# Mensuration – Math – Paper VI – WBCS Main Question Paper

## WBCS Main Question Paper – 2018

2. If a square and a rectangle having the same perimeter and their areas are S and R respectively then

(A) S = R

(B) S > R

(C) S < R

(D) None of the above

3. A parallelogram, a rectangle and triangular region stands on same base and between same parallel and if their area are P, R and T respectively, then

(A) P = R = 2T

(B) P = R = T/2

(C) 2P = 2R = T

(D) P = R = T

6. Which of the following geometric figure has diagonals equal in length ?

(A) Parallelogram

(B) Rhombus

(C) Trapezium

(D) Rectangle

14. The measures of two angles of a triangle are 35°57’4″ and 39°2’56”, then circular value of third angle is

(A) 7π / 12

(B) π / 20

(C) 5π / 12

(D) π

15. If the length of shadow on the ground of a post is √3 times of its height, the angle of elevation of the Sun is

(A) 30°

(B) 45°

(C) 60°

(D) None of the above

16. If the numerical values of total surface area and volume of a cube are equal, then the length of its diagonal is

(A) 6√3

(B) 6

(C) 6√2

(D) 3√6

22. A hemisphere can with internal radius of 9 cm is completely filled with water. Someone is requested to fill this water in a cylindrical bottle with a diameter of 3 cm and height of 4 cm. The number of bottles to be required to make the can empty is

(A) 54

(B) 128

(C) 36

(D) 256

23. The Length of radius of spherical gas balloon increases from 7 cm to 21 cm as air being pumped into it. The ratio of surface areas of the balloon in two cases is

(A) 9 : 1

(B) 49 : 21

(C) 1 : 9

(D) 7 : 441

37. What is the volume of the cube (in cubic cm) whose diagonal measures 4√3 cm ?

(A) 8

(B) 16

(C) 27

(D) 64

52. If the length of radius of a right circular cylinder is doubled and height is halved, the lateral surface area will be

(A) equal

(B) double

(C) half

(D) 4 times

53. The length of a radius of a circle is 13 cm. and the length of a chord of the circle is 10 cm., the distance of the chord from the center of the circle is

(A) 12.5 cm.

(B) 12 cm.

(C) √69 cm.

(D) 24 cm.

54.

The diagonals PR and QS of the rhombus intersect each other at the point O. What is the value of ∠POS∠POS ?

(A) Insufficient information

(B) 90°

(C) Any angle

(D) 45°

55. If (0,0), (4, -3) and (x, y) are collinear then

(A) x = 8, y = – 6

(B) x = 8, y = 6

(C) x = 4, y = – 6

(D) x = – 8, y = 6

56.

In the above figure AD | | BC, AD = 10 cm, BC = 5cm, CD = 10 cm. The area of ABCD is

(A) 150 sq.cm

(B) 75 sq.cm

(C) 500 sq.cm

(D) 250 sq.cm

60. If area of circular field is X sq. unit, perimeter is Y unit and length of diameter is Z unit then the value of X/YZ is

(A) 1/2

(B) 1/4

(C) 1

(D) 1/8

63. A circular lawn has an area of 154 sq. meter. A path of 7 meter width surrounds the lawn. What is the area of the lawn including the path ? (in sq. meter)

(A) 580

(B) 516

(C) 616

(D) 637

70. The area of a circle is 2464 square meters. What will be its circumference ?

(A) 132 m

(B) 176 m

(C) 231 m

(D) 272 m

87. The poles of heights 6m and 11m stand vertically on a plane ground. If the distance between their feet is 12m, what is the distance between their tops ?

(A) 12.8m

(B) 13m

(C) 14m

(D) 15m

91. A circular copper wire of radius 7 cm is bent to form a rectangle. If breadth and length of the rectangle are in the ratio of 4 : 7 respectively, what is the breadth of the rectangle ? (in cm.)

(A) 8 cm.

(B) 14 cm.

(C) 10 cm.

(D) 12 cm.

96. A horse is tied to a post by a rope. If the horse moves along a circular path, always keeping the rope tight and describes 88 m when it traces 72° at the centre, then the length of the rope is

(A) 35m

(B) 70m

(C) 17.5m

(D) 22m

45. A river 1.5 m deep and 36 m wide is flowing at the rate of 3.5 km per hour. The amount of water that runs into the sea per minute (in cubic meter) is

(A) 3150

(B) 31500

(C) 6300

(D) 63000