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JEE Main 2020 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 January 2020, Shift 1, Maths Q60

Question 60 of 75 in this shift, Maths question 10 of 25, Section A.

If

\int\dfrac{\cos x\,dx}{\sin^3 x\,(1+\sin^6 x)^{2/3}}=f(x)\,(1+\sin^6 x)^{1/\lambda}+c

where c is a constant of integration, then

\lambda f\left(\frac{\pi}{3}\right)

is equal to :

(1) $\frac{9}{8}$
(2) $-\frac{9}{8}$
(3) $2$
(4) $-2$ Official answer

Official answer

Option 4

NTA final key (Jan 2020).

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Factoring Highest Power for Substitution

Same idea in other shifts

Asked 2× in all

7 Apr 2025, Shift 2 · Q24If…HardNumerical value

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.