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Saturday, 31 October

JEE Main · Maths · Continuity and Differentiability

Second Order Implicit Chain Rule

JEE Main asked Second Order Implicit Chain Rule 5 times in 5 of the 108 shifts Lumi analysed, in 2020, 2021, 2022 and 2024. It belongs to Chain Rule, in Continuity and Differentiability (Maths). The longest wait between two years asking it was 2 years. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
5
in 5 shifts
Years
4 of 8
First asked
2020
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170.08’200.07’210.04’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 2 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20250 of 8
  • 20241 of 18
  • 20230 of 12
  • 20221 of 24
  • 20212 of 24
  • 20201 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Second derivative relation from inverse trig function
  • Differential equation from implicit relation by differentiation

Difficulty

Easy 0Medium 4Hard 1

2 of the 5 questions had a numerical answer.

Every question

All 5 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 9 Apr 2024, Shift 2 · Q8If log⁡ey=3sin⁡−1x\log_e y=3\sin^{-1}x, then (1−x2)y′′−xy′(1-x^2)y''-xy' at x=12x=\frac{1}{2} is equal toMediumSingle correct
  2. 27 Jun 2022, Shift 1 · Q8If cos⁡−1(y2)=log⁡e(x5)5\cos^{-1}\left(\frac{y}{2}\right) = \log_e\left(\frac{x}{5}\right)^5, ∣y∣<2|y|<2, then :MediumSingle correct
  3. 27 Aug 2021, Shift 1 · Q84If y1/4+y−1/4=2xy^{1/4}+y^{-1/4}=2x, and (x2−1)d2ydx2+αxdydx+βy=0(x^2-1)\frac{d^2y}{dx^2}+\alpha x\frac{dy}{dx}+\beta y=0, then ∣α−β∣|\alpha-\beta| is equal to __________.HardNumerical value
  4. 26 Aug 2021, Shift 1 · Q86If y=y(x)y=y(x) is an implicit function of xx such that log⁡e(x+y)=4xy\log_e(x+y)=4xy, then d2ydx2\frac{d^2y}{dx^2} at x=0x=0 is equal to __________.MediumNumerical value
  5. 3 Sep 2020, Shift 1 · Q57If y2+log⁡e(cos⁡2x)=yy^2+\log_e(\cos^2x)=y, x∈(−π2,π2)x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right), then :MediumSingle correct

Shifts: 3 Sep 2020, Shift 1, 26 Aug 2021, Shift 1, 27 Aug 2021, Shift 1, 27 Jun 2022, Shift 1, 9 Apr 2024, Shift 2.

Same topic

Other ideas in Chain Rule

Chain Rule has 15 ideas JEE Main has asked; 8 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas