Question

Consider the following Assertion (A): \[ 5^{2n}-3^{2n-1} \] is divisible by 2 for all \(n\in\mathbb N\). Reason (R): \[ 5^{2n}+3^{2n-1} \] is divisible by 7 for all \(n\in\mathbb N\).

• A. Both A and R are correct and R is the correct explanation of A
• B. Both A and R are correct and R is not the correct explanation of A
• C. A is correct, but R is not correct
• D. A is not correct, but R is correct \bigskip

Hint:

For Assertion--Reason questions involving divisibility, always test the reason using the smallest possible values such as \(n=1\) or \(n=2\). A single counterexample is enough to disprove a universal statement.

Answer 1

The Correct Option is C