Q92 / 180 · COMEDK 2023 (Memory Based) · Mathematics

If $49^n+16^n+k$ is divisible by 64 for $n \in N$, then the least negative integral value of $k$ is

  • Correct answer
    A
    -1
  • B
    -2
  • C
    -3
  • D
    -4

Solution

Let $P(n)=49^n+16^n+k$ For $n=1$, we get $P(1)=49^{(1)}+16^{(1)}+k=65+k$ As $P(1)$ is divisible by 64 , we take $k=-1$ $P(1)=65-1=64$, which is divisible by 64 . Thus, the least negative integral value of $k$ be -1 .

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

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