JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 July 2021, Shift 1, Maths Q72

Question 72 of 90 in this shift, Maths question 12 of 30, Section A.

The number of real roots of the equation

e^{6x}-e^{4x}-2e^{3x}-12e^{2x}+e^x+1=0

is :

(1) $1$
(2) $2$ Official answer
(3) $4$
(4) $6$

Official answer

Option 2

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Exponential Reducible to Quadratic

Same idea in other shifts

Asked 11× in all

8 Apr 2024, Shift 1 · Q3The sum of all the solutions of the equation $(8)^{2x}-16\cdot(8)^x+48=0$ is :EasySingle correct
1 Feb 2024, Shift 1 · Q2Let $S=\{x\in\mathbb{R}:(\sqrt{3}+\sqrt{2})^x+(\sqrt{3}-\sqrt{2})^x=10\}$ . Then the number of elements in S is :MediumSingle correct
24 Jun 2022, Shift 2 · Q2The sum of all the real roots of the equation $(e^{2x} - 4)(6e^{2x} - 5e^x + 1) = 0$ isEasySingle correct
27 Jun 2022, Shift 1 · Q22If the sum of all the roots of the equation $e^{2x}-11e^x-45e^{-x}+\frac{81}{2}=0$ is $\log_e p$ , then p is equal to ____________.MediumNumerical value
28 Jun 2022, Shift 1 · Q22The number of real solutions of the equation $e^{4x}+4e^{3x}-58e^{2x}+4e^x+1=0$ is __________.HardNumerical value
30 Jun 2022, Shift 1 · Q1Let $S_1 = \left\{x \in \mathbf{R} - \{1, 2\} : \frac{(x+2)(x^2+3x+5)}{-2+3x-x^2} \geq 0\right\}$ and…MediumSingle correct
4 Aug 2021, Shift 1 · Q61The number of roots of the equation $\left(3+\sqrt{5}\right)^{|x^2-4|}+4\left(\frac{3-\sqrt{5}}{4}\right)^{|x^2-4|}=6$ isMediumSingle correct
31 Aug 2021, Shift 1 · Q62The number of real roots of the equation $\mathrm{e}^{4x}+2\mathrm{e}^{3x}-\mathrm{e}^{x}-6=0$ is :MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.