JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 10 April 2023, Shift 2, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

For

\alpha, \beta, \gamma, \delta \in \mathbb{N}

, if

\int \left(\left(\frac{x}{e}\right)^{2x} + \left(\frac{e}{x}\right)^{2x}\right) \log_e x \, dx = \frac{1}{\alpha}\left(\frac{x}{e}\right)^{\beta x} - \frac{1}{\gamma}\left(\frac{e}{x}\right)^{\delta x} + C

, where

e = \sum_{n=0}^{\infty} \frac{1}{n!}

and

C

is constant of integration, then

\alpha + 2\beta + 3\gamma - 4\delta

is equal to

(1) $-8$
(2) $-4$
(3) $1$
(4) $4$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Exponential Factor Manipulation

Same idea in other shifts

Asked 4× in all

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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.