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1. On dividing a number by 5 , we get 3 as remainder, What will be the remainder when the square of this number is divised by 5?
- A. 3
- B. 3
- C. 3
- D. 3
Answer: Option D
Explanation:
When a number is divided by 5 and we get a remainder of 3, it means the number can be expressed as:
Number = 5k + 3
where "k" is an integer.
Now, let's find the square of this number:
(Number)^2 = (5k + 3)^2
Expanding this expression:
(Number)^2 = 25k^2 + 30k + 9
Now, let's consider this expression modulo 5 to find the remainder when the square of the number is divided by 5.
25k^2 is divisible by 5, so it leaves no remainder.
30k is also divisible by 5, so it leaves no remainder.
Finally, 9 divided by 5 leaves a remainder of 4.
So, the remainder when the square of this number is divided by 5 is 4.
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