JEE Main 2026 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 2 April 2026, Shift 1, Maths Q1

Question 1 of 75 in this shift, Maths question 1 of 25, Section A.

Let

\alpha, \alpha+2, \alpha \in \mathbb{Z}

, be the roots of the quadratic equation

x(x+2)+(x+1)(x+3)+(x+2)(x+4)+\ldots+(x+n-1)(x+n+1)=4n

for some

n \in \mathbb{N}

. Then

n+\alpha

is equal to :

(1) $0$
(2) $1$
(3) $2$ Official answer
(4) $3$

Official answer

Option 3

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Root-Coefficient Relation

Same idea in other shifts

Asked 8× in all

5 Apr 2026, Shift 1 · Q1Let $a, b \in \mathbb{C}$ . Let $\alpha, \beta$ be the roots of the equation $x^2 + ax + b = 0$ . If $\beta - \alpha = \sqrt{11}$ and…MediumSingle correct
5 Apr 2026, Shift 2 · Q1Let $\alpha, \beta$ be the roots of the equation $x^2-x+p=0$ and $\gamma, \delta$ be the roots the equation $x^2-4x+q=0$ ;…MediumSingle correct
5 Apr 2026, Shift 2 · Q2Let $z_1, z_2 \in \mathbb{C}$ be the distinct solutions of the equation $z^2+4z-(1+12i)=0$ . Then $|z_1|^2+|z_2|^2$ is equal to :MediumSingle correct
6 Apr 2026, Shift 2 · Q2Consider the quadratic equation $(n^2-2n+2)x^2-3x+(n^2-2n+2)^2=0$ , $n\in\mathbf{R}$ . Let $\alpha$ be the minimum value of the product of…MediumSingle correct
3 Apr 2025, Shift 2 · Q4Let the equation $x(x + 2)(12 - k) = 2$ have equal roots. Then the distance of the point $\left(k, \frac{k}{2}\right)$ from the line…EasySingle correct
28 Jul 2022, Shift 1 · Q30The sum of all real values of $x$ for which $\frac{3x^2-9x+17}{x^2+3x+10}=\frac{5x^2-7x+19}{3x^2+5x+12}$ is equal to __________.MediumNumerical value
6 Sep 2020, Shift 2 · Q52If $\alpha$ and $\beta$ are the roots of the equation $2x(2x+1)=1$ , then $\beta$ is equal to :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 42 of the 174 JEE Main shifts held from 2017 to 2026.