JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 18 March 2021, Shift 1, Maths Q64

Question 64 of 90 in this shift, Maths question 4 of 30, Section A.

Let

\alpha,\beta,\gamma

be the real roots of the equation,

x^3+ax^2+bx+c=0

, (

a,b,c\in\mathbf{R}

and

a,b\ne0

). If the system of equations (in

u,v,w

) given by

\alpha u+\beta v+\gamma w=0

;

\beta u+\gamma v+\alpha w=0

;

\gamma u+\alpha v+\beta w=0

has non-trivial solution, then the value of

\frac{a^2}{b}

is :

(1)0
(2)1
(3)3Official answer
(4)5

Official answer

Option 3

NTA final key.

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Parameter Evaluation in Homogeneous Systems

Same idea in other shifts

Asked 9× in all

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26 Aug 2021, Shift 1 · Q64Let $\theta \in \left(0, \frac{\pi}{2}\right)$ . If the system of linear equations.…MediumSingle correct
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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 108 of the 174 JEE Main shifts held from 2017 to 2026.