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JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 9 January 2020, Shift 2, Maths Q62

Question 62 of 75 in this shift, Maths question 12 of 25, Section A.

If

\int\frac{d\theta}{\cos^2\theta(\tan2\theta+\sec2\theta)}=\lambda\tan\theta+2\log_e|f(\theta)|+C

where

C

is a constant of integration, then the ordered pair

(\lambda,f(\theta))

is equal to :

(1) $(-1,1+\tan\theta)$ Official answer
(2) $(1,1-\tan\theta)$
(3) $(-1,1-\tan\theta)$
(4) $(1,1+\tan\theta)$

Official answer

Option 1

NTA final key (Jan 2020).

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Even Power of Secant Substitution

Same idea in other shifts

Asked 2× in all

5 Apr 2026, Shift 1 · Q20The value of the integral $\int_{\pi/6}^{\pi/3}\left(\frac{4 - \operatorname{cosec}^2 x}{\cos^4 x}\right)dx$ is:MediumSingle correct

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 42 of the 174 JEE Main shifts held from 2017 to 2026.