Mock Quant Test for Trigonometry and Mensuration 1(20 Qn) 15min for all Govt. Exams

Solution

1.The Co-ordinates of the centroid of the triangle ABC are (6, 1). If two vertices A and B are (3, 2) and (11, 4) find the third vertex

(a) (4, –3) (b) (2, 1) (c) (2, 4) (d) (3, 3)

2.In a triangle ABC, the lengths of the sides AB, AC and BC are 3, 5 and 6 cm, respectively. If a point D on BC is drawn such that the line AD bisects the angle A internally, then what is the length of BD ?

(a) 2 cm (b) 2.25 cm (c) 2.5 cm (d) 3 cm

3.Arc ADC is a semicircle and DB  perpendicular to  AC. If AB = 9 and BC = 4, find DB.

(a) 6 (b) 8 (c) 10 (d) 12

4.The perimeter of the triangle whose vertices are (– 1,4),(– 4, –2), (3, –4), will be :

(a) 38 (b) 16 (c) 42 (d) None of these

5.The distance between two parallel chords of length 8 cm each in a circle of diameter 10 cm is

(a) 6 cm (b) 7 cm (c) 8 cm (d) 5.5 cm

6.Two parallel chords of a circle of diameter 20 cm are 12 cm and 16 cm long. If the chords are in the same side of the centre, then the distance between them is

(a) 28 cm (b) 2 cm (c) 4 cm (d) 8 cm

7.Two circles with radii 25 cm and 9 cm touch each other externally. The length of the direct common tangent is     

(a) 34 cm (b) 30 cm (c) 36 cm (d) 32 cm

8.A and B are centres of the two circles whose radii are 5 cm and 2 cm respectively. The direct  ommon tangents to the circles meet AB extended at P. Then P divides AB.

(a) externally in the ratio 5 : 2 (b) internally in the ratio 2 : 5 (c) internally in the ratio 5 : 2 (d) externally in the ratio 7 : 2

9.When two circles touch externally, the number of common tangents are

(a) 4 (b) 3 (c) 2 (d) 1

10.If the inradius of a triangle with perimeter 32 cm is 6 cm, then the area of the triangle in sq. cm is

(a) 48 (b) 100 (c) 64 (d) 96

11.If the diagonal of a square is doubled, then its area will be

(a) three times (b) four times (c) same (d) none of these

12.A square is inscribed in a circle of radius 8 cm. The area of the square is

(a) 16 cm² (b) 64 cm² (c) 128 cm² (d) 148 cm²

13.A wire is bent into the form of a circle, whose area is 154 cm². If the same wire is bent into the form of an equilateral triangle, the approximate area of the equilateral triangle is

(a) 93.14 cm² (b) 90.14 cm² (c) 83.14 cm² (d) 39.14 cm²

14.A metal pipe of negligible thickness has radius 21 cm and length 90 cm. The outer curved surface area of the pipe in square cm is

(a) 11880 (b) 11680 (c) 11480 (d) 10080

15.A garden is 24 m long and 14 m wide. There is a path 1 m wide outside the garden along its sides. If the path is to be constructed with square marble tiles 20 cm × 20 cm, the number of tiles required to cover the path is

(a) 1800 (b) 200 (c) 2000 (d) 2150

16.If the radius of a sphere is increased by 2 cm, then its surface area increases by 352 cm². The radius of the sphere before the increase was:

(a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm

17.A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio 5 : 12, then the ratio of the total surface area of the cylinder to that of the cone is

(a) 3 : 1 (b) 13 : 9 (c) 17 : 9 (d) 34 : 9

18.A cylinder is filled to 4/5th its volume. It is then filled so that the level of water coincides with one edge of its bottom and top edge of the opposite side, In the process, 30 cc of the water is spilled. What is  the volume of the cylinder?

(a) 75 cc (b) 96 cc (c) Data insufficient (d) 100 cc

19.A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of  radius 9 cm. The percentage of the wood wasted is:

(a) 25% (b) 30% (c) 50% (d) 75%

20.A conical vessel, whose internal radius is 12 cm and height 50 cm, is full of liquid. The contents are emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the liquid rises in the cylindrical vessel.

(a) 18 cm (b) 22 cm (c) 24 cm (d) None of these