Q.1 When the persons shake hands with one another , in how many ways is it possible ?

A) 25

B) 40

C) 20

D) 45

Ans. D

10C2 = 10!/8! 2! = 10*9*8!/8! * 2

=10*9/2

=90/2 = 45

Or

10*9/2*1 = 45

Q.2 A person has four notes of rupee 1,2,5,10 denomination. The number of different sums of money he can form from them is:

A) 15

B) 12

C) 16

D) 8

Ans. B

4! / 2 = 4*3*2*1 / 2

=12

Q.3 In how many ways can four children be made to stand in a line such that two of them A & B are always together ?

A) 12

B) 6

C) 18

D) 24

Ans. A

AB + 2 = 3 persons

Therefore, 3! = 3 * 2 ways = 6 ways

 A & B can interchange in 2 ways

Total no. of arrangement = 6 * 2 = 12 ways

Q.4 How many three digit nos. can be generated from 1,2,3,4,5,6,7,8,9 such that digits are in ascending order ?

A) 84

B) 81

C) 80

D) 83

Ans. A

Nos. are = 1,2,3,4,5,6,7,8,9 from which three digit nos are to be formed in ascending order

Taking 1 as fixed, no of 3 digits in ascending order = 8c2

Now,Taking 2 as fixed no of 3 digits in ascending order = 7c2

In this way, if 3,4,5,6,7 used as fixed nos then the nos of 3 digits in ascending order are = 6c2, 5c2, 4c2, 3c2, & 2c2

Therefore required nos in ascending order are:-

8c2 + 7c2+6c2+5c2+4c2+3c2+ 2c2

= 28+21+15+10+6+3+1 = 84

Q.5 A person has 4 coins of different denominations. What is the number of different sums of money person can form using one or more coins at a time?

A) 15

B) 12

C) 11

D) 16

Ans. A

4c1+4c2+4c3+4c4

= 4+6+4+1 = 15