JEE Main 2022 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 30 June 2022, Shift 1, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A.

Let

S_1 = \left\{x \in \mathbf{R} - \{1, 2\} : \frac{(x+2)(x^2+3x+5)}{-2+3x-x^2} \geq 0\right\}

and

S_2 = \{x \in \mathbf{R} : 3^{2x} - 3^{x+1} - 3^{x+2} + 27 \leq 0\}

. Then,

S_1 \cup S_2

is equal to :

(1) $(-\infty, -2] \cup (1, 2)$
(2) $(-\infty, -2] \cup [1, 2]$ Official answer
(3) $(-2, 1] \cup [2, \infty)$
(4) $(-\infty, 2]$

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
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
31 Aug 2021, Shift 2 · Q63The sum of the roots of the equation, $x+1-2\log_2(3+2^x)+2\log_4(10-2^{-x}) = 0$ , 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.