If two solid hemispheres of same base radius r units are joined together along their bases, then curved surface area of this new solid is

(a)

4\(\pi\)r² sq.units

(b)

6\(\pi\)r² sq.units

(c)

3\(\pi\)r² sq.units

(d)

8\(\pi\)r² sq.units

If the radius of the base of a right circular cylinder is halved keeping the same height, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

(a)

1:2

(b)

1:4

(c)

1:6

(d)

1:8

In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If its height is 20 cm, the volume of the material in it is

(a)

5600\(\pi\) cm³

(b)

1120\(\pi\) cm³

(c)

56\(\pi\) cm³

(d)

3600\(\pi\) cm³

The total surface area of a hemi-sphere is how much times the square of its radius.

(a)

\(\pi\)

(b)

4\(\pi\)

(c)

3\(\pi\)

(d)

2\(\pi\)

A solid sphere of radius x cm is melted and cast into a shape of a solid cone of same radius. The height of the cone is

(a)

3x cm

(b)

x cm

(c)

4x cm

(d)

2x cm

A shuttle cock used for playing badminton has the shape of the combination of

(a)

a cylinder and a sphere

(b)

a hemisphere and a cone

(c)

a sphere and a cone

(d)

frustum of a cone and a hemisphere

The volume (in cm³) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

(a)

\(\frac{4}{3}\pi\)

(b)

\(\frac{10}{3}\pi\)

(c)

\(5\pi\)

(d)

\(\frac{20}{3}\pi\)

The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height is

(a)

1:2:3

(b)

2:1:3

(c)

1:3:2

(d)

3:1:2

If S₁ denotes the total surface area at a sphere of radius ૪ and S₂ denotes the total surface area of a cylinder of base radius ૪ and height 2r, then ___________

(a)

S₁ = S₂

(b)

S₁ > S₂

(c)

S₁ < S₂

(d)

S₁ = 2S₂

How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius cm?

(a)

64

(b)

216

(c)

512

(d)

16

The radius of a wire is decreased to one-third of the original. If volume the same, then the length will be increased _______of the original.

(a)

3 times

(b)

6 times

(c)

9 times

(d)

27 times

The curved surface area of a cylinder is 264 cm² and its volume is 924 cm². The ratio of diameter to its height is ___________

(a)

3:7

(b)

7:3

(c)

6:7

(d)

7:6

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 wood wasted is

(a)

45%

(b)

56%

(c)

67%

(d)

75%

If a letter is chosen at random from the English alphabets {a, b....,z}, then the probability that the letter chosen precedes x ____________

(a)

\(\frac { 12 }{ 13 } \)

(b)

\(\frac { 1 }{ 13 } \)

(c)

\(\frac { 23 }{ 26 } \)

(d)

\(\frac { 3 }{ 26 } \)