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Number System: Cyclicity Test-1

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Question 1
What will be the unit digit of 1341  ?
A
3
B
0
C
1
D
9
Question 1 Explanation: 
As we know the last digit depends upon the unit digit of the multiplier numbers so the unit digit of 1341
is same as the last digit of 341 and we know that the cyclicity of 3 is 4
On dividing the number 41 with 4 and we will   get the remainder as 1 and the last digit will be 31 = 3
Question 2
What will be the unit digit when 4545
A
5
B
0
C
1
D
9
Question 2 Explanation: 
Here the last digit is depend upon the 5
The cyclicity of 5 is 1 so there is no need to divide the power with 1
because whatever is the power of 5 the last digit will remains 5 so the last
digit of 4545 will be 5 .
51 = 5
52 = 25
53 = 125
Question 3
What will be the last digit of 34 x 45 x 56
A
8
B
0
C
9
D
3
Question 3 Explanation: 
Last digit of 34 = 1
Last digit of 45 = 4
Last digit of 56 = 5
So as we discussed earlier that the last digit depends upon the last digits
So 1 x 4 x 5 = 20 so the last digit is 0; also whenever 5 is multiplied by even
number then last digit will be 0
Question 4
Identify the last digit of (794 + 875)
A
8
B
0
C
7
D
4
Question 4 Explanation: 
Last digit of 794 is depends upon the the 94 i.e 1
Last digit of 875 is depends upon the the 75i.e 7
So the last digit of the whole expression will be 1 +7 = 8
So the last digit will be 8
Question 5
What will be the last digit of 4356 x 567 x 4534
A
8
B
5
C
7
D
4
Question 5 Explanation: 
Last digit of 4356 = 1 because cyclicity of 3 is 4 and 56 is completely
divisible by 4 so the last term of 34 is 1.
Last digit of 567 is 5 and last digit of 4534 is also 5
so that means the last digit of whole of the expression is 1 x 5x 5 = 5 therefore the digit is 5.
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