the centre of the circle, Calculate all the angle of

the rhombus OABC.

[Ans: A = C= 60, B = O = 120]

(b) PA and PB are the tangents from

an external point P to the circle

with centre at O. Calculate the

values of x and y if BAE =

106. [Ans: x = 32, y = 148]

Group 'B' [16 4 = 64]

10. In a class of 75 students, 28 like football but not cricket and

32 liked cricket but not football. If 7 students did not like

both games, find

(i) how many students liked both the games?(ii) how many students liked football?

(iii) how many students liked cricket?

(iv) illustrate the above information in Venn-diagram. [Ans: 8, 36, 40]

11. Find the H.C.F. of

2x3 5x

2+ 2x, 3x

3 8x

2+ 4x, 2x

4 16x [Ans: x(x 2)]

12. Solve:5x 1

5x + 1 = 1 +5x 1

2 [Ans:9

5]

13. Simplify:1

x 3

2

2x + 3 +

1

x + 3

2

2x 3[Ans:

54x

4x4+ 5x

2+ 81

]

14. A number of two digits is equal to four times the sum of its

digits. If 18 is added to the number, the digits are reserved.

Find the number.

[Ans: 24]

15. Compute the arithmetic mean of the following data:[Ans: 57.75]

A

D

C

B

N M

RP 18 cm

y

O

x

A

B

DC

65

OC

BA

y O

106A

E

Px

BD


7/35

13 14

Marks

obtained

25

35

65 75 75

85

35

45

45

55

85

95

55

65

No. ofstudents

3 5 4 5 9 2 12

16. An observer finds an angle of depression of 60 when he

observes a car on the road from the roof of his house. If the

car is at a distance of 50m from the foot of the house, find

the height of the house. [Ans: 86.6m]

17. The volume of a cone is equal to the volume of cylinder

whose height is 9 cm and diameter 40cm. If the height of

the cone is 108 cm then find its radius of circular base.[Ans: 10cm]

18. Find the total surface area of the solidobject given in the figure. [Ans: 92.5m

2]

19. Praful can do as much work in 4 days as Safal can do it in 5

days. If they work together, they can finish it in 20 days.

What time will each take to finish the work? [Ans: 45 days, 36 days]20. If a tourist paid Rs. 5610 for a carved window made of

wood with a discount of 15% including 10% VAT, what is

the marked price of the window? [Ans: Rs. 6000]

21. Deepa has invested a certain sum of money at compound

interest added annually. She gets an interest of Rs. 225

added in her investment at the end of second year. Find the

sum invested and the rate of compound interest.[Ans: Rs. 3750, 6%]22. In the given figure, rectangle ABCD

and parallelogram EBCF are on the

same base BC and between the same

parallels AF and BC. Prove that

(i) ABE DCF

(ii) Area of the rectangle ABCD = Area of the

parallelogram EBCF.

23. In the given figure, CD is the

angular bisector of BDE of a

cyclic quad. ABCD. Prove that

ABC is an isosceles triangle.

24. Verify experimentally that the angle at the centre of a circle

is double of the angle at the circumference standing on the

ame arc (Two different figures are necessary but the radii of

the circles must not be less than 3cm)

25. Construct a trapezium ABCD in which AD//BC, AB = 4.6cm, BC = 2.5cm, DAB = 60 and BCD = 90. Also

construct a triangle equal in area to the trapezium.

2.5m

A D E F

CB

A

B C

D E


8/35

15 16

SET IVSET IVSET IVSET IV


Group 'A' [9 (2 + 2) = 36]

1. (a) Simplify :x

5m + 3n x

3m 2n

x

2m + n [Ans: x4n

]

(b) Evaluate:

20

a5

10

a51 5

a5 [Ans: 1]

2. (a) Solve:5

x + 9 = 1 [Ans: 8]

(b) If 11 is added to the square of a number the result is

47. Find the number. [Ans: 6]

3. (a) If the lower quartile class is 20 30, cumulative

frequency of pre-lower quartile class is 6, the frequency

of quartile class is 14 and the total number of data is 30

then find the value of lower quartile.

[Ans: 31.7]

(b) Find the value of p and q in the following table:

C.I. f c.f.

0 4 5 5

4 8 7 12

8 12 p 20

12 16 10 q

[Ans: p = 8, q = 30]

4. (a) Two coins are tossed at the same time. Find the

probability of getting the same event in both the toss.[Ans:1

2]

(b) There are 9 white and 11 black balls of the same shape

and size in a bag. If two balls are drawn randomly in

succession without replacement from the bag. Show the

probability of all the possible outcomes in a tree

diagram.

5. (a) In the given figure, find the length AB if

the area of ABC is 27 cm2

[Ans: 9 cm]

(b) Find the total surface area of the

given triangular prism. [Ans: 768

cm2]

6. (a) The height and radius of base of a

cylinder are in the ratio 3 : 1. If its volume is 1029

cm3, find its height. [Ans: 7 cm]

(b) Find the total surface area of the solid cone obtained by

revolving the given right angles ABC about BC. [Ans:

942 cm2]

7. (a) A watch is priced at Rs. 1530 including

121

2% VAT. Calculate the price of the

watch without VAT. [Ans: Rs. 1360]

(b) The share of a bank depreciates every year by 2.5%. If

the amount depreciation of the share this year is Rs. 15,

find the present value of the share. [Ans: Rs. 600]8. (a) The area of the rhombus ABCD is 36 cm

2 and the

diagonal AC = 8cm. Find the length of the diagonal

BD. [Ans: 9 cm]

(b) O is the centre of the circle. Find the

value of x if OBA = 35 [Ans: 55]

9. (a) Find the values of x and y if BC{=

CD{ and DCE = 90

[Ans: x = 42, y = 45]

12 cm30

A C

B

B C5 cm

A

x

35

O

AB

C

32

xy

60

T

PQ

C

30 cm

A

B C

D

E

x

48y


9/35

17 18

(b) Find the value of x and y where O is the centre of the

circle and PQ is the tangent. [Ans: x = 62, y = 59]

Group 'B' [16 4 = 64]

10. In a group of 150 music lovers, it was found that 90 people

liked folk songs, 70 people liked modern songs and 30 didnot like both songs.

(i) How many liked both songs?

(ii) Show the above information in a Venn-diagram.[Ans: 40]

11. Find the H.C.F. and L.C.M. of M

(x3+ 1) (x 1) and (x

4+ x

2+ 1) (x

2 3x + 2)

[Ans: H.C.F. = (x 1) (x2 x + 1), L.C.M. =(x 2) (x

3+ 1) (x

3 1)]

12. Solve : x + 7 + x =28

x + 7 [Ans: 9]

13. Simplify :

1

1 + xb a

+ xc a+

1

1 + xc b

+ xa b+

1

1 + xa c

+ xb c[Ans: 1]

14. One year ago, the father was 8 times as old as his son. Now,

his age is equal to the square of his son's age, find their

present ages.

[Anrs: 49 yrs, 7 yrs]

15. If the mean of the data is 30.75, find the value of x. [Ans: 7]

Class 0-10 10 - 20 20 30

30 40

40 50

50 60

No. of

students

5 x 6 9 8 5

16. From the top of the 40m hight house, the angles of

depression to the two points on the same side of the house

observed are 60 and 45 respectively. Find the distance

between two points. [Ans: 16.9 m]

17. Find the surface area and volume of given

cylinder with a hemisphere at one end.[Ans: 555.5cm

2, 859.83 cm

3]

18. Find the total surface area and volume of

the given solid. [Ans: 289.98 cm2, 384cm

3]

19. 4 boys and 6 girls can do a piece of work in

5

2 days. 8 boys

and 3 girls can do the same work in 2 days. In how many

days will 1 boy and 1 girl do the work separately? [Ans: 20 days, 30 days]

20. The marked price of an electric heater is R. 3200. If the

shopkeeper allows a certain discount and a customer bought

it for Rs. 2640 including 10% VAT, what is the discount

percent? [Ans: 25%]

21. A man borrowed a sum of money and paid back in 2 yearsin two equal installments. If the rate of compound interest

was 4% p.a. and if he paid back Rs. 676 annually, what sum

did he borrow? [Ans: Rs. 1275]

22. In the given parallelogram ABCD, P

and Q are the mid points of AB and

AD respectively. Prove that area of fig.

