JEE Main 2024 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 1 February 2024, Shift 1, Maths Q3

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

A=\begin{bmatrix}\sqrt{2}&1\\-1&\sqrt{2}\end{bmatrix}

B=\begin{bmatrix}1&0\\1&1\end{bmatrix}

C=ABA^T

and

X=A^TC^2A

, then

\det X

is equal to :

(1)27
(2)729Official answer
(3)891
(4)243

Official answer

Option 2

NTA final key.

Chapter: Determinants
Topic: Matrix Multiplication
Idea tested: Determinant of Product

Same idea in other shifts

Asked 6× in all

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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.