Learn

Friday, 9 October

JEE Main Maths · Limits and Derivatives

Determining Unknown Constants from Finite Limits

Determining Unknown Constants from Finite Limits (Limits and Derivatives) was asked 4 times in 4 JEE Main shifts, 2022–2026, out of the 42 shifts Lumi analysed.

Times asked
4
in 4 shifts
Years
2022–2026
Usual format
Single correct
Multi-step
Pattern
Frequent
repeats across shifts

How it is asked

  • Unknown constants from finite limit
  • Unknown constants for finite limit

Difficulty

Easy 0Medium 3Hard 1

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 4 questions

Newest first, each with its options and official answer.

  1. 2 Apr 2026, Shift 1 · Q16If lim⁡x→2sin⁡(x3−5x2+ax+b)(x−1−1)log⁡e(x−1)=m\lim_{x\to2}\frac{\sin\left(x^3-5x^2+ax+b\right)}{\left(\sqrt{x-1}-1\right)\log_e(x-1)}=m, then a+b+ma+b+m is equal to :HardSingle correct
  2. 2 Apr 2025, Shift 1 · Q7For α,β,γ∈R\alpha, \beta, \gamma\in\mathbf{R}, if lim⁡x→0x2sin⁡αx+(γ−1)ex2sin⁡2x−βx=3\lim_{x\to0}\frac{x^2\sin\alpha x+(\gamma-1)e^{x^2}}{\sin2x-\beta x}=3, then…MediumSingle correct
  3. 2 Apr 2025, Shift 2 · Q17If lim⁡x→0cos⁡(2x)+acos⁡(4x)−bx4\lim_{x\to0} \frac{\cos(2x) + a\cos(4x) - b}{x^4} is finite, then (a+b)(a+b) is equal to :MediumSingle correct
  4. 25 Jul 2022, Shift 1 · Q5If lim⁡n→∞(n2−n−1+nα+β)=0\lim_{n\to\infty}\left(\sqrt{n^2-n-1}+n\alpha+\beta\right)=0, then 8(α+β)8(\alpha+\beta) is equal to :MediumSingle correct