JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 31 August 2021, Shift 2, Maths Q67

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

\alpha = \lim_{x\to\pi/4}\frac{\tan^3 x-\tan x}{\cos\left(x+\frac{\pi}{4}\right)}

and

\beta = \lim_{x\to 0}(\cos x)^{\cot x}

are the roots of the equation,

\mathrm{a}x^2+\mathrm{b}x-4 = 0

, then the ordered pair

(\mathrm{a}, \mathrm{b})

is :

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

Official answer

Option 3

NTA final key.

Chapter: Limits and Derivatives
Topic: L'Hopital's Rule
Idea tested: Indeterminate Power Forms

Same idea in other shifts

Asked 5× 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.