### Find solutions for all the questions at the end of each set:

### Set A

1.Ratio of the number of sides of two regular polygons is 5 : 6 and the ratio of their each interior angle is 24 : 25. Then the number of sides of these two polygons are

(1) 20,24

(2) 15, 18

(3) 10, 12

(4) 5, 6

2.The base of a right prism is a trapezium. The lengths of the parallel sides are 8 cm and 14 cm and the distance between the parallel sides is 8 cm. If the volume of the prism is 1056 cm3, then the height of the prism is

(1) 44 cm

(2) 16.5 cm

(3) 12 cm

(d) 10.56 cm

3.The right angled sector of radius r cm is rolled up into a cone in such a way that the two binding raddi are joined together. Then the curved surface area of the cone is

(1) pi.r^2 cm^2

(2) 4pi.r^2 cm^2

(3) (pi.r^2)/4 cm^2

(4) 2pi.r^2 cm^2

4.The areas of curved surface of a right circular cylinder and a sphere are equal. If the raddi of the cylinder and the sphere be equal, then the ratio of their volumes will be

(1) 2 : 3

(2) 3 : 2

(3) 3 : 4

(4) 4 : 3

5.If the four equal circles of radius 3 cm touch each other externally, then the area of the region bounded by the four circles is

(1) 4(9-pi)sq.cm

(2) 9(4-pi)sq.cm

(3) 5(6-pi)sq.cm

(4) 6(5-pi)sq.cm

6.The adjacent sides of a parallelogram are 36 cm and 27 cm in length. If the distance between the shorter sides is 12 cm, then the distance between the longer sides is

(1) 10 cm

(2) 12 cm

(3) 16 cm

(4) 9 cm

7.The height of a solid right circular cylinder is 6 metres and three times the sum of the area of its two end faces is twice the area of its curved surface. The radius of its base, in metre, is

(1) 4

(2) 2

(3) 8

(4) 10

8.Two circles touch each other externally at point A and PQ is a direct common tangent which touches the circles at P and Q respectively. Then angle PAQ =

(1) 45°

(2) 90°

(3) 80°

(4) 100°

9.The in-radius of an equilateral triangle is of length 3 cm. Then the length of each of its medians is

(1) 12 cm

(2) 9/2 cm

(3) 4 cm

(4) 9 cm

10.ABCD is a cyclic trapezium whose sides AD and BC are parallel to each other. If angle ABC = 72°, then the measure of the angle BCD is

(1) 162°

(2) 18°

(3) 108°

(4) 72°

ANSWER KEY:

1. (3) 10, 12

2. (3) 12 cm

3. (3) (pr^2)/4 cm^2

4. (2) 3 : 2

5. (2) 9(4-p)sq.cm

6. (4) 9 cm

7. (1) 4

8. (1) 45°

9. (4) 9 cm

10. (4) 72°

### Find solutions for all the questions at the end of each set:

### Set B

1.The ratio of the ages of Maala and Kala is 4 : 3. The total of their ages is 2.8 decades. The proportion of their ages after 0.8 decades will be [1 Decade = 10 years]

A) 4:3

B) 12:11

C) 7:4

D) 6:5

2.In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is :

A) 19

B) 29

C) 39

D) 49

3.Sivagami is 2 years elder than Meena. After 6 years the total of their ages will be 7 times of their current age. Then age of Sivagami is :

A) 19 years

B) 17 years

C) 15 years

D) data inadequate

4. Proportion of Yuvaraj’s age to Ganguly’s age is 4:3. Yuvaraj willl be 26 years old after 6 years. What is the age of Ganguly now ?

A) 17 years

B) 15 years

C) 19 years

D) 12 years

5.A person’s present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?

A) 36

B) 38

C) 40

D) 42

6.If Raj was one-third as old as Rahim 5 years back and Raj is 17 years old now, How old is Rahim now?

A) 40

B) 41

C) 36

D) 48

7.A man’s current age is (2/5) of the age of his father. After 8 years, he will be (1/2) of the age of his father. What is the age of father at now ?

A) 50

B) 40

C) 33

D) 30

8.The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A ?

A) 12

B) 13

C) 14

D) 15

9.A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is

A) 20

B) 21

C) 22

D) 23

10.A father said his son , ” I was as old as you are at present at the time of your birth. ” If the father age is 38 now, the son age 5 years back was :

A) 14

B) 19

C) 33

D) 38

Answers

1.D

2.C

3.D

4.B

5.C

Let the mother’s present age be X years

Then,the person’s present age = 2/5*x years

therefore, 2/5*X+8 = 1/2*(X+8)

X = 40

6.B

7.B

let, Father’s current age is A years

then, Man’s current agr = (2/5)A years

therefore (2/5)A+8 = (1/2)(A+8)

A= 40

8.A

9.C

10.A

let the son’s present age be X years. Then (38-X)= x

x = 19

son’s age 5years back = (19-5)= 14 YEARS

### Find solutions for all the questions at the end of each set:

### Set C

1. Find the number of bricks, each measuring 24 cm x 12 cm x 8 cm, required to construct a wall 24 m long, 8m high and 60 cm thick, if 10% of the wall is filled with mortar?

A) 35000

B) 45000

C) 55000

D) 65000

2. How many bricks each measuring 25cm x 11.25cm x 6cm, will be needed to build a wall 8m x 6m x 22.5m

A) 5600

B) 600

C) 6400

D) 7200

3. In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

A) 75 m3

B) 750 m3

C) 7500 m3

D) 75000 m3

4. A cuboidal block 6cmx9cmx12cm is cut up into an exact number of equal cubes.The least possible number of equal cubes will be

A) 6

B) 9

C) 24

D) 30

5. A rectangular box measures internally 1.6m long, 1m broad and 60cm deep. The number of cubical box each of edge 20cm that can be packed inside the box is:

A) 30

B) 60

C) 90

D) 120

6. Find the ratio of the surfaces of the inscribed and circumscribed spheres about a cube.

A) 1:2

B) 1;3

C) 1:4

D) 1:5

7. If the volume of the cube is 729cm^3, then the surface area of the cube will be

A) 486cm^2

B) 456cm^2

C) 446cm^2

D) 476cm^2

8. 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

A) 84

B) 90

C) 168

D) 336

9. A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8m, the volume of the box (in m3) is:

A) 4830

B) 5120

C) 6420

D) 8960

10. The diagonal of the floor of a rectangular closet is 7 1/2 feet. The shorter side of the closet is 4 1/2 feet. What is the area of the closet in square feet?

A) 5 1/4

B) 13 1/2

C) 27

D) 37

Answers:

1.B

Volume of the wall = (2400 x 800 x 60) cm^3

Volume of bricks = 90% of the volume of the wall= [(90/100) x 2400 x 800 x 60] cm^3

Volume of 1 brick = (24 x 12 x 8) cm^3

Number of bricks=(90/100) x (2400 x 800 x 60) / (24 x 12 x 8)=45000

2.C

no. of bricks= volume of the wall/volume of 1 brick = (800 x 600 x 22.5) / (25 x 11.25 x 6) = 6400

3.B

4.C

Volume of block=(6x9x12) cm^3 = 648 cm^3

Side of largest cube = H.C.F of 6,9,12 = 3cm

Volume of the cube=(3x3x3)=27 cm^3

Number of cubes=(648/27)=24

5. D

6. A

7. A

8. A

9. B

10.c