Q43 / 160 · AP EAMCET 2024 (20 May Shift 2) · Mathematics

If $2.4^{2 \mathrm{n}+1}+3^{3 \mathrm{n}+1}$ is divisible by $k$ for all $n \in N$, then $k=$

  • A
    209
  • Correct answer
    B
    11
  • C
    8
  • D
    3

Solution

Let $\mathrm{P}(x)=2.4^{2 \mathrm{n}+1}+3^{3 \mathrm{n}+1}=2^{4 \mathrm{n}+3}+3^{3 \mathrm{n}+1}$ $\begin{aligned} & \therefore P(1)=2^7+3^4=128+81=209 \\ & P(2)=2^{11}+3^7=2048+2187=4235 \end{aligned}$ H.C.F. of 209 and 435 is 11
So, $\mathrm{P}(x)$ is divisible by 11 .

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

Relevant Questions