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Friday, 9 October

JEE Main Maths · Limits and Derivatives

Choosing Series Expansion over L'Hopital

Choosing Series Expansion over L'Hopital (Limits and Derivatives) was asked 6 times in 6 JEE Main shifts, 2021–2026, out of the 42 shifts Lumi analysed. 2 of the 6 had a numerical answer.

Times asked
6
in 6 shifts
Years
2021–2026
Usual format
Single correct
Calculation
Pattern
Asked most years
repeats across shifts

How it is asked

  • Unknown constants from finite limit
  • Limit of indeterminate trig expression

Difficulty

Easy 0Medium 4Hard 2

Where it sits

Chapter: Limits and Derivatives. Topic: L'Hopital's Rule, 24 questions over 8 ideas.

Other repeat ideas in this topic

Every time it came

All 6 questions

Newest first, each with its options and official answer.

  1. 6 Apr 2026, Shift 1 · Q17The value of lim⁡x→0(x2sin⁡2xx2−sin⁡2x)\lim_{x\to 0}\left(\frac{x^2\sin^2 x}{x^2-\sin^2 x}\right) is:MediumSingle correct
  2. 8 Apr 2025, Shift 2 · Q16Given below are two statements: Statement I :…MediumTwo statements
  3. 8 Apr 2024, Shift 1 · Q26The value of lim⁡x→02(1−cos⁡xcos⁡2xcos⁡3x3⋯cos⁡10x10x2)\lim_{x\to0}2\left(\frac{1-\cos x\sqrt{\cos2x}\sqrt[3]{\cos3x}\cdots\sqrt[10]{\cos10x}}{x^2}\right) is ____________.MediumNumerical value
  4. 31 Jan 2024, Shift 2 · Q25If lim⁡x→0ax2ex−blog⁡e(1+x)+cxe−xx2sin⁡x=1\lim_{x\to0}\frac{ax^2e^x-b\log_e(1+x)+cxe^{-x}}{x^2\sin x}=1, then 16(a2+b2+c2)16(a^2+b^2+c^2) is equal to ________.HardNumerical value
  5. 13 Apr 2023, Shift 2 · Q9If lim⁡x→0eax−cos⁡(bx)−cxe−cx21−cos⁡(2x)=17\lim_{x\to0}\dfrac{e^{ax}-\cos(bx)-\dfrac{cxe^{-cx}}{2}}{1-\cos(2x)}=17, then 5a2+b25a^2+b^2 is equal toHardSingle correct
  6. 18 Mar 2021, Shift 1 · Q72If lim⁡x→0sin⁡−1x−tan⁡−1x3x3\lim_{x\to0}\dfrac{\sin^{-1}x-\tan^{-1}x}{3x^3} is equal to L, then the value of (6L+1)(6L+1) is :MediumSingle correct