MISSION CGL MAINS 2015 : Advanced Quant Quiz

1.The diagonal of a square is 4√2 cm. The diagonal of another square,whose area is double that of the first square, is

(1) 8√2

(2) 16 cm

(3) √32 cm

(4) 8 cm

2. The volume of cuboide is twice that of a cube. If the dimension of the cuboid are 9 cm, 8cm and 6cm, the total surface area of the cube is

(1) 72 cm^2

(2) 216 cm^2

(3) 432 cm^2

(4) 108 cm^2

3. Base of a right prism is an equilateral triangle of side 6 cm.If the Volume of the prism is 108√3 cc,its height is

(1) 9 cm

(2) 10 cm 

(3) 11 cm 

(4) 12 cm

4. The ratio of a radii of two right circular cylinder is 2:3 and their heights are in the ratio 5:4 .The ratio of their curved surface area is

(1) 5 : 6

(2) 3 : 4

(3) 4 : 5

(4) 2 : 3

5. If the length of a rectangle is increased by 50 % and the breath is decreased by p per cent to maintain the same area, then p equals

(1) 33(1/4)

(2) 32(1/2)

(3) 33(1/3)

(4) 35(1/3)

6.Sphere A and B have their radii 40 cm and 10 cm respectively.Ratio of  surafce area of A to  to the surafce area of B is.

(1) 16:1

(2) 1:16

(3) 4:1

(4) 8:1

Answers........

1(4)
Diagonal of Square = 4√2 cm.
So Area of square = 1/2 (4√2)^2
=> 1/2*16*2 = 16 cm^2
Area of other square  = 2*16 = 32 cm^2

so Diagonal = 8 cm.

2.(2)
Volume of cuboide = 9*8*6 = 432 cm^2
According to the question ,
volume of cube = 432/2 = 216 cm^3
So Edge of cube = 6 cm
So Total surface area of cube = 6*(6)^2 = 216 cm^2

3(4).
Area of base = √3/4*(side)^2
= √3/4*6*6 = 9√3 sq.cm.
so volume of the prism  = Area of base*height
=> 108√3 = 9√3*h
=> h = 108√3/9√3 = 12 cm.

4.(1)
First cylinder   second cylinder
r1 = 2r            r2 = 3r
h1 = 5h            h2 = 4h
so Required ratio = 2pr1h1 : 2pr2h2
= 2*5 : 3*4 = 5 : 6
5.(3)
Area remains same.
so 50 - p - (50*p)/100 = 0
=> 100 - 2p - p = 0 => 3p = 100
=> p = 100/3 =33(1/3)
6.  (1)
7.  (c)
8.  (a)
9.  (c)
10.(a)