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 ?
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
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
(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
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
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 ?
52. If the length of radius of a right circular cylinder is doubled and height is halved, the lateral surface area will be
(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.
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
(C) Any angle
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
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
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)
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 ?
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
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