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

A polygon has 44 diagonals. Find the number of sides.

• 8

• 10

• 11

• 13

In how many ways, words can be made from the letters of the word BHARAT in which B and H are never together ?

• 360

• 300

• 240

• 120

In how many ways can 5 keys be put in a ring ?

• 4!

• 5!

• $\frac{4!}{2}$

• $\frac{5!}{2}$