Divisibility Rule for 37

Q. The expression ${333}^{555}+{555}^{333}$ is divisible by

1. 2
2. 3
3. 37
4. All of these

Q. The remainder when ${75}^{{75}^{75}}$ is divided by 37:

1. 0
2. 1
3. 5
4. 7

Q. The number $444,444\dots \left(999times\right)$ is definitely divisible by:

1. All of these
2. 22
3. 44
4. 222

Q.

The remainder obtained when$3^{450}$ is divided by 108 is

1. 81

2. 1

3. 57

4. 3

Q.

The remainder obtained when $(1^1+2^2+3^3+4^4+5^5+\dots {10}^{10})$ is divided by 4 is

1. 0

2. 1

3. 3

4. 2

Q.

The remainder obtained when ${96}^{96}$ is divided by 7 is

1. 0

2. 95

3. 1

4. 94

Q.

What is the remainder obtained when $2^{2008}$ is divided by 7?

1. 0

2. 1

3. 2

4. 6

Q.

The remainder obtained when ${51}^{50}$+${49}^{50}$is divided by 50 is

1. 1

2. 2

3. 0

4. 49