Number System Practice Problems 3 | Hamaraguru

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