Divisibility Rule for 11

Q. Find the remainder when ${50}^{{56}^{52}}$ is divided by 11.

1. 5
2. 9
3. 10
4. 7

Q. Find the remainder when ${30}^{{72}^{87}}$ is divided by 11.

1. 5
2. 9
3. 6
4. 3

Q. The remainder when $(888!{)}^{9999}$ is divided by 77 is:

1. 1
2. 3
3. 2
4. none of these

Q. $7^{74}-4^{74}$ is divisible by:

1. 11
2. 3
3. 7
4. both (a) and (b)

Q. What will be remainder when $1212121212\dots 300$ times is being divided by 99?

1. 18
2. 81
3. 54
4. 36

Q. Find the remainder when ${50}^{{51}^{52}}$ is divided by 11.

1. 6
2. 4
3. 7
4. 3

Q. Find the remainder when ${32}^{{33}^{34}}$ is divided by 11.

1. 4
2. 1
3. 10
4. 5

Q. The supercomputer at Ram Mohan Roy Seminary takes an input of a number N and an X where X is a factor of the number N. In a particular case, N is equal to 83p796161q and x is equal to 11 where 0 < p < q. Find the sum of remainders when N is divided by (p + q) and p successively.

1. 6
2. 3
3. 2
4. 9

Q. X! is completely divisible by ${11}^{51}$ but not by ${11}^{52}$. What is the sum of digits of largest such number X?___

Q. N = abcdefghij is a ten-digit number. All of the digits (a, b, c, d, …) are different from one another.
If 11111 divides N evenly, find the remainder if the greatest possible abcdefghij is divided by 8?

1. 7

2. 2

3. 4

4. 3