Advance Quant Quiz For SSC Mains And SSC CHSL Exam

1. The base of a right prism is a triangle whose side are 13, 14 and 15 cm. If the height of the prism be 10 cm, then its volume is

(a) 420 cubic cm

(b) 840 cubic cm

(c) 588 cubic cm

(d) 580 cubic cm

2. If the total surface area of a cube is 96 cm^2, then its volume is

(a) 125 cm^3

(b) 108 cm^3

(c) 96 cm^3

(d) 64 cm^3

3. If the radius of a cylinder is decreased by 50% and the height is increased by 50% to form a new cylinder, then the volume will be decreased by

(a) 45.2%

(b) 52.5%

(c) 62.5%

(d) 72.5%

4. A cylinder is circumscribed about a hemisphere and a cone is inscribed in the cylinder so as to have its vertex at the centre of the top surface of the cylinder and its base coincides with the base of the cylinder. The ratio of the volumes of the cylinder, hemisphere and the cone is:

(a) 1 : 2 : 3

(b) 2 : 3 : 1

(c) 3 : 2 : 1

(d) 1 : 3 : 2

5. Three horses are tethered at 3 corners of a triangular plot having sides 20 m, 30 m and 40 m with ropes of 7 m length each. What is the portion of the field (plot) which can be grazed by the horses?

(a) 40 m^2

(b) 80 m^2

(c) 70 m^2

(d) 77 m^2

6. A reservoir is in the shape of a frustum of a right circular cone. It is 8 m across at the top and 4 m across at the bottom. If it is 6 m deep, then its capacity (assuming π=22/7) is

(a) 110 m^3

(b) 176 m^3

(c) 196 m^3

(d) 200 m^3

7. A sphere is inscribed in a cuboid of side 14 cm. The volume of the sphere (taking π=22/7)

(a) 1337.42 cm^3

(b) 1437.33 cm^3

(c) 1347.23 cm^3

(d) 1743.23 cm^3

8. If x = 3-2√2, then x+1/x is

(a) 12

(b) 4

(c) 6

(d) 8

9. If x = 3(1/4), y = 4(2/3), z = -7(11/12), then x^3+y^3+z^3-3xyz is

(a) 0

(b) 1

(c) -1

(d) 6(5/7)

10. If x^2-3x+1=0, then the value of 2x/(3x^2-5x+3) is 

(a) 1

(b) 2

(c) 1/2

(d) 1/4

Answers and Solution:

1. (b)
Semi perimeter of triangle(s) = (13+14+15)/2 = 21 cm
Area of triangle = √21*(21-13)*(21-14)*(21-15)
= 84 cm^2
The volume of prism = 84*10 = 840 cm^2
2. (d)
3- (c)
4- (c)
5- (d)
6- (b)
7- (b)
8- (c)
9- (a)
10-(c)