JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 September 2020, Shift 2, Maths Q54

Question 54 of 75 in this shift, Maths question 4 of 25.

Let a, b, c

\in \mathbf{R}

be all non-zero and satisfy

a^3+b^3+c^3=2

. If the matrix

A=\begin{pmatrix} a & b & c \\ b & c & a \\ c & a & b \end{pmatrix}

satisfies

A^T A=I

, then a value of abc can be :

(1) $-\frac{1}{3}$
(2) $\frac{1}{3}$ Official answer
(3) $\frac{2}{3}$
(4) $3$

Official answer

Option 2

NTA final key (Sep 2020).

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Orthogonal Matrix Properties

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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.