PQDCB =7

8(area of //gm ABCD)

23. In the adjoining figure, O is the centre of

the circle and AB is a diameter. If arc BC

= arc CD, prove that AD // OC.

24. In the cyclic quadrilateral ABCD, Verify experimentally

that ABC + ADC = 180 and BAD + BCD = 180

A Q D

CB

P

OA B

CD

20 cm

6cm

4cm


10/35

19 20

(Two different figures are necessary but the radii of the

circles must not be less than 3cm)

25. Construct a triangle ABC in which AB = 5.7 cm, BC =

5.3cm and CA = 6.2 cm. Also construct a parallelogram

equal in area to the ABC if one side of the parallelogram

is 7.5 cm.

SET VSET VSET VSET V


Group 'A' [9 (2 + 2) = 36]

1. (a) Simplify :

6n + 2

+ 7 6n

6n + 1 8 5 6n [Ans: 1]

(b) Evaluate:4

128 a3

42

1a

9 [Ans: 4a

3]

2. (a) Solve: 5x 1 = 2 x + 3 [Ans: 13]

(b) Divide 81 into two parts whose product is 1260.[Ans: 60,21]

3. (a) The mean of a,b,c,d is 9 and the

mean of a,b,c,d,e, f is 12. Find

the mean of e and f.[Ans: 18]

(b) From the given ogive, find the

median [Ans: 12]

4. (a) What is the probability that a leap year will have 53

Tuesdays? [Ans:2

7]

(b) Two cards are drawn from a well-suffled deck of 52

cards. Drawing a tree diagram find the probability that

both the cards are knaves. [Ans:1

221]

5. (a) The area of ABC is 12 cm2. If AC = 6 cm and AB =

8cm, find the value of BAC. [Ans: 30]

(b) Find the volume of given prism.

[Ans: 124.70 cm3]

6. (a) Find the volume of the following

square based pyramid. [Ans: 384

cm3]

(b) The circumference of the base of a cylinder is 132 cm

and the area of its curved surface is 1584 cm2. Find its

height. [Ans: 12 cm]

7. (a) The VAT on a crarte of beer is Rs. 90. If VAT was

levied at 10%, find the cost of the crate of beer

including VAT. [Ans: Rs.990]

(b) Calculate the population of a town three years ago ifthe present population is 83,65,427 and the annual

growth rate is 10%.

[Ans: 62,85,069]

8. (a) In the given figure ABCD is asquare and EBCF is a

parallelogram. If AB = 4cm,calculate the area of parallelogram

EBCF. [Ans: 16 cm2]

(b) O is the centre of the circle and OA //

BC. If reflex AOC = 230, find thevalues of x and y. [Ans: x = y = 50]

Y

X4O 8 12 16 20

4

8

12

10

20

Marks obtained

12 cm

P

A B

CD

A D E F

CB

y

230O

A

B

C

x


11/35


12/35

23 24

AF and BC. Prove that area of //gm ABCD = area of //gm

EBCF.

23. In a circle with centre O, chords ABand CD intersect outside the circle at

E. Prove that AOC BOD =

2AEC.

24. Verify experimentally that the inscribed angle is half of the

angle at the centre standing on the same arc. (Two different

figures are necessary but the radii of the circles must not beless than 3cm)

25. Construct a parallelogram ABCD with AB = 3.6 cm, A =

60 and AD = 4.4 cm. Also construct a triangle with one

side = 5.5 cm and making its area equal to the area of the

parallelogram.

SET VISET VISET VISET VI


Group 'A' [9 (2 + 2) = 36]

1. (a) Simplify :(a b) (b2

a2

)

Ans:a + b

a2b

2

(b) Evaluate:

34 27

3 9

5

816 33

Ans:

1

81

2. (a) Solve: 2a + 1 + a = 5. [Ans: 4]

(b) 10 pencil and 2 eraser cost Rs. 40 and 25 pencils and 4

erasers cost Rs. 90. Find the cost of a pencil and an

eraser.

[Ans: Rs. 2 and Rs. 10]

3. (a) The mean of 6 observations is

48 but one of the data was

misread as 43 instead of 34, find the correct mean.[Ans: 46.50]

(b) From the given ogive, find the modal class. [Ans: 60

80]

4. (a) The odds in favour of an event is 2 : 3. Find theprobability of occurance of this event. [Ans: 2/5]

(b) A bag contains 5 blue and x yellow balls. A ball is

taken out and without replacing the first ball another

ball is taken out. Draw a probability tree diagram and

find the value of x, if the probability getting both

yellow balls is3

28 [Ans: 3]

5. (a) Find BAD of a rhombus ABCD with sides 12cm and

area 72 cm2 [Ans: 30]

(b) Find the volume of the givensolid. [Ans: 1400 cm

3]

6. (a) If the surface area of a marble is1

4 cm

2, find its

volume

Ans:1

482cm

3

(b) Find the curved surface area of the given

cone. [Ans: 137.5 cm2]

7. (a) Find the percentage discount if an article labelled at Rs.

4200 is sold for Rs. 3822. [Ans: 9%]

E D C

A

B O

Y

X20O 40 60 80 100

10

20

30

4050

Marks

16 cm

5cm

7cm


13/35

25 26

(b) The population of a place was 2000. Within a year the

population increased 3% by brith rate and 2% by

migration. Find the present population. [Ans: 2100]

8. (a) In the figure alongside PQRS is a

parallelogram, PX and PY are the

altitudes. If QR = 12cm, SR =10cm and area of PQRS = 96

cm2, calculate PX and PY .[Ans:

9.6 cm, 8 cm]

(b) Find the values of a, b, and c. [Ans: a =

22, b = c = 68]

9. (a) In the given figure, if DAB =

80, EDF = 15 and DF //

BC, find the value of ABC.[Ans: 115]

b) Find the values of a, b and c.

[Ans: a = 65, b = 130, c = 25]

Group 'B' [16 4 = 64]

10. A college awarded 38 medals in football, 15 in basketball

and 20 in cricket. If these medals went to a total of 58 men

and only three men got medals in all three games, howmany received medals in exactly two of the three games. [Ans: 9]

11. Find the H.C.F. of:

8a3 27, 8a

3 18a and 16a

2 16a 12 [Ans: (2a 3)]

12. Solve :

x + 2 x 2

x + 2 + x 2 =

1

2

Ans:5

2

13. Simplify:

x + 3

x2+ 3x + 9

+x 3

x2 3x + 9

54

x4+ 9x

2+ 81

Ans:2(x 3)

x2 3x + 9

14. Rs. 200 is divided equally among a certain number of

children. If there were 25 children more, each would have

received 40 paisa less, find the number of children.[Ans: 100]

15. Calculate the value of 'a' from the following data, if the

upper quartile (Q3) is 74 [Ans: a = 10]

Marks 20

40

40

60

60

80

80

100

No. ofstudents

8 12 a 6

16. A ladder 16m long leans against the wall of a house. If the

foot of the ladder is 8m from the house, (i) at what height

did the top of the ladder lean against the house from itsfoot? (ii) find the angle made by the ladder with the ground.

