JEE Main 2021 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 31 August 2021, Shift 1, Maths Q67

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

\lim_{x\to0}\frac{\sin^2(\pi\cos^4x)}{x^4}

is equal to :

(1) $2\pi^2$
(2) $\pi^2$
(3) $4\pi^2$ Official answer
(4) $4\pi$

Official answer

Option 3

NTA final key.

Chapter: Limits and Derivatives
Topic: L'Hopital's Rule
Idea tested: Simplifying with Standard Limits Before L'Hopital

Same idea in other shifts

Asked 13× in all

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31 Jan 2024, Shift 1 · Q6 $\lim_{x\to0}\frac{e^{2|\sin x|}-2|\sin x|-1}{x^2}$ MediumSingle correct
8 Apr 2023, Shift 1 · Q10 $\lim_{x\to0}\left(\left(\frac{1-\cos^2(3x)}{\cos^3(4x)}\right)\left(\frac{\sin^3(4x)}{\left(\log_e(2x+1)\right)^5}\right)\right)$ 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 108 of the 174 JEE Main shifts held from 2017 to 2026.