Question

Assertion (A): $P\left(n\right) = 7^{n} - 3^{n}$ is divisible by $4$.
Reason (R) : If $a \ne b$, then expansion $a^{n} - b^{n}$ is divisible by $a - b$ if n is odd or even.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A).
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true

Answer 1

Answer: (A)

$P\left(n\right) = 7^{n} - 3^{n}, n$ is either even or odd, $\left(a = 7, b = 3\right)$ is divisible by $a - 6 = 7 - 3 = 4$ Hence Assertion $\left(A\right)$ followed by Reason $\left(R\right)$.