[Ans: 8 3 m, 60]

17. A cone is placed on a cylinder as shown in

the figure. The area of the base of the

cylinder is 125 cm2and height of the cylinderis 3cm. If the volume of the whole solid is

625 cm3, find the height of the solid. [Ans: 9

cm]

18. The given figure is a solid object made

of a pyramid and a prism. Find the

P

QY

X

R

S

22

ab

cC

B

A

O

10 cm

19 cm

80

E

F

D

C

B

A15

C

B

A

D

E

a

bO

c

65


14/35

27 28

volume of the solid object. [Ans: 148 cm3]

19. A man undertakes to do a cerain job in 40 days. He hires

15men for the job. At the end of 10 days, only one-fifth ofthe work was completed. How many extra men must be

employed in order to complete the work in time?[Ans: 5 men]

20. A shopkeeper sold his goods for Rs. 16950 allowing 25%

discount and then levied 13% VAT. Find the amount of

discount. [Ans: Rs. 5000]

21. The compound amount of a sum of money in 2 years is Rs.

8820 and in 3 years is Rs. 9261. Find the sum and the rateof interest

[Ans: Rs. 8000, 5%]

22. On the given figure, AE // CD, AB

//EC//FD and CB //DA//FE. Prove that

area of //gm ABCG = area of //gm

EGDF.

23. O is the centre of the circle in which inscribed angle ABC

and central angle AOC are standing on the same arc. AC.

Prove that AOC = 2ABC.

24. Verify experimentally that the inscribed angles standing on

the same arc are equal (Two different figures are necessary

but the radii of the circles must not be less than 3cm)

25. Construct a parallelogram ABCD in which AB = 3.2 cm,

BC = 5cm and AC = 3.5cm. Also, construct a parallelogram

equal in area to the parallelogram ABCD whose one angle

is 60.

SET VIISET VIISET VIISET VII


Group 'A' [9 (2 + 2) = 36]

1. (a) Simplify :(x1

+ y1

) (x2

y2

) (x1

y1

) [Ans: 1]

(b) Evaluate : 2

3

8

4

64

2

43 16

4 [Ans: 8192]

2. (a) Solve: x 3 = 2 x [Ans: 9]

(b) Find the two numbers such that 5 times the larger plus

3 times the smaller is 47 and 4 times the larger minus

twice the smaller is 20.

[Ans: 7, 4]

3. (a) The mean of a continuous serieswhich has 80 terms is 40. When

class 5 15 is included in the

series, the new mean is 30. Find

the frequency of the class

interval 5 15. [Ans: 10]

(b) Give the Q3class from the

adjoining figure. [Ans: 30 40]

4. (a) What is probability of giving a child birth by a pregnant

lady on a Tuesday? [Ans: 1/7]

(b) A coin is biased so that the probability that it lands

showing heads up is2

3. The coin is tossed three times.

Draw a tree diagram to show the possible outcomes andfind the probability that more heads than tails are

obtained. [Ans:20

27]

5. (a) In the given figure, ABCD is a

parallelogram. If BC = 5cm, and

DAB = 30. Find the length of

AB if the area of ABC = 15 cm2

.

Y

X10O 20 30 40 50

5

10

15

20

25

Class Interval

30

60

D C

BA

30

A E

F

DC

BG


15/35

29 30

[Ans: 6cm]

(b) The perimeter of a triangular field is 540 m and its

sides are in the ratio 25 : 17 : 12. Find the area of the

triangle. [Ans: 9000 cm2]

6. (a) Find the area of the triangular

faces of the given pyramid if theheight of the pyramid is 5cm and

the base is a square of side 24 cm .

[Ans: 312 cm2]

(b) If the circumference of great circle of a sphere is cm,

find its volume.

Ans:

6cm

3

7. (a) Hari sold three bags for Rs. 645 bearing a loss of Rs.

51. At what rate did he buy the bags. [Ans: Rs. 232]

(b) What is the rate of compound depreciation of a

machine worth Rs. 1,00,000 which is sold after 2 yearsfor Rs. 81,000. [Ans: 10%]

8. (a) Calculate the area of the given quadrilateral.

Ans:1

2h(a + b)

h

a

b

(b) Find the values of a and b. [Ans: a = b = 60]

9. (a) In the given figure, O is the centre ofthe circle and ABCD is a cyclic

quadrilateral where BC is produced

to E. If AB = AD and ADB = 48

find the value of DCE. [Ans: 84]

(b) From the given figure, find the values ofa, b and c. [Ans: a= b = c= 45]

Group 'B' [16 4 = 64]

10. In a survey of a group of students, it was found that 40% of

the students like folk songs, 30% like modern songs and

20% like both songs. If 90 students like neither folk normodern songs, find the number of students in the school and

the number of students who like only folk songs.

[Ans: 180, 36]

11. Find the LCM of

1 + 4a + 4a2 16a

4and 1 + 2a 8a

3 16a

4.

[Ans: (1 + 2a)(1 2a) (1 + 2a 4a2) (1 + 2a + 4a

2)]

12. Solve: 4x+ 4

x= 16 1

16 [Ans: 2, 2]

13. Simplify:a 1

(2a 1)(a + 2) +

3

(a + 2) (a 1)

1

(1 a)(1 2a)

Ans:a + 4

(a + 2) (2a 1)

14. A year hence a father will be 5 times as old as his son. Two

years ago the father was 3 times as old as his son will be4years hence. Find their present ages. [Ans: 29 yrs, 5 yrs]

15. Calculate the median from the given data: [Ans: 11.83]

Marks

obtained

0

5

5 10 10

15

15

20

20

25

25

30

30

35

No. of

students

11 6 15 6 8 5 4

24 cm

P

A B

C

ba

O

30B

AD

C

a 2ac

O

b

OB

C

D

E

A


16/35

31 32

16. A man 1.6 m tall is 30m away from a tower and he

observers the angle of elevation of the top of the tower to be

30. What is the height of the tower? [Ans: 18 .92m]

17. Find the volume of the given solid made up ofcone on both sides.[Ans: 2310 cm

3]

18. In the given solid, the upper part has a

pyramid of slant height 5cm and thelower part is a prism of side 8cm. If the

volume of the solid figure is 448 cm3,

find the height of the prism.

[Ans: 6 cm]

19. Amit and Ankit can do a piece of work in 16 days and 24

days respectively. Amit worked alone for 4 days and Ankit

worked alone for 6 days. In how many days will the

remaining work be finished if they work together?

Ans: 44

5days

20. A shopkeeper allows a discount of 10% and still makes a

profit of 15% on selling an article. If the marked price ofthe article is Rs. 15000, find its selling price, cost price and

profit.

[Ans: Rs. 13500, Rs.11739.13, Rs. 1760.87]

21. The difference between the compound interest and thesimple interest on a sum of money for 2 years at a rate of

10% interest per annum is Rs. 20. Find the sum.[Ans: Rs. 2000]

22. In the given tranpezium ABCD,

AD // BC and AP = PB. Prove that

PCD =1

2trap. ABCD.

23. In the cyclic quadrilateral ABCD, Prove that i) BAD +

BCD = 180 and (ii) ABC + ADC = 180.

24. Verify experimentally that the angle in the semi-circle a

right angle. (Two different figures are necessary but the

radii of the circles must not be less than 3cm)

25. Construct a quadrilateral ABCD in which AB = BC = 6cm,

AC = AD = 6.5 cm and BAD = 60. Also construct atriangle equal in area to the quadrilateral ABCD.

8 cm

P

A DMO

CB

A D

B C

P

14 cm


17/35

33 34

SET VIII

S.L.C. Question 2065 CDR

2065 (2009)Attempt allthe questions.

Group'A' [9(2+2)]=36

1= (a) Simplify :132x+1+ 5 169x

9 169x [Ans: 2]

(b) Evaluate:4

216a9b

5

46

1a

3b [Ans: 6a

3b]

2= (a) Solve : 9x2

20 = 3x 2 [Ans: 2]

(b) If 6 is added to the square of a number, the result is 31.

