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Saturday, 31 October

JEE Main 2024 · MathsNumerical answerNumerical valueHardCalculation

JEE Main 1 February 2024, Shift 1, Maths Q26

Question 26 of 90 in this shift, Maths question 26 of 30, Section B.

Let {x}\{x\} denote the fractional part of xx and f(x)=cos⁡−1(1−{x}2)sin⁡−1(1−{x}){x}−{x}3f(x)=\frac{\cos^{-1}(1-\{x\}^2)\sin^{-1}(1-\{x\})}{\{x\}-\{x\}^3}, x≠0x\neq0. If L and R respectively denotes the left hand limit and the right hand limit of f(x)f(x) at x=0x=0, then 32π2(L2+R2)\frac{32}{\pi^2}(L^2+R^2) is equal to __________.

Official answer

18

NTA final key.

Chapter
Limits and Derivatives
Topic
L'Hopital's Rule
Idea tested
L'Hopital with Inverse Trigonometric Functions

Same idea in other shifts

Asked 2× in all
  1. 26 Jun 2022, Shift 1 · Q6lim⁡x→12sin⁡(cos⁡−1x)−x1−tan⁡(cos⁡−1x)\lim_{x \to \frac{1}{\sqrt{2}}} \frac{\sin(\cos^{-1}x) - x}{1 - \tan(\cos^{-1}x)} is equal to :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.