JEE Main 2021 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 17 March 2021, Shift 1, Maths Q63

Question 63 of 90 in this shift, Maths question 3 of 30, Section A.

If A

=\begin{pmatrix}0 & \sin\alpha\\ \sin\alpha & 0\end{pmatrix}

and

\det\left(A^{2}-\frac{1}{2}I\right)=0

, then a possible value of

\alpha

is :

(1) $\frac{\pi}{4}$ Official answer
(2) $\frac{\pi}{3}$
(3) $\frac{\pi}{6}$
(4) $\frac{\pi}{2}$

Official answer

Option 1

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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27 Jan 2024, Shift 1 · Q22Let $A=\begin{bmatrix}2&0&1\\1&1&0\\1&0&1\end{bmatrix}$ , $B=[B_1, B_2, B_3]$ , where $B_1, B_2, B_3$ are column matrices, and…MediumNumerical value
30 Jun 2022, Shift 1 · Q4Let $A = \begin{bmatrix} 1 & -2 & \alpha \\ \alpha & 2 & -1 \end{bmatrix}$ and…MediumSingle correct
30 Jun 2022, Shift 1 · Q5Let A and B be two square matrices of order 2. If $\det(A) = 2$ , $\det(B) = 3$ and…MediumSingle correct
4 Sep 2020, Shift 2 · Q55Suppose the vectors $x_1$ , $x_2$ and $x_3$ are the solutions of the system of linear equations, $Ax=b$ when the vector b on the right side…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 108 of the 174 JEE Main shifts held from 2017 to 2026.