JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 25 February 2021, Shift 2, Maths Q67

Question 67 of 90 in this shift, Maths question 7 of 30, Section A.

The minimum value of

f(x) = a^{a^x} + a^{1-a^x}

, where

a, x \in \mathbf{R}

and

a > 0

, is equal to :

(1) $a+1$
(2) $a + \frac{1}{a}$
(3) $2\sqrt{a}$ Official answer
(4) $2a$

Official answer

Option 3

NTA final key.

Chapter: Application of Derivatives
Topic: Maxima and Minima
Idea tested: Optimization via AM-GM Inequality

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.