Q67 / 155 · WBJEE 2023 · Mathematics

Let \(P(n)=3^{2 n+1}+2^{n+2}\) where \(n \in \mathbb{N}\). Then

  • A
    \(\mathrm{P}(\mathrm{n})\) is not divisible by any prime integer.
  • Correct answer
    B
    there exists prime integer which divides \(P(n)\).
  • C
    \(P(n)\) is divisible by 5 for all \(n \in \mathbb{N}\).
  • D
    \(\mathrm{P}(\mathrm{n})\) is divisible by 3 for all \(\mathrm{n} \in \mathbb{N}\).

Solution

Hint : \(P(1)=3^3+2^3\) which is divisible by \((3+2)=5\) which is prime \(\therefore\) There exists prime integer which divides \(\mathrm{P}(\mathrm{n})\)

Hence, the correct answer is option: 'B'.

Relevant Questions