Ques 1 Number System

Find the number of trailing zero in 100! ?

a) 20

b) 22

c) 24

d) 25

c is the correct option

By using the above formula..

no of trailing zero=(

no of trailing zero in

`100!`

=(no of trailing zero in

`100!`

=20+4+0no of trailing zero in

`100!`

=24Ques 2 Number System

Find the number of Unit Digit of 13^{45 }?

a) 3

b) 9

c) 7

d) 1

a is the correct option

The unit digit of power of 13 is repeated

`3,9,7,1`

.so as we see the power is 45 so if we repeat

`3,9,7,1`

so at 45th place, the unit digit is 3.or

This is for finding the unit digit every times this

45%4 so we will get the reminder is 1 so for 1th place 3 present in

`3,9,7,1`

numbers so 3 is the unit digit.Ques 3 Number System

What is the greatest five-digit number that is completely divisible by 8, 15, 16, 21 and 5 ?

a) 95760

b) 95765

c) 95120

d) 95769

c is the correct option

Ques 4 Number System

When (2^{24} – 1) is divided by 7 , the remainder is

a) 4

b) 2

c) 1

d) 0

d is the correct option

Ques 5 Number System

If the five-digit number 672 xy is divisible by 3, 7 and 11, then what is the value of (6x + 5y) ?

a) 16

b) 32

c) 17

d) 43

c is the correct option

Ques 6 Number System

If the nine-digit number 87605x31y is divisible by 72, then the value of 2x-3y is:

a) 0

b) 1

c) 2

d) 3

c is the correct option

Ques 7 Number System

If 71^{83} +73^{83} is divided by 36, the remainder is:

a) 0

b) 4

c) 7

d) 9

a is the correct option

Ques 8 Number System

If 31^{47} +43^{47} is divided by 37, the remainder is:

a) 0

b) 4

c) 7

d) 9

a is the correct option

Ques 9 Number System

If the number 4A306768B2 is divisible by both 8 and 11, then the smallest possible values of A and B will be

a) A = 3, B = 5

b) A = 5, B = 4

c) A = 5, B = 2

d) A = 5, B = 3

d is the correct option

The correct answer is d) A = 5, B = 3.

For a number to be divisible by 8, the last 3 digits must be divisible by 8.

In this case, the last 3 digits are 8B2.

The only values of B that make 8B2 divisible by 8 are 0, 4, and 8.

For a number to be divisible by 11, the difference between the sum of the digits at the odd and even places must be divisible by 11.

In this case, the sum of the digits at the odd places is 4 + 3 + 6 + 8 + B = 21 + B.

The sum of the digits at the even places is 0 + 7 + 6 + 2 = 15.

Therefore, the difference between the sum of the digits at the odd and even places is 21 + B - 15 = 6 + B.

The only values of B that make 6 + B divisible by 11 are 3 and 8.

Therefore, the possible values of A and B are A = 5, B = 3 or A = 5, B = 8.

However, A = 5, B = 3 is the smallest possible values of A and B.

Ques 10 Number System

The unit digit in the product (124)^{372} + (124^{373} is.

a) 10y+8

b) y+8

c) 11y-8

d) y-8

a is the correct option