In an examination there are three multiple choice questions and each question has 5 choices. Number of ways in which a student can fail to get all answer correct is

(a)

125

(b)

124

(c)

64

(d)

63

The number of ways in which the following prize be given to a class of 30 boys first and second in mathematics, first and second in physics, first in chemistry and first in English is

(a)

30⁴\(\times\) 29²

(b)

30³\(\times\) 29³

(c)

30²\(\times\) 29⁴

(d)

30\(\times\)29⁵

The number of 5 digit numbers all digits of which are odd is

(a)

25

(b)

5⁵

(c)

5⁶

(d)

625

If ^a2-a \(C_2 = ^{a^2-a}\) C₄ then the value of 'a' is

(a)

2

(b)

3

(c)

4

(d)

5

There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is

(a)

45

(b)

40

(c)

39

(d)

38

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.

(a)

6

(b)

9

(c)

12

(d)

18

Everybody in a room shakes hands with everybody else. The total number of shake hands is 66. The number of persons in the room is

(a)

11

(b)

12

(c)

10

(d)

6

Number of sides of a polygon having 44 diagonals is

(a)

4

(b)

4!

(c)

11

(d)

22

If 10 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then the total number of points of intersection are

(a)

45

(b)

40

(c)

10!

(d)

2¹⁰

In ²ⁿC₃ : ⁿC₃ = 11 : 1 then n is

(a)

5

(b)

6

(c)

11

(d)

7