**1. The remainder when 7 ^{84} is divided by 342 is**

- 1
- 0
- 49
- 341

**2. What is the right most non-zero digit of the number 30 ^{2720}?**

- 9
- 7
- 3
- 1

**3. 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**

- 5
- 3
- 9
- 7

**4. What is the remainder when 4 ^{96} is divided by 6?**

- 4
- 3
- 0
- 2

**5. After the division of a number successively by 3, 4 and 7, the remainders obtained are 2, 1 and 4 respectively. What will be the remainder if 84 divides the same number?**

- 53
- 80
- 41
- 75

**6. What is the digit in the unit's place of 2 ^{51}?**

- 4
- 2
- 8
- 1

**7. Let n! = 1 × 2 × 3 × ... × n for integer n ? 1. If p = 1! + (2 × 2!) + (3 × 3!) + ... + (10 × 10!), then p + 2 when divided by 11! leaves a remainder of**

- 10
- 0
- 1
- 7

**8. When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?**

- 8
- 5
- 7
- 6

**9. Let N = 55 ^{3} + 17^{3} – 72^{3}. N is divisible by**

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

**10. Consider the set S = {2, 3, 4, ......, 2n + 1}, where 'n' is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X – Y?**

- 0
- n/2
- (n+1)/2n
- 1

### Answers

- A
- D
- C
- A
- A
- C
- C
- D
- C
- D