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

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