1) Find the remainder of \( \frac{1000^{1000}}{11} \)

(a) 1 (b) 3 (c) 5 (d) 7 (e) None of these

2) Find the remainder of \( \frac{5^{121}}{35} \)

(a) 5 (b) 15 (c) 25 (d) 24 (e) None of these

3) A number \( p \) when divided by 111 leaves remainder 7. What will be remainder when \( 6p \) is divided by 74?

(a) 12 (b) 19 (c) 26 (d) 42 (e) None of these

4) Find the remainder of \( \frac{5^{73}}{73} \)

(a) 5 (b) 11 (c) 17 (d) 31 (e) None of these

5) Find the remainder of \( \frac{100!}{101} \)

(a) 1 (b) 100 (c) 11 (d) 39 (e) None of these

6) Find the remainder of \( \frac{2^{1234567891011\ldots100}}{5} \)

(a) 5 (b) 15 (c) 25 (d) 24 (e) None of these

7) Find the remainder of \( \frac{1!+2!+3!+\cdots+100!}{40} \)

(a) 5 (b) 15 (c) 25 (d) 24 (e) None of these

8) Find the remainder of \( \frac{3^{1501}}{17} \)

(a) 7 (b) 9 (c) 12 (d) 6 (e) 8

9) Find the remainder of \( \frac{415(415^{88}-1)}{89} \)

(a) 17 (b) 13 (c) 21 (d) 67 (e) 0

10) A monomial in \( x \) gives remainder 4 when divided by \( x-3 \), and 7 when divided by \( x-4 \). Find the remainder when divided by \( x-7 \).

(a) 12 (b) 5 (c) 11 (d) 16 (e) 17

11) Find the remainder when \( N \) divided by 625 where \( N = 111\ldots111 \) (111 ones)

(a) 435 (b) 456 (c) 486 (d) 457 (e) None of these

12) Find the remainder of \( \frac{7^{1200}}{114} \)

(a) 109 (b) 112 (c) 49 (d) 1 (e) None of these

13) Find the remainder of \( \left( (((15)^{15})^{16})^{17}\ldots^{100} \right)/11 \)

(a) 12 (b) 1 (c) 10 (d) 6 (e) 7

14) Find the remainder of \( \frac{25^{25^{25^{25}}}}{7} \)

(a) 2 (b) 3 (c) 4 (d) 5 (e) None of these

15) Find the remainder of \( \frac{80!}{83} \)

(a) 51 (b) 57 (c) 55 (d) 29 (e) None of these

16) Find the remainder of \( \frac{5^{5^6}}{144} \)

(a) 112 (b) 64 (c) 16 (d) 48 (e) None of these

17) Find the remainder of \( \frac{135791113\ldots \text{(100 digits)}}{9} \)

(a) 0 (b) 1 (c) 3 (d) 4 (e) None of these

18) Find the remainder of \( \frac{5^{2450}}{126} \)

(a) 2 (b) 25 (c) 27 (d) 29 (e) None of these

19) Find the remainder of \( \frac{7^{12121}}{180} \)

(a) 49 (b) 163 (c) 61 (d) 7 (e) None of these

20) Find the remainder of \( \frac{555555\ldots\text{(100 digits)}}{187} \)

(a) 77 (b) 66 (c) 132 (d) 165 (e) None of these