Question

Assertion :$n^2-n$ is divisible by $2$ for every positive integer. Reason: $\sqrt{2}$ is not a rational number.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
• B. Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion.
• C. Assertion is correct, but Reason is incorrect.
• D. Assertion is incorrect, but Reason is correct.

Answer 1

The correct option is B Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion.

$n^2-n=n(n-1)$
If $n$ is odd, $n-1$ will be even.

When $n$ is even, $n-1$ will be odd.

Their product $n(n-1)$ will be even in either case, thus making it divisible by $2$.
So given statement is true.
$\sqrt{2}$ is not rational, it is irrational.

Thus, both statements are correct but reason is not the correct explanation to assertion.