2
###
If n is any odd number greater than 1, then n(n^2 - 1) is

If n is any odd number greater than 1, then n(n^{2} - 1) is

- divisible by 24 always
- divisible by 96 always
- divisible by 48 always
- None of these

3
###
Let N = 55^3 + 17^3 - 72^3. N is divisible by

Let N = 55^{3} + 17^{3} - 72^{3}. N is divisible by

- both 3 and 17
- both 7 and 13
- both 3 and 13
- both 17 and 7

4
###
What will be remainder when (67^67 + 67) is divided by 68

What will be remainder when (67^{67} + 67) is divided by 68?

- 67
- 63
- 66
- 1

5
###
Find the minimum integral value of n such that the division

Find the minimum integral value of n such that the division 55n/124 leaves no remainder

- 124
- 123
- 31
- 62

6
###
Let k be a positive integer such that k+4 is divisible by 7

Let k be a positive integer such that k+4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k+2n is divisible by 7 equals

- 7
- 5
- 9
- 3

7
###
Let p be a prime number greater than 5. Then (p^2 - 1) is

A positive integer is said to be a prime number if it is not divisible by any positive integer other than itself and 1. Let p be a prime number greater than 5. Then (p^{2} - 1) is

- always divisible by 6, and may or may not be divisible by 12
- always divisible by 24
- never divisible by 6
- always divisible by 12, and may or may not be divisible by 24