Find the number. [Ans: +5, 5]

3. (a) The mean weight of some men is 56 kg and the sum of

their weight is 392 kg, find

the number of men. [Ans: 7]

(b) From the given graph, find

the third qnartile class. [Ans:

40 60]

4. (a) A number card is drawn

randomly from the set of

numbered cards, numbered from 6 to 39. Find the

probability that the card may be a prime number or a

cubed number. [Ans:5

7]

(b) An urn contains 7 green and 9 black balls of the same

shape and size. Two balls are drawn at random oneafter the other without replacement. Draw a tree

diagram showing all the probabilities and also find the

probability of getting both black balls. [Ans:3

10]

5. (a) In the given figure, PQRS is a

parallelogram in which QR is

produced to the point T. If the area ofthe parallelogram is 27 3 sq. cm, the

side QP = 6 cm and the side PS = 9 cm, determine the

measure of the SRT. [Ans: 60]

(b) Given figure is a triangular prism

whose volume is 1,800 cubic cm.

If AB = 15 cm, BC = 8 cm andABC = 90

o, find the length of

the prism. [Ans: 30 cm]

6. (a) Obtain the total surface area of a hemisphere having the

diameter 21 cm. [Ans: 1039.50 cm2]

(b) The curved surface area of the givencone is 8,800 sq. cm. If the slant height is

100 cm, determine the height PO of the

cone. [ Ans: 96 cm2]

7. (a) At 18% loss the selling price article of an article is Rs.

164. Calculate the cost price of the article. [Ans: 200]

(b) A radio costing Rs. 6,000 is depreciated per year and 2

years later its price becomes to Rs. 5,415. Find the rate

of depreciation in percent.

[An: 15%]

8. (a) In the given figure, ABCD is arhombus in which the

diagonal AC = 20 cm and the

diagonal BD = 28 cm. If AD is produced to E, find the

area of the BCE. [Ans: 140 cm2]

(b) In the given figure O is the centre of the

circle. If QOR = 110o, calculate the

value of the PSQ. [Ans: 35]

Y

X20O 40 60 80 100

50

100

150

200

250

Marks obtained

C'

A'A

B

C

B'

O R

P

Q

B C

EDA

P Q

R

S O 110

R Q

PS

T


18/35

35 36

9. (a) In the given figure, ABCD is a cyclic

quadrilateral in which AB is produced

to F. If DC || BE, DAB = 92oandFBE = 10

o, evaluate the ADC.

[Ans: 98]

(b) In the given figure, PT is a tangent in

which T is the point of contant. If

PTQ= 75 and STQ = 35, calculatethe QST. [ Ans: 105]

Group 'B' [16 4 = 64]

10. If n(A) = 48, n(B) = 51, n(C) = 40, n(AB) = 11, n(BC) =

10, n(CA) = 9, n(ABC) = 4 and n(U) = 120, find the

values of n(ABC) and n (ABC). Present the above

information in a Venn diagram. [Ans: 113,7]

11. Find the H.C. F. of:

9x2

4y2 8yz 4z

2, 4z

2 4y

2 9x

2 12xy and 9x

2+ 12xz

+ 4z2

4y2

[Ans: 3x + 2y + 2z]

12. Solve : 7x+

343

7x = 56 [Ans: 1,2]

13. Simplify:x + 3

x2+ 3x + 9

+x 3

x2 3x + 9

54

x4+ 9x

2+ 81

[Ans:

2(x 3)

x23x + 9

]

14. A number consists of two digits whose sum is 9. It three

times the number is equal to eight times the number formed

by interchanging the digits, find the number. [Ans: 72]

15. Compute the median from the table given below: [Ans:

49.16]

Marks obtained 2535

3545

4555

5565

6575

7585

No. of students 5 10 12 8 3 2

16. From the roof of a house of 6m tall, the angle of elevation

of the top of a tower was observed and found to be 30. If

the distance between the house and the tower was 19 3 m,

determine the height of the tower.

[Ans: 63 m]

17. Given figure is s solid composed of a cylinder

with hemisphere at one end. If the total surface

area and the height of solid are 770 sq cm. and

14 cm respectively. Find the height of the

cylinder.[Ans: 7cm]

18. Given figure is a square based pyramid. If

the slant height of the pyramid is 17cm and

the side of the base 16 cm, determine the

volume of the pyramid.

[Ans: 1280 cm]

19. A man undertook a contract to finish a piece of work in 32

days and he immediately employed 28 labourers to do the

work. After 24 days only two third of the work was

finished. How many labours should be added to finish thework in time? [Ans: 14]

92

F

E

B

C

D

A10

T

P75

35

S

Q

16cm


19/35

37 38

20. After allowing 16% discount on the marked price of an

article and levying 13% value added tax, then the price of

the article becomes to Rs. 9,492. Find the value added tax.

[Ans: Rs. 1092]

21. A person took a loan of Rs. 46,875. If the rate of compound

interest is 4 paisa per rupee per year, in how many yearswill the compound interest be Rs. 5,853. [Ans 3 yrs]

22. Prove that the centre angle MCN at the center C of a circle

is twice the angle MPN at the circumference standing on the

same arc MN.

23. In the given figure, ABCD is a

parallelogram. If M and N are any pointson CD and DA respectively, prove that

AMB = CDN + ANB.

24. Verify experimentally that the sum of the opposite angles of

a cyclic quadrilateral is two right angles (Two circles of

radii not less than 3cm are necessary).25. Construct a quadrilateral PQRS having PQ = 4.4 cm, QR =

4.9cm, RS = 4.2 cm, SP = 2.8 cm and SQ = 6.6 cm. Draw a

PST equal in area to the quadrilateral.

SET IX

Send-Up Test: 2009

SEDIPSSEDIPSSEDIPSSEDIPS

Answer all the questionsGroup 'A' [9 (2 + 2) = 36]

1. (a) Simplify :5

x + 2 45.5

x 1

16.5x [Ans: 1]

(b) Evaluate:3

24a7b

11

33a

4b

5 [Ans: 2ab

2]

2. (a) Solve: x + 16 = x + 2 [Ans: 9]

(b) Divide 25 into two parts such their product is 156.[Ans: 12, 13]3. (a) Find arithmetic mean from given data: [Ans: 2.94]

x 1 2 3 4 5

f 2 4 6 5 1

(b) Find the class and frequency of first quartile from the

following graph. [Ans: 2 4, 20]

0

20406080

100

120140

2 4 6 8 10 12

Marks

Y

X

4. (a) A card is drawn at a random from a well shuffled packof 52 cards. Find the probability that it is a king or red

card. [Ans:7

13]

(b) A bag contains 10 white and 15 black balls. Two balls

are drawn randomly one by one without replacement.

By drawing tree diagram, show all

the probabilities with possible

outcomes.

MD C

BA

N

S R

QP


20/35

39 40

A

B C

FE

D

12cm

9cm

5. (a) The area of rhombus PQRS is 18 3 sq cm and side of

rhombus is 6cm. Find SPQ. [Ans: 60]

(b) Find the lateral surface area ofgiven triangular prism.

[Ans: 720 cm2]

6. (a) The total surface area of a hemisphere is 1848 sq cm,

find its radius. [Ans: 14 cm]

(b) If the area of the curved surface of a circular prism of

radius 5cm is 660 cm2, find its volume. [Ans: 1650 cm

3]

7. (a) A fruit seller bought 1200 oranges at Rs. 1.50 each . Ifhe sold them at Rs. 21.60 per dozen, find his profit or

loss percent.

[Ans: 20%]

(b) The cost of a motorbike after 3 years becomes Rs.92583 at the rate of depreciation of 10% per annum.

Calculate the original price of the motorbike.[Ans: 127000]

8. (a) In the adjoining figure, AB =

4cm, AC = 5cm and ABC =

90, find the area of

parallelogram ABDE.

[Ans: 12 cm2]

(b) In the given figure, AB is thediameter of a circle with

center O and BOD = 120,

find the value of x. [Ans: 30]

9. (a) In the given circle, O is the

centre of the circle. If QRS

= 130. Find the value of

QOS

[Ans: 100]

(b) In the given figure, ABE is atangent where B is the point

of contact. If AB = BC and

CBE = 50, find DBC. [Ans: 105]

Group 'B' [16 4 = 64]

10. In a class X, 20% students passed in all three subjects, 46%failed in Maths, 57% failed in English, 42% failed in

Science, 35% failed in Math and English, 25% failed in

English and Science, 15% failed in Science and Maths.

