JEE Main 2024 · MathsMultiple choiceTwo statementsMediumMulti-step

JEE Main 31 January 2024, Shift 1, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

For

0<c<b<a

, let

(a+b-2c)x^2+(b+c-2a)x+(c+a-2b)=0

and

\alpha\neq1

be one of its root. Then, among the two statements (I) If

\alpha\in(-1,0)

, then

b

cannot be the geometric mean of

a

and

c

(II) If

\alpha\in(0,1)

, then

b

may be the geometric mean of

a

and

c

(1)only (I) is true
(2)only (II) is true
(3)Both (I) and (II) are trueOfficial answer
(4)Neither (I) nor (II) is true

Official answer

Option 3

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Zero Sum of Coefficients Shortcut

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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.