JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 31 January 2024, Shift 2, Maths Q3

Question 3 of 90 in this shift, Maths question 3 of 30, Section A.

Let

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 -

(1) $30\sqrt{3}$
(2) $15\sqrt{15}$
(3) $25\sqrt{3}$
(4)75Official 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

2 Apr 2026, Shift 2 · Q1Let $\alpha, \beta$ be the roots of the equation $x^2 - 3x + r = 0$ , and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation…MediumSingle correct
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
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.