(a) Find the percentage of students who failed in all three

subjects.

(b) Draw a Venn -diagram to show the above information. [Ans: 10%]11. Find the HCF of :

8a3 1, 4a

3 2a

2+ 2a 1 and 6a

2+ 11a 7 [Ans: 2a 1]

12. Solve: 51 x

+ 5x 1

=26

5 [Ans: 2, 0]

13. Simplify :1

x 3

2

2x + 3+

1

x + 3

2

2x 3

Ans:54x

(x2 9)(4x

2 9)

14. The sum of the digits of a two digits number is 13. If thedigits are reversed, the new number is 9 less than the

original number. Find the number. [Ans: 76]

15. Find the median from the table given below: [Ans: 60]

Marks

obtained

35

45

45

55

55

65

65

75

75

85

No. of

students

7 8 10 9 6

DE

A B

C

xO

120

B

DA

C

O

S

P

Q

R

O

B

DA

C

E


21/35

41 42

O

A B

CD

O

B

C

D

A

E

F

16. The upper part of the tree broken down by the wind makes

an angle of 30 with the ground and the distance from the

foot to the point where the top of the tree touches the

ground is 50m. What was the original height of the tree?[Ans: 86.6 = 50 3 m]

17. Find the volume of the given solid:

[Ans: 718.66 + 3080 + 616 = 4414.66 cm3]

14 cm

32 cm

12 cm

18. In the given figure, the total

surface area of the given square

based pyramid is 384 sq cm. and

the side of a square base is 12 cm,find the slant height of pyramid.[Ans: 10 cm]

19. Ram takes 16 days and Shyam takes 24 days to finish a

piece of work separately. Ram alone worked for 4 days and

Shyam alone for 6 days. In how many days will theremaining work be finished if they worked together?[Ans: 4.8 days ]

20. A shopeeer sells an article at 8% discount and gains Rs. 40.

If he does not allow any discount, he will gain Rs. 60. At

what price did the purchase the article?[Ans: MP = Rs. 250, CP = Rs. 190]

21. The compound amount of a sum of money in 3 years and 4

years are Rs. 3240 and Rs. 3888 respectively, find the rate

of interest compounded yearly and the sum.[Ans: R = 20%, Rs. 1875]

22. Prove that the parallelograms standing on the same base and

between same parallels are equal in area.

23. In the given figure, O is the

centre of a circle. AB is a

chord, C and D are two points

on AB. If AC = BD and arc

AE = arc BF, Prove that

ACE = BDF.

24. Verify experimentally that the opposite angles of a cyclic

quadrilateral are supplementary. (Two figures with radii of

circle more than 3 cm are necessary)25. Construct a quadrilateral ABCD in which AB = 6.1 cm, BC

= 5.4 cm, CD = 4.9cm, AD = 5.1cm and BD = 5.9 cm. Also

construct a triangle equal to the area of quadrilateral ABCD.


22/35

43 44

O

B

D

A

C

O

BC

DA

SET X

Send-Up Test: 2009

SEDIPSSEDIPSSEDIPSSEDIPS


Group 'A' [9 (2 + 2) = 36]

1. (a) Simplify :7. 3

a 9.3

a 2

3a+2

3a + 1 [Ans: 1]

(b) Evaluate:3

54a7b

9

34a

2b

3 [Ans: 6a

3b

4]

2. (a) Solve: x 4 = x 2 [Ans: 4]

(b) The sum of two numbers is 10 and their product is 21.

Find the numbers. [Ans: 7, 3]3. (a) Find the arithmetic mean from given data: [Ans: 5.06]

x 2 4 6 8

f 3 4 5 3

(b) Find the class and frequency of median from thefollowing graph

[Ans: 40 60, f = 10]

Y

X20O 40 60 80 100

10

20

30

40

50

Mark obtained

60

4. (a) Find the probability of having a number which is prime

or odd when a dice is thrown. [Ans:2

3]

(b) If three children are born in a family, calculate the

probability that all children are girls by drawing a tree

diagram. [Ans:1

8]

5. (a) ABCD is a parallelogramin which ABC = 30,

BC = 12cm and area of

parallelogram ABCD = 54

cm2. Find the measure of

AB. [Ans: 9 cm]

(b) Find the volume of the given prism.[Ans: 30 7 = 79.37cm3]

4 cm 4 cm

6 cm

E D

CB

A

F

6. (a) If the surface area of a sphere is 1386 sq cm, find its

radius.

[Ans: 10.5 cm]

(b) A cone has radius of base 7cm and its slant height is25cm. Find its volume. [Ans: 1232 cm

3]

7. (a) Pravin bought a second hand bike for Rs. 45000. He

spent Rs. 3260 on its repair. If he sold it for Rs. 44520,

find his gain or loss percent. [Ans: 7.74 %](b) The price of a machine is depreciated from Rs. 50000

to Rs. 40500 in two years. Find the rate of depreciation.[Ans: 10%]

8. (a) PQRS is a parallelogram in which the altitude SM on

the side PQ is 6 cm, the altitude SN on the side QR is

5cm and its area is 45 sq cm. Find the sides of the

parallelogram.

[Ans: QR = 9cm, PQ = 7.5 cm]

(b) In the given figure, O is the

centre of the circle. If ACB

= 30, find the value of

DBA. [Ans: 60]

30B C

DA

9 ( ) I h i i l O i h 16 A b h i 1 5 ll i fl i ki Wh h l h f


23/35

45 46

O

B

DA

C

E O

P

C

A

B

E FNM

9. (a) In the given circle, O is the

centre and ABCD is a cyclic

quadrilateral. If ADB = 30,

what will be the value of

BCD? [Ans: 120]

(b) In the given figure, ABE is a

tangent where B is the point

of contact. If AB = BC and

DBC = 105, find DBA .[Ans: 25]

Group 'B' [16 4 = 64]10. In the class IX, 58% students failed in Account, 39% in

English and 25% in Statistics, 32% in Account and English,

19% in Account and Statistics, 17% in English and

Statistics, 13% in all the three subjects.

(a) Draw a Venn -diagram to show above information.

(b) What percent passed in all three subjects. [Ans: 33%]

11. Find HCF of :m

6 1, m

5 + m

3+ m and m

3+ 2m

2+ 2m + 1[Ans: m

2+ m + 1]

12. Solve : 4. 3x + 1

9x= 27 [Ans: 2,1]

13. Simplify:1

x + 1+

2

x2+ 1

+4

x4+ 1

+8

x8 1

Ans:1

x 1

14. A number of two digits is 36 less than the number with the

digits reversed. If the unit digit exceeds twice the tens digit

by 1, find the number [Ans: 37]

15. Find the first quartile from the table given below:[Ans: 88.75]

Wages (Rs.) 50

70

70

90

90

110

110

130

130

150

No. of

workers

5 8 15 12 10

16. A boy who is 1.5m tall is flying a kite. When the length of

the string of kite is 200m, it makes an angle of 30 with

horizontal. At what height is the kite from the ground [Ans: 101.5m]

17. Find the total surface area of

given solid made ofhemisphere and cone.

[Ans: 858 cm2]

24 cm

O

C

C

31 cm

18. The figure is the squarepyramid in which vertical

height OP is 8 cm, and length

of base side is 12 cm, find its

total surface area.[Ans: 384 cm2]

19. A and B can do a piece of work in 24 days. A takes 40 days

to complete the same work. After they work for 8 days, A

leaves. If B completes the remaining work, in how many

days was the whole work completed?

[Ans: 48 days]

20. A shopkeeper sells an article at 5% discount and makes a

profit of Rs. 15. If he does not allow any discount, he will

gain Rs. 25. At what price did he purchase the article?[Ans: MP = Rs. 200,

21. Find the difference between interest compounded yearly

and half yearly on Rs. 16000 in 2 years at 10% p.a.[Ans: Rs. 88.1]22. Prove that the triangles standing on the same base and

between ame parallels are equal in area.

