Q.1  2 Men & 1 women board a bus in which 5 seats are vacant. One of these five seats are vacant. One of these five seats are reserved for ladies. A women may or may not sit on the seat reserved for ladies but a man cannot sit on the seat reserved for ladies. In how many ways can five seats occupied by these passangers ?

A) 36

B) 48

C) 15

D) 60

Ans. A

Case:

1) lady sits on the reserved seat

2)  lady does not sit on the reserved seat

i) If lady sits on the reserved seat

seats left = 4 (no reserved)

1st man can take any of the 4 seats

2nd man can take any of the left 3 seats = 4*3 = 12 ways

ii) If lady does not sit on the reserved seat

lady can take any of the left over 4 seats

now, 2 men can occupy any of the three seats

1st man can take any one of the three seats (no reserved)

Number of ways = 4*3*2 = 24

Hence, total number of ways = 24+12 = 36

Q.2 In how many ways 4 girls and 3 boys can be selected from 8 girls and 6 boys such that if a girl named A is selected, a boy named K should also be selected?

A) 350

B) 1,050

C) 700

D) 1,400

Ans. B

If A is selected, K should also be selected or if A is not selected,  K can be selected or not.

If A is selected, different ways are 7C3 × 5C2

If A is not selected, the different ways are  7C4 × 6C3

So, the answer is  7C3 × 5C2 + 7C4 × 6C3 = 1,050

Q.3 In how many ways 10 persons (A to J) can stand in 2 rows as 5 persons per row such that ‘A’ should be always in the second row and C should always be in the first row?

A) 25   8!

B) 5R2 × 5P2

C) 4P2 × 4P2

D) 8!

Ans. A

A and C are in 2nd and 1st row. This can be done in 5 5 ways. So, the remaining 8 persons can be arranged in 8! ways.

Q.4 In a question paper it had ten questions. Each question could be answered as true or false. Each candidate answered all the questions. Yet, no two candidates wrote the answers in an identical sequence. How many different sequence of answers are possible ?

A) 1024

B) 20

C) 512

D) 40

Ans. A

Since each question can be answered in two ways

Therefore, 10 questions can be answered = 210 = 1024 ways

Q.5 Each person’s performance compared with all other person is to be done to rank them. How many comparisons are  needed in total, if there are 11 persons ?

A) 66

B) 54

C) 55

D) 45

Ans. C

11C2 = 11 * 10/2 = 55