JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 April 2026, Shift 2, Maths Q1

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

Let

\alpha, \beta

be the roots of the equation

x^2 - 3x + r = 0

, and

\frac{\alpha}{2}, 2\beta

be the roots of the equation

x^2 + 3x + r = 0

. If the roots of the equation

x^2 + 6x = m

are

2\alpha + \beta + 2r

and

\alpha - 2\beta - \frac{r}{2}

, then

m

is equal to:

(1) $-135$
(2) $-567$
(3) $135$
(4) $567$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Symmetric Functions

Same idea in other shifts

Asked 5× in all

3 Apr 2025, Shift 1 · Q4Let $z \in \mathbb{C}$ be such that $\frac{z^2 + 3i}{z - 2 + i} = 2 + 3i$ . Then the sum of all possible values of $z^2$ isMediumSingle correct
31 Jan 2024, Shift 2 · Q3Let $z_1$ and $z_2$ be two complex numbers such that $z_1+z_2=5$ and $z_1^3+z_2^3=20+15i$ . Then, $|z_1^4+z_2^4|$ equals -HardSingle correct
24 Jun 2022, Shift 1 · Q7If the sum of the squares of the reciprocals of the roots $\alpha$ and $\beta$ of the equation $3x^2+\lambda x-1=0$ is 15, then…MediumSingle correct
29 Jun 2022, Shift 1 · Q8Let $\alpha$ and $\beta$ be the roots of the equation $x^2 + (2i - 1) = 0$ . Then, the value of $|\alpha^8 + \beta^8|$ 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.