# Number System Practice Problems 3 | Hamaraguru

21. A number is formed by writing the 1st 35 natural numbers side by side. Find the remainder when same number is divided by 4.

a) 1

b) 2

c) 3

d) none

22. A fifty digit number is formed by writing natural numbers side by side starting from 1. Find the remainder when same number is divided by 8.

a) 3

b) 4

c) 5

d) 6

23. A 6 digit number is formed by repeating a three-digit number for example 369369 is formed by repeating 369. Any number which is in the same form is divisible by which of the following:

a) 7 only

b) 11 only

c) 13 only

d) 1001

24. 4^100 + 4^101 + 4^102 + 4^103 is divisible by

a) 3

b) 10

c) 11

d) 13

25. 3^20 + 3^21 + 3^22 + 3^23 is divisible by

a) 11

b) 16

c) 25

d) 30

26. 5^90 + 5^91 + 5^92 is divisible by

a) 150

b) 160

c) 155

d) 30

27. 49^21 − 1 is exactly divisible by

a) 50

b) 51

c) 29

d) 8

28. Find the unit digit of 9!.

a) 9

b) 0

c) 2

d) 8

29. What will be unit digit of 7^309?

a) 1

b) 3

c) 9

d) 7

30. The unit of 133^99 is

a) 3

b) 9

c) 7

d) 1

Answer Key:

21.c

22.c

23.d

24.b

25.d

26.c

27.d

28.b

29.a

30.c

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