23. In the given figure, M and N are

the mid points of arc AB and arc

AC respectively. Prove that AE =

AF.

(ii) H t d t h d l th 25


24/35

47 48

3cm

5cm

15cm

24. Verify experimentally that inscribed angles standing on the

same arc of a circle are equal. (Two circles of radii at least

3cm are necessary.)

25. Construct a quadrilateral ABCD in which AB = BC = 5cm,

CD = DA = 6 cm and BAD = 60. Also construct atriangle whose area is equal to the area of quad ABCD.

SET XI

National PABSON


Group 'A' [9 (2 + 2) = 36]

1. (a) Simplify :a

2x. a

x 1 a

x

a3x

ax + 1 [Ans:

1

a]

(b) Evaluate:5

32a2b

1c

524a

3b

1c

6 [Ans:

2a

3c]

2. (a) Solve:

3

x

2

1 2 = 0 [Ans:

3](b) When a number increases by 25% it becomes 10. Find

the number.

[Ans: 80]

3. (a) Find the class of the upper quartile of the data.[Ans: 50 60]

Class 0-10 10-

20

20-

30

30-

40

40-50 50-60

No. of

workers

3 4 6 5 11 10

(b) Study the given ogive and answer the following

questions.

(i) How many students have secured distinctionmarks? [Ans: 10]

(ii) How many students have secured less than 25

marks?

[Ans:25]

10 20 3 0 40 50 60 70 80 90 1 00

10

O

20

30

40

5060

70

80

90

100

Marks 4. (a) From a well shuffled pack of cards, a card is drawn at

random. Find the probability of getting the card red or

ace. .

Ans: 7

13

(b) In a bag there are 3 green and 4 red identical balls. If

two balls are drawn at random one after another. Show

all the probabilities in a tree diagram and find the

probability of not getting both balls green without

replacement . [Ans:1

7

]

5. (a) In ABC, AB = 6cm, A = 100 and C = 20. Find

the side BC, if the area of ABC is 12 3 cm2[Ans: 8 cm]

(b) Find the total surface area of the

given triangular prism.

[Ans: 72cm2

]

6. (a) If the radius and height of a right circular cone are 3cmand 4cm respectively, find its total surface area.[Ans: 75.43 cm

2]

(b) The sum of the radius and height of a cylinder is 15cm.

If its base circumference is 44cm, find its volume[Ans: 1235 cm3]

7. (a) An article was sold for Rs. 1560 at the profit of 30%.Find the cost price. [Ans: Rs. 1200]

(b) In how many years will the population of a town be only 40 are fond of playing basketball only If 20 students


25/35

49 50

B M C

DA

O

P

M N

110

Q

O

FE

C

B

A

D

14 cm6cm

12cm12cm

(b) In how many years will the population of a town be

209475 from 190000 at the growth rate of 5% per

annum? [Ans: 2 yrs]

8. (a) In the adjoining figure, ABCD

is a trapezium in which AD //

BC and AD =1

2BC. If the area

of ABCD is 120 cm2and height

(DM) = 5cm, find the area of

ADC. [Ans: 40 cm2]

(b) In the given circle, O is thecentre and ABC = 150. Findthe value of x. [Ans: 60]

9. (a) In the given circle O is the

centre and MNQP is a cyclic

quadrilateral. If MPQ = 110,

find QMN. [Ans: 20]

(b) In the given figure O is the

centre of the circle EBF is a

tangent where B is the point of

contact. If AB is a diameter and

DBF = 72, find the value of

BCD. [Ans: 108]

Group 'B' [16 4 = 64]

10. In a survey of 200 students, 70 are fond of playing cricket,

80 football and 100 basketball. Similarly 20 are fond of

playing cricket and football only, 30 cricket and basketball

only, 40 are fond of playing basketball only. If 20 students

are fond of playing football and basketball only, by drawing

a Venn-diagram. Find

(i) the number of students who play all games.

(ii) how many students don't play any game? [Ans: 10, 40]

11. Find the HCF and LCM of :a

2+ b

2 c

2 + 2ab, b

2+ c

2 a

2+ 2bc and c

2+ a

2b

2+ 2ca.

[Ans: HCF = a + b + c, LCM = (a + b + c) (a + b c)

(a + c b) (b + c a)]

12. Solve:5x 4

5x + 2 = 2 +

5x 3

2 [Ans: 5]

13. Simplify:

1

a 3

1

a 1+

1

a + 3

1

a + 1[Ans:

16a

(a2 9) (a2 1) ]

14. A number of two digits exceeds seven times the sum of the

digits by 6. If 45 subtracted from the number, the digits are

interchanged. Find the number. [Ans: 83]

15. Find the median from the given data. [Ans: 16.875]

Age 5 -10 10

15

15

20

20

25

25

30

30

35

No. ofstudents

6 7 8 4 5 2

16. A man of height 1.68 m observes a pillar of height 31.68m

and finds the angle of elevation of the top of the pillar to be

60. How far is the man from the base the pillar. [Ans: 17.32m]

17. Find the volume of the solid given alone side. [Ans 667.33 cm2]

7 cm

15 cm

18. Find the total surface area of the

given solid figure which is the

combination of prism and pyramid. [Ans: 672 cm2]

O

BA

C150x

19 A tap can fill 25% of a tank in 3 hours and another tap can SET XII


26/35

51 52

A

B

C

D

F

P

Q

A

B C

D

40

80

43cm

26cm

19. A tap can fill 25% of a tank in 3 hours and another tap can

empty whole tank in 15 hours. If both the taps are opened at

the same time and the capacity of a tank is 1000 liter in

what time 100 liter water will be collected in the tank.[Ans: 6 hrs]

20. After allowing 7% discount on the marked price and

levying 11% VAT, an article is sold. If the amount of VATis Rs. 102.30, find the marked price of the article and the

discount amount.

[Ans: MP = Rs. 1000, Discount = Rs. 70]

21. The simple interest on certain sum of money in 3 years at

30% per annum will be Rs. 1188 less than the compound

interest. Find the sum.

[Ans: Rs. 4000]

22. Prove that a rectangle and the parallelogram standing on the

same base and between the same parallel lines are equal in

area.

23. In the given figure if BC{ = DC{ ,

prove that PQ // DB.

24. Verify experimentally that the length of two tangents to a

circle at the point of contact from an external point are

equal. (Two circles of radii more than 3cm are necessary)

25. Construct a triangle PQR in which PQ = 7cm, QR = 5.5cm

and PR = 6cm. Construct a parallelogram OMNQ equal in

area to the triangle PQR such that OQ = 8cm.

SET XII

J.S.T. Examination, 2065

Attempt all the questions.

Group "A" [9 (2 + 2) = 36]

1. (a) Evaluate:

356 24

7 5

426 2076 [Ans: 1]

(b) Simplify:

3128 +

454

3250

4

500 108

[Ans:1

21

3

]

2. (a) Solve: 3x 3

= 32 x

[Ans: 1,9]

(b) A number is such that it is as much greater than 21 as itis less than 37. Find the number. [Ans: 29]

3. (a) In a data X

= 10.4, fx = 1040 and N = 25P what is

the value of P?

[Ans: 4]

(b) From the given ogive in thefigure, find the first quartile.

[Ans: 8 .67]

4. (a) A dice is rolled once. Write the sample space and find

the probability that the outcome is either a prime

number or an even numbers. [Ans: S = {1,2,3,4,5,6};5

6)

(b) There are 5 black and 8 white balls of same shape andsize in a basket. If two balls are drawn randomly in

succession without replacement from the basket. Show

the probability of all possible outcomes in tree diagram.

