Divisibility Rule for 11

Q.

If the sum of a number and its square is 182, what is the number?

1. None of these

2. 15

3. 26

4. 91

5. 28

Q.

Fill in the missing number:
13, 21, 29, 34, 43, 92, 12, ?

1. 84
2. 31
3. None of the above
4. 12
5. 92

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

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

Q. The number 311311311311311311311 is

1. Divisible by 3 but not by 11
2. Divisible by 11 but not by 3
3. Divisible by both 3 and 11
4. Neither divisible by 3 nor by 11

Q. What is the remainder when ${19}^{92}$ is divided by 92?

1. 0
2. 1
3. 40
4. none of these
5. 48

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

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

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 ${30}^{{72}^{87}}$ is divided by 11.

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

Q. How many four-digit numbers divisible by 11 are not palindromes?(A palindrome is a number that reads the same in either direction. E.g. 121)

1. 819
2. 900
3. 625
4. 729
5. 602

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

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

Q. How many four-digit numbers divisible by 11 are not palindromes? (A palindrome is a number that reads the same in either direction, e.g. 121)

1. 819
2. 900
3. 625
4. 729

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

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

Q.

If xxyy is a perfect square then x + y =?

1. 9

2. 11

3. 10

4. 12

Q. What is the remainder when 123456789123456789…… upto 180 digits is divided by 11?___

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. The remainder when 678678 is divided by 1001 is _____________ .
___

Q.

Find the remainder when ${13}^{73}+{18}^5$ is divided by 11.

1. 8

2. 7

3. 10

4. 4

Q. Given a number 12345678901234567890..... up to 500 digits. Find the smallest number n that should be added to the number such that the sum is exactly divisible by 11.

1. 6
2. 5
3. 8
4. 1

Q. What is the highest power of $5$ that divides $90\times 80\times 70\times 60\times 50\times 40\times 30\times 20\times 10$?

1. $10$
2. $12$
3. $14$
4. $15$

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

Q. The number of positive integers not greater than 100, which are not divisible by 2, 3 or 5 is : (CAT 1993)

1. 26
2. 18
3. 31
4. None of these

Q.

What is the remainder obtained when ${25}^{68}$ is divided by 9?

1. 0

2. 5

3. 8

4. 1

Q.

The given question consists of a set of statements. Find out whether the data provided in the statements are sufficient to answer the question and mark the option:

What is the two – digit number whose first digit is 'a' and the second digit is 'b'?
I. The sum of both the digits is 6.
II. The number is a multiple of 51.

1. if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.

2. if the data in statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.

3. if the data even in both Statements I and II together are not sufficient to answer the question.

4. if the data even in both Statements I and II together are not sufficient to answer the question.

5. if the data in both statements I and II together are necessary to answer the question.

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

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

Q.

what least number should be subtracted from 1222 to get a number exactly divisible by 42?