Divisibility Rule for 3 & 9

Q. The number from 1 to 33 are written side by side as follows: 123, 456 $\dots$ 33. What is the remainder when this number is divided by 9?

1. 0
2. 6
3. 1
4. 3

Q. The remainder when $(3{)}^{67!}$ is divided by 80:

1. can't be determined
2. 0
3. 1
4. 2

Q. Digital sum of a number is obtained by adding all the digits of a number until a single digit is obtained. Find the digital sum of ${19}^{100}$.

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

Q. What will be the value of x for $\frac{({100}^{17}-1)+({10}^{34}+x)}{9}$; the remainder =0?

1. 3
2. 6
3. 9
4. 8

Q. How many numbers between 1 and 200 are exactly divisible by exactly two of 3, 9 and 27?

1. 14
2. 16
3. 17
4. 15

Q. Digital sum of a number is obtained by adding all the digits of a number until a single digit is obtained. What is the digital sum of ${4444}^{4444}$?

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

Q. $\frac{{32}^{{32}^{32}}}{9}$ will leave a remainder

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

Q. The remainder when $2^2+{22}^2+{222}^2+{2222}^2+....(222....49twos{)}^2$ is divided by 9 is

1. 5
2. 2
3. 6
4. 7

Q. The remainder when $(2^{54}-1)$ is divided by 9 is:

1. 0
2. 8
3. 7
4. none of these

Q. abcde is a five digit number when multiplied by 13 it gives a number, purely formed by the digit 9. Then the value of a + b + c + d + e is:

1. divisible by 8
2. equal to 27
3. divisible by 11
4. all of these