A number divided by 11 leaves a remainder 3. What is the remainder when the square of the same number is divided by 11?
a) 7
b) 5
c) 9
d) 11
Ans : c) 9
UP Police SI Exam Paper – Mathematics
Solution :
Let the number be N. We are given that when N is divided by 11, the remainder is 3.
This means we can express N as: N=11k+3 (for some integer k)
N2 = (11k+3)2 = 121k2 +66k + 9
When N2 is divided by 11, the terms 121k2 and 66k are divisible by 11. Therefore only 9 will be remainder.