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 3× 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
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

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 42 of the 174 JEE Main shifts held from 2017 to 2026.