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Friday, 9 October

JEE Main Maths · Limits and Derivatives

Simplifying with Standard Limits Before L'Hopital

Simplifying with Standard Limits Before L'Hopital (Limits and Derivatives) was asked 6 times in 6 JEE Main shifts, 2023–2026, out of the 42 shifts Lumi analysed. 1 of the 6 had a numerical answer.

Times asked
6
in 6 shifts
Years
2023–2026
Usual format
Single correct
Multi-step
Pattern
Comes in cycles
repeats across shifts

How it is asked

  • Parameter values from trigonometric limit
  • Count solutions after evaluating limit

Difficulty

Easy 0Medium 3Hard 3

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. 5 Apr 2026, Shift 1 · Q17The product of all possible values of α\alpha, for which…HardSingle correct
  2. 5 Apr 2026, Shift 2 · Q17Let f(x)=lim⁡y→0(1−cos⁡(xy))tan⁡(xy)y3f(x)=\lim_{y\to 0}\frac{(1-\cos(xy))\tan(xy)}{y^3}. Then the number of solutions of the equation f(x)=sin⁡xf(x)=\sin x, x∈Rx \in \mathbf{R}…MediumSingle correct
  3. 7 Apr 2025, Shift 1 · Q16…MediumSingle correct
  4. 7 Apr 2025, Shift 2 · Q23For t>−1t>-1, let αt\alpha_t and βt\beta_t be the roots of the equation…HardNumerical value
  5. 31 Jan 2024, Shift 1 · Q6lim⁡x→0e2∣sin⁡x∣−2∣sin⁡x∣−1x2\lim_{x\to0}\frac{e^{2|\sin x|}-2|\sin x|-1}{x^2}MediumSingle correct
  6. 8 Apr 2023, Shift 2 · Q9If α>β>0\alpha > \beta > 0 are the roots of the equation ax2+bx+1=0ax^2 + bx + 1 = 0, and…HardSingle correct