UPSC CDS Math Number System Questions

1. Number-Unit digit
71−7
72−9
73−3
74−1
75−7
7174−(7)43×4−1×9=9
2. Let n is a add number then (n+2) is also a odd number,
‌ Now, ‌(n+2)−(n)2=(2n+2).2
‌‌=4(n+1) As n is odd, so (n+1) is even number and must be divisible by 2 .
Hencedifference of square of two odd number is away divisible by 8 .

3.Let n and (n+2) are two odd number,
Now, n(n+2)+1=n2+2n+1=(n+1)2
This is perfect square Hence, statement 2 and 3 are true