JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 26 July 2022, Shift 1, Maths Q24

Question 24 of 90 in this shift, Maths question 24 of 30, Section B.

The number of distinct real roots of the equation

x^5(x^3 - x^2 - x + 1) + x\ (3x^3 - 4x^2 - 2x + 4) - 1 = 0

is ___________.

Official answer

NTA final key.

Chapter: Application of Derivatives
Topic: Maxima and Minima
Idea tested: Analyzing Polynomial Roots via Extrema

Same idea in other shifts

Asked 6× in all

4 Apr 2025, Shift 2 · Q16Let $f$ be a differentiable function on $\mathbf{R}$ such that $f(2)=1$ , $f'(2)=4$ . Let…HardSingle correct
30 Jul 2022, Shift 2 · Q83The number of integral values of $b$ for which $2x^3 - 3x^2 - 12x + b = 0$ has three distinct real roots is ________.MediumNumerical value
27 Jun 2022, Shift 1 · Q6The number of distinct real roots of $x^4-4x+1=0$ is :MediumSingle correct
27 Aug 2021, Shift 1 · Q85The number of distinct real roots of the equation $3x^4+4x^3-12x^2+4=0$ is __________.MediumNumerical value
3 Sep 2020, Shift 2 · Q58Suppose $f(x)$ is a polynomial of degree four, having critical points at $-1$ , 0, 1. If $T = \{x \in \mathbf{R} \mid f(x) = f(0)\}$ , then…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.