(D) Let $P(n) = 7^{2n} + 16n - 1$.For $n = 1$, $P(1) = 7^2 + 16(1) - 1 = 49 + 16 - 1 = 64$.For $n = 2$, $P(2) = 7^4 + 16(2) - 1 = 2401 + 32 - 1 = 2432

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(D) Let $P(n) = 7^{2n} + 16n - 1$.For $n = 1$, $P(1) = 7^2 + 16(1) - 1 = 49 + 16 - 1 = 64$.For $n = 2$, $P(2) = 7^4 + 16(2) - 1 = 2401 + 32 - 1 = 2432$.Since $2432 / 64 = 38$, the expression is divisible by $64$ for all $n \in N$.

Class 11 Mathematics Binomial Theorem Divisibility problems

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$7^{2n} + 16n - 1$ $(n \in N)$ is divisible by

WBJEE 2019 All WBJEE

A
$65$
B
$63$
C
$61$
D
$64$

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