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Saturday, 10 October

JEE Main Maths · Class 11

Limits and Derivatives: JEE Main previous year questions

Limits and Derivatives had 24 questions in the 42 JEE Main shifts Lumi analysed, about 0.5 a shift, asked in 23 of 42 shifts. It ranks 21 of 22 Maths chapters by questions; 33% of its questions were hard.

Questions
24
in 23 of 42 shifts
A shift, on average
0.5
of 25 Maths questions
Since 2024
+0.0
0.5 a shift in 2017–23, 0.6 in 2024–26
Numerical answer
6
25% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
0361’172’202’211’223’236’246’253’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 20171
  • 20202
  • 20212
  • 20221
  • 20233
  • 20246
  • 20256
  • 20263
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

2 topics and 8 distinct ideas; 4 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions

1 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
4 repeat

Study it on Lumi

Limits and Derivatives: the interactive lesson

Every question

All 24 Limits and Derivatives questions

Newest first. Each opens with its options and the official answer.

2026 3 questions

  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. 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

2025 6 questions

  1. 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
  2. 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
  3. 3 Apr 2025, Shift 2 · Q25If lim⁡x→0(tan⁡xx)1x2=p\lim_{x \to 0}\left(\frac{\tan x}{x}\right)^{\frac{1}{x^2}} = p, then 96log⁡ep96 \log_e p is equal to ___________.MediumNumerical value
  4. 7 Apr 2025, Shift 1 · Q16…MediumSingle correct
  5. 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
  6. 8 Apr 2025, Shift 2 · Q16Given below are two statements: Statement I :…MediumTwo statements

2024 6 questions

  1. 6 Apr 2024, Shift 2 · Q9lim⁡n→∞(12−1)(n−1)+(22−2)(n−2)+⋯+((n−1)2−(n−1))⋅1(13+23+⋯+n3)−(12+22+⋯+n2)\lim_{n\to\infty}\frac{(1^2-1)(n-1)+(2^2-2)(n-2)+\cdots+((n-1)^2-(n-1))\cdot 1}{(1^3+2^3+\cdots+n^3)-(1^2+2^2+\cdots+n^2)} is equal to :MediumSingle correct
  2. 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
  3. 9 Apr 2024, Shift 2 · Q5lim⁡x→0e−(1+2x)12xx\lim_{x\to0}\frac{e-(1+2x)^{\frac{1}{2x}}}{x} is equal toHardSingle correct
  4. 29 Jan 2024, Shift 1 · Q8…MediumSingle correct
  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. 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

2023 3 questions

  1. 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
  2. 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
  3. 13 Apr 2023, Shift 2 · Q25Let f(x)=∑k=110k xkf(x)=\sum_{k=1}^{10}k\,x^k, x∈Rx\in\mathbb{R}. If 2f(2)+f′(2)=119(2)n+12f(2)+f'(2)=119(2)^n+1 then nn is equal to ______HardNumerical value

2022 1 questions

  1. 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

2021 2 questions

  1. 3 Aug 2021, Shift 2 · Q68lim⁡x→0(1+x)1ex−1\lim_{x\to0}(1+x)^{\frac{1}{e^x-1}} is equal toEasySingle correct
  2. 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

2020 2 questions

  1. 8 Jan 2020, Shift 1 · Q57lim⁡x→0(3x2+27x2+2)1/x2\lim_{x\to 0}\left(\dfrac{3x^2+2}{7x^2+2}\right)^{1/x^2} is equal to :EasySingle correct
  2. 2 Sep 2020, Shift 1 · Q72If lim⁡x→1x+x2+x3+…+xn−nx−1=820, (n∈N)\lim_{x\to 1}\frac{x+x^{2}+x^{3}+\ldots+x^{n}-n}{x-1}=820,\ (n\in\mathbf{N}) then the value of n is equal to ___________.MediumNumerical value

2017 1 questions

  1. 2 Apr 2017 (offline) · Q70lim⁡x→π2cot⁡x−cos⁡x(π−2x)3\lim_{x\to\frac{\pi}{2}}\frac{\cot x-\cos x}{(\pi-2x)^3} equals :HardSingle correct

Pattern: Asked most years.