For x geq 0 , the least value of K , for which 4 1+x +4 1-x , frac K 2 , 16 x +16 - x are three consecutive terms of an A.P. is equal to :

Mathematics · Application of Derivatives

JEE Main 2024 — 5 April, Shift 2 — Question 20

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

Option A:
10
Correct
Option B:
4
Option C:
8
Option D:
16

Answer: A

Step-by-step solution

$\mathrm{k}=4\left(4^{\mathrm{x}}+\frac{1}{4^{\mathrm{x}}}\right)+\left(4^{2 \mathrm{x}}+\frac{1}{4^{2 \mathrm{x}}}\right)$ $

                          $ \geq 2 \quad \geq 2 $

$\mathrm{k} \geq 10$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 5 April, Shift 2
Subject: Mathematics
Chapter: Application of Derivatives
Topic: Maxima and Minima