Y

X4O 8 12 16 20

4

8

12

16

20

Marks obtained

9 (a) In the figure O is the centre of


27/35

53 54

A

B

C

A'

B'

C'h

6cm

8cm

8 cm

140cm

O

CD

A 35

x

B

OC

AB

8 cm

5. (a) Find the area of the adjoining

parallelogram.[Ans: 968.18 cm2]

(b) What value of h in the prism

shown in the figure makes itstotal surface area 528 cm

2?[Ans: 20cm]

6. (a) Find the curved surface area

of the given cylinder.[Ans: 3520 cm2]

(b) A cone whose radius of base is 7cm has a volume of1232 cm

3, Find the height of the cone. [Ans: 24cm]

7. (a) If a shopkeeper sold a watch for Rs. 640 at a loss of

20% . Find the cost price of the watch. [Ans: 800]

(b) A motorcycle which was purchased at Rs. 90000 wassold for Rs. 81000 after one year. At what percent was

it depreciated?

[Ans: 10 %]

8. (a) In the given figure parm. BCDE

and AED stand on same base

and between the same parallel

lines. The area of AED is

32cm2. Find the area of BCD.[Ans: 32 cm

2]

(b) In the adjoining figure O is the

centre of circle. Find the value

of x. [Ans: 125]

9. (a) In the figure, O is the centre of

circle. If OBC = 60 and BC

//OE, then find the measure of

BAE. [Ans: 60]

(b) From the given information infigure, find the measure of AB.[Ans: 15 cm]

Group "B" [16 4 = 64]10. In a survey of a group of people, showed that: 60 liked tea,

45 liked coffee, 30 liked milk, 25 liked coffee as well as tea.

20 liked tea well as milk, 15 liked coffee as well as milk

and 10 liked all the three. How many people were asked this

question? Solve by drawing the Venn-diagram. [Ans: 85]

11. Find the LCM of :

3x

2

+ 12x + 12, x

2

ax + 2x 2a, x

2

3x 10[Ans: 3(x + 2)

2(x a) (x 5)]

12. If a + b + c = 0 prove that:

1

xb+ x

c+ 1

+1

xc+ x

a+ 1

+1

xa

+ xb

+ 1 = 1

13. Simplify:

1

1 + yx

+1

xy y

x

1

1 + y

2

x2

1

x

2

y2 y

2

x2

[Ans:x

2y

2

x

4

y

4]

14. The product of the present ages of two brothers is 160. 4

years ago. elder brother was twice as old as is younger

brother. Find their present ages. [Ans: 16 yrs, 10 yrs]

15. The following table shows the age of the workers of a

factory in a village. Find the third quartile. [Ans: 51.5]

Age 20 - 30 - 40 50 60

B C

D

A

E

O

C

E

A

60

B

30 40 50 60 70 23. In the figure, AB // ED, BF //DC


28/35

55 56

O

A

P

A'

A B

C

DE

F

30 40 50 60 70

No. of

worker

5 9 10 6 4

16. A man 1.6m tall, observes the top of a pillar of the height

26.6m situate d in front of him and the angle of elevation to

be 30. How far is the man from the pillar? Find it. [Ans: 43.3 m]

17. The given figure is a solid made of

cone and an hemisphere in which

OA = OA' = 7cm. A'P = 25cm, find

the volume of the given solid

objects. [Ans: 1950.67 cm3]

18. Given figure is combined form of

pyramid and cubical prism. If the

area of the base of cubic prism is

144 cm2and height of the obtained

figure is 20cm. Find the total

surface area of the given figure.[Ans: 960 cm2]

19. A man undertakes to do a certain job in 32 days. He hires12 men for the job. At the end of 8 days only one fifth of

the work was completed. How many extra men must be

employed in order to complete the work in time. [Ans: 4]

20. When an article is sold at a discount of 10% of marked

price, a profit of Rs. 8 is earned by the seller. If the same

article was sold without allowing a discount a profit of Rs.20 is earned. What should be the cost price of the article.[Ans: Rs. 100]

21. Find the compound amount and compound interest on Rs.

600 at 5% p.a. for 11

2 years interest is payable half yearly. [Ans: 646.13, Rs. 46.13]

22. Prove that the opposite angles of cyclic quadrilateral are

supplementary.

23. In the figure, AB // ED, BF //DC

and BF = DC. Prove that AFE =1

2 quadrilateral BFDC.

24. Verify experimentally that the angle at the circumference isequal to half of the angle at the centre, both standing on the

same arc of a circle. (Two circles of radii not less then 3cm

are necessary.)

25. Construct a triangle ABC having AB = 7.1cm, BAC = 60

and AC = 5.7cm. Also construct a parallelogram having one

side 7.5cm and equal in area to the triangle ADC.

20 cm

SET XIII

the probability that he will solve at least two problems


29/35

57 58

010

30

40

50

10X

Y

20

60

20 30 40 50 60 7 0 80Markes obtained

8 cm

20 cm

M N

RP

6 cm

SET XIII

Joint S.L.C. Send-up Examination 2065

(KUHS/RBS/SXG/SXT]


Group 'A' [9 (2 + 2) = 36]

1. (a) Simplify :3. 9

x + 1+ 9.3

2x 1

12. 32x

6.9x [Ans: 5]

(b) Evaluate :4

128 a3

42

1a

9 [Ans: 4a

3]

2. (a) Solve : x + x 20 = 10 [Ans: 36]

(b) 250 bananas were divided equally among a certain

number of students. If there were 25 more students,each would receive half banana less. Find the total

number of students. [Ans: 25]

3. (a) The arithmetic mean of 15 members is 12. When two

numbers are eliminated the mean becomes 11. If the

difference of the two eliminated numbers is 3, find the

numbers. [Ans: 20, 17]

(b) Find the median of the

data related to the figure

given alongside.

[Ans: 40]

4. (a) A boy can solve a problem accurately with a

probability of4

5

. If he is given three problems, what is

p y p

accurately? [Ans:48

125]

(b) A bag contains 15 red balls and 20 white balls. Two

balls are taken randomly one after the other without

replacement. Find the probability of getting the balls ofsame color showing all the possible outcomes in the

tree diagram. [Ans:59

119]

5. (a) In the given figure along side, if

the area of the kite is 48 cm2,

find the measure of PRQ. [Ans: 30]

(b) Find the volume of the given

triangular prism. [Ans: 346.4 cm3]

6. (a) The circumference of the base of the cylinder is 44cm

and the sum of its radius and height is 17cm. Find the

total surface area of the cylinder. [Ans: 748 cm2]

(b) If the total surface area of the hemisphere is 462 cm2,

find its volume. [Ans: 718.67 cm3]

7. (a) If the selling price of an article is less by1

4 of the cost

price, find the profit or loss percentage. [Ans: 25%]

(b) A computer, which is supposed to depreciate at the rate

of 5% per annum, was sold at Rs. 36100 after two

years. At what price was it bought? [Ans: Rs. 40,000]

8. (a) In the given figure, MNRP is a

trapezium in which MN // PR,

MNR = PRN = 90, NR =

8cm, PM = 10cm and MN =

6cm. Calculate the area of thetrapezium MNRP.

R

S

P

Q

OO8 cm


30/35

22. Prove that the areas of the parallelogram on the same bas e

SET XIV


31/35

61 62

E

C

BH

D

A

LK

and between the same parallel lines are equal.

23. ABCD is a cyclic quadrilateral. AB

and DC produced to meet at E, the

circle with center E and radius EC

cuts AB at H and HC, BC meet ADat K, L, respectively. Prove that CL

= KL.

24. Verify experimentally that the sum of the opposite angles of

a cyclic quadrilateral is 180. (Two circles of radii not less

than 3 cm are necessary)

25. Construct a triangle equal on area with the given

quadrilateral ABCD in which AB = 4cm, BC = 5cm, CD =

4.5cm, DA= 6cm, and diagonal AC = 7cm.

JOINT S.L.C. SEND-UP EXAMINATION-2065

Attempt all the questions.

