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JEE Main 2020 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 9 January 2020, Shift 1, Maths Q61

Question 61 of 75 in this shift, Maths question 11 of 25, Section A.

If

f'(x)=\tan^{-1}(\sec x+\tan x)

,

-\frac{\pi}{2}<x<\frac{\pi}{2}

, and

f(0)=0

, then

f(1)

is equal to :

(1) $\frac{\pi-1}{4}$
(2) $\frac{\pi+2}{4}$
(3) $\frac{\pi+1}{4}$ Official answer
(4) $\frac{1}{4}$

Official answer

Option 3

NTA final key (Jan 2020).

Chapter: Integrals
Topic: Inverse Trig Identities
Idea tested: Periodic Reduction of tan-1(tan x) and cot-1(cot x)

Same idea in other shifts

Asked 2× in all

27 Aug 2021, Shift 2 · Q67If…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 108 of the 174 JEE Main shifts held from 2017 to 2026.