JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 8 April 2023, Shift 2, Maths Q22

Question 22 of 90 in this shift, Maths question 22 of 30, Section B.

Let

m

and

n

be the numbers of real roots of the quadratic equations

x^2 - 12x + [x] + 31 = 0

and

x^2 - 5|x + 2| - 4 = 0

respectively, where

[x]

denotes the greatest integer

\leq x

. Then

m^2 + mn + n^2

is equal to __________.

Official answer

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Roots of Modulus Quadratics

Same idea in other shifts

Asked 12× in all

8 Apr 2025, Shift 2 · Q2The sum of the squares of the roots of $|x-2|^2 + |x-2| - 2 = 0$ and the squares of the roots of $x^2 - 2|x-3| - 5 = 0$ , isMediumSingle correct
5 Apr 2024, Shift 1 · Q22The number of distinct real roots of the equation $|x||x+2|-5|x+1|-1=0$ is ________.MediumNumerical value
8 Apr 2024, Shift 2 · Q21The number of distinct real roots of the equation $|x+1|\,|x+3| - 4|x+2| + 5 = 0$ , is ________MediumNumerical value
30 Jan 2024, Shift 2 · Q22The number of real solutions of the equation $x\left(x^2 + 3|x| + 5|x-1| + 6|x-2|\right) = 0$ is ________.MediumNumerical value
13 Apr 2023, Shift 1 · Q2The set of all $a \in \mathbb{R}$ for which the equation $x|x-1|+|x+2|+a=0$ has exactly one real root, isHardSingle correct
15 Apr 2023, Shift 1 · Q2The number of real roots of the equation $x|x|-5|x+2|+6=0$ , isMediumSingle correct
30 Jul 2022, Shift 2 · Q81The number of solutions of the equation $|x^2 + 3x + 2| + |x + 5| - 2 = 0$ , $x \in \mathbb{R}$ , is ________.MediumNumerical value
24 Feb 2021, Shift 2 · Q90The number of the real roots of the equation $(x+1)^2+|x-5|=\frac{27}{4}$ is ________.MediumNumerical value

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.