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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Exponential Reducible to Quadratic

JEE Main asked Exponential Reducible to Quadratic 11 times in 11 of the 108 shifts Lumi analysed, in 2020, 2021, 2022 and 2024. It belongs to Quadratic Roots, in Complex Numbers and Quadratic Equations (Maths). The longest wait between two years asking it was 2 years. In 2021, 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
11
in 11 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.

00.10.20’170.08’200.14’210.14’220’230.09’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 4 in 24 shifts · 2022: 4 in 24 shifts · 2023: 0 in 12 shifts · 2024: 2 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
  • 20242 of 18
  • 20230 of 12
  • 20224 of 24
  • 20214 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.

  • Count real roots of exponential equation
  • Number of real roots of exponential equation

Difficulty

Easy 2Medium 6Hard 3

2 of the 11 questions had a numerical answer.

Every question

All 11 questions

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

  1. 1 Feb 2024, Shift 1 · Q2Let S={x∈R:(3+2)x+(3−2)x=10}S=\{x\in\mathbb{R}:(\sqrt{3}+\sqrt{2})^x+(\sqrt{3}-\sqrt{2})^x=10\}. Then the number of elements in S is :MediumSingle correct
  2. 8 Apr 2024, Shift 1 · Q3The sum of all the solutions of the equation (8)2x−16⋅(8)x+48=0(8)^{2x}-16\cdot(8)^x+48=0 is :EasySingle correct
  3. 30 Jun 2022, Shift 1 · Q1Let S1={x∈R−{1,2}:(x+2)(x2+3x+5)−2+3x−x2≥0}S_1 = \left\{x \in \mathbf{R} - \{1, 2\} : \frac{(x+2)(x^2+3x+5)}{-2+3x-x^2} \geq 0\right\} and…MediumSingle correct
  4. 28 Jun 2022, Shift 1 · Q22The number of real solutions of the equation e4x+4e3x−58e2x+4ex+1=0e^{4x}+4e^{3x}-58e^{2x}+4e^x+1=0 is __________.HardNumerical value
  5. 27 Jun 2022, Shift 1 · Q22If the sum of all the roots of the equation e2x−11ex−45e−x+812=0e^{2x}-11e^x-45e^{-x}+\frac{81}{2}=0 is log⁡ep\log_e p, then p is equal to ____________.MediumNumerical value
  6. 24 Jun 2022, Shift 2 · Q2The sum of all the real roots of the equation (e2x−4)(6e2x−5ex+1)=0(e^{2x} - 4)(6e^{2x} - 5e^x + 1) = 0 isEasySingle correct
  7. 25 Jul 2021, Shift 1 · Q72The number of real roots of the equation e6x−e4x−2e3x−12e2x+ex+1=0e^{6x}-e^{4x}-2e^{3x}-12e^{2x}+e^x+1=0 is :HardSingle correct
  8. 31 Aug 2021, Shift 2 · Q63The sum of the roots of the equation, x+1−2log⁡2(3+2x)+2log⁡4(10−2−x)=0x+1-2\log_2(3+2^x)+2\log_4(10-2^{-x}) = 0, is :MediumSingle correct
  9. 31 Aug 2021, Shift 1 · Q62The number of real roots of the equation e4x+2e3x−ex−6=0\mathrm{e}^{4x}+2\mathrm{e}^{3x}-\mathrm{e}^{x}-6=0 is :MediumSingle correct
  10. 4 Aug 2021, Shift 1 · Q61The number of roots of the equation (3+5)∣x2−4∣+4(3−54)∣x2−4∣=6\left(3+\sqrt{5}\right)^{|x^2-4|}+4\left(\frac{3-\sqrt{5}}{4}\right)^{|x^2-4|}=6 isMediumSingle correct
  11. 9 Jan 2020, Shift 1 · Q52The number of real roots of the equation, e4x+e3x−4e2x+ex+1=0\mathrm{e}^{4x}+\mathrm{e}^{3x}-4\mathrm{e}^{2x}+\mathrm{e}^{x}+1=0 is :HardSingle correct

Shifts: 9 Jan 2020, Shift 1, 25 Jul 2021, Shift 1, 4 Aug 2021, Shift 1, 31 Aug 2021, Shift 2, 31 Aug 2021, Shift 1, 24 Jun 2022, Shift 2, 27 Jun 2022, Shift 1, 28 Jun 2022, Shift 1, 30 Jun 2022, Shift 1, 1 Feb 2024, Shift 1, 8 Apr 2024, Shift 1.

Same topic

Other ideas in Quadratic Roots

Quadratic Roots has 22 ideas JEE Main has asked; 13 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas