MISSION CGL MAINS 2015 : Advanced Quant Quiz

1.A cylindrical can whose base is horizontal and is of internal radius 3.5 cm contains sufficient water so that when a solid sphere is placed inside, water just covers the sphere. The sphere fits in the can exactly. The depth of water in the can before the sphere was put is
(1) 35/3 cm
(2) 17/3 cm
(3) 7/3  cm
(4) 14/3 cm

2.The lengths of three medians of a triangle are 9 cm, 12 cm and 15 cm. The area (in sq. com) of the triangle is
(1) 24
(2) 72
(3) 48
(4) 144
3.The height of a circular cylinder is increased six times and the base area is decreased to one-ninth of its value. The factor by which the lateral surface of the cylinder increases is
(1) 2
(2) 1/2 
(3) 2/3  
(4) 3/2
4.The volume of a right circular cone is 1232 cm^3 and its vertical height is 24 cm. Its curved surface area is  
(1) 154 cm^2
(2) 550 cm^2
(3) 604 cm^2
(4) 704 cm^2
5.A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. The area of the circle is.
(1) 125 cm^2
(2) 230 cm^2
(3) 550 cm^2
(4) 616 cm^2
6.The area of a circle is increased by 22 cm^2 when its radius is increased by 1 cm. The original radius of the circle is 
(1) 3 cm
(2) 5 cm
(3) 7 cm
(4) 9 cm
7.The sum of all interior angles of a regular polygon is twice the sum of all its exterior angles. The number of sides of the polygon is
(1) 10
(2) 8
(3) 12
(4) 6
8.The height of a right prism with a square base is 15 cm. If the area of the total surfaces of the prism is 608 sq. cm, its volume is
(1) 910 cm^3
(2) 920 cm^3
(3) 960 cm^3
(4) 980 cm^3
9.If the diagonals of a rhombus are 8 and 6, then the square of its size is
(1) 25
(2) 55
(3) 64
(4) 36
10.The volume of a solid hemisphere a 19404 cm^3. Its total surface area is
(1) 4158 cm^2
(2) 2858 cm^2
(3) 1738 cm^2
(4) 2038 cm^2

Answers and Solution:
1. (3) Increase in water level = volume of sphere/Area of base of cylinder
(4/3πr^3)/(πr^2)
= 4/3 r = 4/3*3.5 = 14/3 cm
so Required water level = 7 – 14/3 => 7/3 cm

2. (2)
3. (1)
Curved Surface area of cylinder  = 2πrh
case II
Radius = 1/3r:height = 6h
curved surface = 2π*1/3*r*6h = (2πrh)*2
so increase will be twice.

4. (2)
5. (4)
2πr = 2(18+26)
=> 2 *22/7*r = 44*2
r = 14 cm
Area of circle = 616 sq.m

6.(1)
7. (4)
8. (3)
9. (1)
10. (1)
2/3 πr^3 = 19404
=> 2/3*22/7*r^3 = 19404
r = 21 cm
so Total surface area = 3πr^2
= 3*22/7*21*21 = 4158.sq.cm.


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