Remainder Theorem

Q. Fill in the missing number:
4, 5, 9, 18, 34, ?

1. 42
2. 59
3. None of the above
4. 38
5. 40

Q.

D4P:H4L:P5R: ? What Is Next

ADCD EFGH IJKL MNOP QRSTU VWXYZ

Q. The remainder obtained when a prime number greater than 6 is divided by 6 is:

1. 1 or 3
2. 1 or 5
3. 3 or5
4. 4 or 5

Q. When a number 'N' is divided by a proper divisor D' then it leaves a remainder of 14 and if the thrice of that number i.e., 3N is divided by the same divisor D, the remainder comes out to be 8. Again if the 4 times of the same number i.e., '4N' is divided by D the remainder will be :

1. 35
2. 22
3. can't be determined
4. 5

Q. The remainder when $7^{84}$ is divided by 342 is

1. 341
2. 1
3. 49
4. 0

Q. The remainder when $({15}^{23}+{23}^{23})$ is divided by 19, is:

1. 15
2. 0
3. 4
4. 18

Q. Let $n!=1\times 2\times 3\dots \dots n$ for integer n > 1. If $p=1.1!+(2.2!)+(3.3!)+\dots \dots +(10.10!)$, then p + 2 when divided by 11! leaves a remainder of

1. 10
   
2. 1
3. 7
   
4. 0
   

Q. What is the remainder when $7^7+7^{77}+7^{777}+7^{7777}.........+7^{77777777}$ is divided by 8?

1. -1

2. 1

3. 7

4. 0

Q. Find the least number which must be subtracted from 9269 so that resulting number is exactly divisible by 73.

1. 17
2. 57
3. 71
4. 63

Q. What is the remainder when $3^{444}+4^{333}$ is divided by 5?

1. 0
2. 1
3. 2
4. 4

Q. Find the remainder if ${30}^{40}$ is divided by 17?

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

Q.

What is the remainder of ${2000}^{1000}$ divided by $13$?

Q. There are a certain number of chairs inside the hall. If the chairs are arranged 5 chairs per row, 7 chairs per row, and 8 chairs per row then 3, 2 and 5 chairs remain respectively. It is known that there are more than 600 chairs and less than 700 chairs inside the hall. Find the number of chairs remaining if the chairs are arranged 13 chairs per row.

1. 2

2. 3

3. 4

4. 5

Q. Given that N= abcdefghij is a ten-digit number . All of the digits (a, b, c, d, ...) are different from one another. If 1 1 1 1 1 divides it evenly, how many different possibilities are there for abcdefghij?

1. 3024

2. 3456

3. 1692

4. 5076

Q. What is the remainder when ${}_{20}{51}^{97}$ is divided by 17?

1. 15
2. 10
3. 7
4. 9

Q.

Fill in the missing number
99, 95, 86, 70, ?

1. 45
2. 62
3. 65
4. 55
5. None of these

Q. What is the remainder when 77, 777... up to 56 digits is divided by 19?

1. 1
2. 13
3. 7
4. 9

Q. What is the remainder when ${34}^{23}$ is divided by 23

1. 11
2. 0
3. 12
4. 1

Q. There are 48 cricket balls, 72 hockey balls and 84 tennis balls and they have to be arranged in several rows in such a way that every row contains the same number balls of one type. What is the minimum number of rows required for this to happen?

1. 12
2. 16
3. 17
4. 19
5. None of these

Q. What is the remainder when $(1^1+2^2+3^3+...+{100}^{100})$ is divided by 4?

1. 0
2. 1
3. 2
4. 3

Q. ABCABC is a six digit number where A, B, C are three consecutive natural numbers. Find the remainder when ABCABC is divided by 1001?

1. 997

2. cant be determined

3. 1

4. none of these

Q.

What is the remainder when ${10}^{25}-7$ is divided by 3?

1. 2

2. 1

3. 3

4. 0

Q.

The remainder obtained when (1! + 2! + 3! + …..50!) is divided by 15 is

1. 3

2. 1

3. 2

4. 0

Q. Find the remainder when $3^{40}$ is divided by 7?

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

Q. What is the remainder when $2^{96}$ is divided by 96?

1. 16
2. 64
3. 80
4. 32

Q. $4^{109}+6^{109}$ is divided by 25, the remainder is

1. 10
2. 15
3. 5
4. 20

Q. Find the remainder when ${300}^{1000}$ is divided by 19?___

Q. When a number is divided by 39 the remainder is 29. When the same number is divided by 13, what will be the remainder?

1. 0
2. 5
3. 3
4. 1

Q. $2^{16}-1$ divisible by

1. 19
2. 17
3. 13
4. 11

Q. $If289={17}^{x\frac{1}{5}},thenx=?$

1. $32$
2. $16$
3. $83$
4. $\frac{2}{5}$
5. None of the above