JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 31 January 2024, Shift 1, Maths Q7

Question 7 of 90 in this shift, Maths question 7 of 30, Section A.

Let

a

be the sum of all coefficients in the expansion of

(1-2x+2x^2)^{2023}(3-4x^2+2x^3)^{2024}

and

b=\lim_{x\to0}\left(\frac{\int_0^x\frac{\log(1+t)}{t^{2024}+1}dt}{x^2}\right)

. If the equations

cx^2+dx+e=0

and

2bx^2+ax+4=0

have a common root, where

c,d,e\in\mathbb{R}

, then

d:c:e

equals

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

Official answer

Option 2

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Complex Conjugate Roots

Same idea in other shifts

Asked 4× in all

4 Apr 2026, Shift 2 · Q2Let $S=\{z\in\mathbb{C}:z^2+4z+16=0\}$ . Then $\sum_{z\in S}|z+\sqrt{3}\,i|^2$ is equal to:EasySingle correct
4 Apr 2026, Shift 2 · Q4If $\alpha=1$ and $\beta=1+i\sqrt{2}$ , where $i=\sqrt{-1}$ are two roots of the equation $x^3+ax^2+bx+c=0$ , $a,b,c\in\mathbb{R}$ , then…MediumSingle correct
8 Jan 2020, Shift 1 · Q52If the equation, $x^2+bx+45=0$ ( $b\in R$ ) has conjugate complex roots and they satisfy $|z+1|=2\sqrt{10}$ , then :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.