JEE Main 2021 · MathsNumerical answerNumerical valueMediumApplication

JEE Main 24 February 2021, Shift 2, Maths Q90

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

The number of the real roots of the equation

(x+1)^2+|x-5|=\frac{27}{4}

is ________.

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
8 Apr 2023, Shift 2 · Q22Let $m$ and $n$ be the numbers of real roots of the quadratic equations $x^2 - 12x + [x] + 31 = 0$ and $x^2 - 5|x + 2| - 4 = 0$ …HardNumerical 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

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.