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JEE Main 20245 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
5 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Sequences and Series

JEE Main 2024 · 5 April · Evening Shift · Mathematics · Sequences and Series

For x ≥ 0 , the least value of K , for which 4^ 1+x +4^ 1-x , K 2 ,...

For x⩾0x \geqslant 0, the least value of K\mathrm{K}, for which 41+x+41−x,K2,16x+16−x4^{1+x}+4^{1-x}, \frac{\mathrm{K}}{2}, 16^x+16^{-x} are three consecutive terms of an A.P., is equal to :

Options

  1. A8
  2. B4
  3. C10
  4. D16

Correct answer

C. 10

Step-by-step solution

(\begin{gathered}\mathrm{k}=4\left(4^{\mathrm{x}}+\frac{1}{4^{\mathrm{x}}}\right)+\left(4^{2 \mathrm{x}}+\frac{1}{4^{2 \mathrm{x}}}\right) \\ \qquad \geq 2 \quad\qquad\qquad \geq 2\end{gathered}) k≥10\mathrm{k} \geq 10
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