31.

20 persons are invited for a party. In how many different ways can they and the host be seated at circular table, if the two particular persons are to be seated on either side of the host?

• 20!

• 2(18!)

• 18!

• None of these

There are 5 letters and 5 different envelopes. The number of ways in which all the letters can be put in wrong envelope, is

• 119

• 44

• 59

• 40

The number of ways of painting the faces of a cube of six different colours is

• 1

• 6

• 6!

• 36

In how many ways 6 letters be posted in 5 different letter boxes?

• 5⁶

• 6⁵

• 5!

• 6!

In how many number of ways can 10 students be divided into three teams, one containing four students and the other three?

• 400

• 700

• 1050

• 2100

Let A = {1, 2, 3, ... , n} and B = {a, b, c}, then the number of functions from A to B that are onto is:

• 3ⁿ - 2ⁿ

• 3ⁿ - 2ⁿ - 1

• 3(2ⁿ - 1)

• 3ⁿ - 3(2ⁿ - 1)

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

• 9

• 12

• 10

• 14

In a group G = {1, 3, 7, 9} under multiplication modulo 10, the inverse of 7 is :

• 7

• 3

• 9

• 1

The sides AB, BC, CA of triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices

• 201

• 120

• 205

• 435

The number of ways of distributing 8 distinct toys among 5 children will be

• 5⁸

• 8⁵

• ${}^8\mathrm{P}_5$

• 40