Group A [ 10(2+2)=40]

1. a Simplify:

3.4x + 3

2.4x + 2

5.42 + x

3.4x + 1

[Ans:

40

17]

b. Evaluate:3

16x5

y7

52x

2y

4 [Ans: 2xy]

2. a. Solve : x + x2- 3 = 3 [Ans: 2]

b. Rs.60 was divided equally among a certain number of

boys. If there were 2 more boys, each would receive

Rs.1 less. Find the total number of boys and the total

amount of money.[Ans:Rs. 60, Rs.10]

3. a. The arithmetic mean of 25 numbers is 8. If the three

numbers, which are in the ratio of 2:3:4 are added, the

mean becomes 8.75, find those three number

[Ans: 10,15,20]

b. Find the median of the data related to the figure given

alongside.[Ans: 15]

0

10

30

40

50

5X

Y

20

60

10 15 20 25 30 35Age of people

4. a. The probability of a day to be fine is 2/5. What is the

probability of having only one day to be fine out of

three days ? [Ans: 54/125]

b. A bag contains 5 red balls and 4 white balls of same

size. Two balls are taken randomly one after otherwithout replacement . Find the probability of getting

the balls of different colors showing all the possible

i h di [A 5/9]


32/35

63 64

R

S

P

Q

OO

8 cm

6 cm

10 cm

O

40

D

B

E

A

C

QAD

C

B

P

outcomes in the tree diagram . [Ans: 5/9]

5. a. In the given figure along side, if

QR=8cm,PR=12cm and

PRQ=30, find the area ofkite. [Ans: 48cm

2]

b. Find the surface area of the

given triangular prism.[Ans: 155cm2]

6. a. The circumference of the base of a cylinder is 88cmand the sum of its radius and height is 40 cm. Find the

volume of the cylinder

[Ans: 3520cm3]

b. If the total surface area of a hemisphere is 462 cm2, find

its curved surface area. [Ans: 308cm2]

7. a. If the cost price of an article is less by 1/4 of its selling

price, find the profit of loss percentage. [Ans: 33%]

b. The population of a town at the beginning of the

previous year was 10,000. If it is believed that the

population is growing at the rate of 4%,6% and 8% in

the respective years, what will be the population at the

end of the next year ? [Ans: 11906]

8. a. In the given figure, ABCD is a

trapezium in which AB//DC,

ABC = BCD = 900 , BC =8cm and AD = 10cm . If the

area of the trapezium is 72 cm2,

calculate the length of the AB.[Ans: 6cm]

b. In the given figure , If AE//CD,

CBA = 920

and EAR=200

.find the value of BCD.[Ans: 108

0]

9. a. In the given figure, AB is the

diameter and AB//CD. If

BEC= 400, find the value of

BCD. [Ans: 500

]

b. P and Q are centers of circleswhich touch at A. BC is a direct

common tangent. Find the

measure of

BAC.[Ans: 90]

Group - B [164=64]

10. In a group of students, 20 study accountancy, 21 studymathematics,18 study history, 7 study accountancy only, 10

study mathematics only, 6 study accountancy and

mathematics only, 3 study mathematics and history only .

(i) Represent the above information in the Venn diagram.

(ii) How many students study all the subjects ?

(iii) How many students are there altogether ? [Ans: 2, 41]

11. Find the H.C.F. of :

( a + c)( a - c ) + b ( 2a + b )( b + a ) ( b - a ) + c ( 2b + c )

and ( c + b ) ( c - b ) + a ( 2c + a ) [Ans: a + b

+c]

12. Solve : 5x-5

+ 54-x

= 11

5 [Ans: 4 and 5 ]

13. Simplify :1

x + 1+

2

x2+ 1

+4

x4+ 1

+8

x8 1

[Ans:1

x 1]

14. Tara said to Sabittre, '' I am half as old as you will be when

I will be as old as you are.'' If the sum of therir present ages

is 50, find their present ages. [Ans: 20 years,30 years]

A B

CD

R

E

AB

C

D

92 20


33/35

PY

24


34/35

67 68

20 cm

3.5 cm

W

X Y

Z

O

O

Q R

3525

DC

AB

32

70

E

P

QS

T

R

36

X4O 8 12 16 20

4

8

12

16

20

Marks24

4. a. A Card is drawn from a well shuffeled pack of 52

cards. Find the probability of not getting a black face

card . [Ans: 23/26]

b. A ball is drawn from a bag containing 4 black and 7

white balls randomly and not replaced, then another

ball is drawn, Draw the tree diagram to show the

probabilities.5. a. Find the area of Quadrilateral

ABCD. [Ans: 45 cm2]

b. Find the volume of given

triangular prism. [Ans: 480cm

3]

6. a. What is the total surface area of

given hemisphere .[Ans: 115.5cm2]

b. Find the area of the curved surface of a cone whoseslant height is 25 cm and height is 24 cm. [Ans: 550cm

2]

7. a. Find the profit percent when 6 pens are sold for the cost

price of 9 pens. [Ans: 50%]

b. A motorcycle of Rs. 1,00,000 is depreciated at 10% p.a.

find its value after one year . [Ans: 90000]

8. a. In given figure WZ// XY Provethat WOX=YOZ .

b. Find QPR From figure.

[Ans: 60]

9. a. In adjoining figure,

BDC=320, ABE= 70

0find

the measure of ACB.[Ans: 380]

b. In figure PTQ=360 and

PT=TQ then find the value of

STQ. [Ans: 72]

Group 'B'

Group - B ( 164=64)

10. Among 100 students of a school, 85 students like

Arithmetics, 65 like Geometry and 10 students did not like

both. Then, find .(i) How many like both ( Geometry and Arithmetic)

(ii) How many like Geometry only .

(iii) Show these information in Venn-diagram [Ans: 60, 5]

11. Find the LCM of :

2a3+ a

2+ a +2 and a

3- a

2+ a - 1 [Ans: a + 1]

12. Solve :

a 4

a 2 = a + 16 [Ans: 9]

75

115

35

BA

D C

8 cm

13. Simplify:1

a + x +

2a

a2

+ x2 +

4a3

a4

+ x4

8a7

a8

x8 [Ans:

1

x a]

23. In figure, O Is the center of circle,

AC is the chord If BT=TC Prove


35/35

69 70

20 cm

5.6 cm

O

C

A

T

E

p ya + x a + x a + x a - x x a

14. The difference between the length and breadth of arectangular field is 4 m. If the area of the field is 96 m

2, find

its perimeter. [Ans: 40 m]

15. Calculate third quartile(Q3) from data : Ans: 16.43]Marks obtained 25 35 45 55 65 75

No. Of Student 5 6 8 10 7 4

16. The angle of elevation of a tower was observed to 450.

From a point on walking 100m away from the tower. it was

found to be 300. Find the height of the tower . [Ans: 136.6m]

17. Find the volume and total surface

area of given cylinder with

hemispherical ends. [Ans: 2707.11cm3, 1098.24cm

2]

18. Find the total surface area of square based pyramid whose

base is 6 cm and height is 4 cm . [Ans: 96cm2]

19. Madan Bahadur and Hari Bahadur can do a piece of work in20 days and 50 days respectively. They both started the

work together and Hari Bahadur left after 5 days. In how

many days will Madan Bahadur finish the remaining work? [Ans: 13 days]

20. The price of an article is marked at 25% above the costprice. If it is sold at a profit of Rs. 125 after allowing 15%

discount, what will be the selling price. [Ans: 132.80]

21. A certain sum of money amounts to Rs. 1323 in 2 years and

Rs. 1389.15 in 3 years. Find the compound rate of interest

and sum.

[Ans: R=5%, Rs.145.86]

22. Prove that the parallelograms standing on same base and

between the same parallels are equals in area.

AC is the chord. If BT=TC. Prove

that OAT=OBT.

24. Experimentally verify that sum of opposite angle of a cyclicquadrilateral are supplementary. (Two circles of radii not

less than 3 cm are necessary)

25. Construct a triangle ABC in which AB = 4.2 cm, BC = 5.4

cm and AC =5.8 cm Construct a parallelogram with an

angle 600and its area equal to triangle ABC.

slc que coln

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