JEE Main 2022 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 30 June 2022, Shift 1, Maths Q4

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

Let

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

and

B = \begin{bmatrix} 2 & \alpha \\ -1 & 2 \\ 4 & -5 \end{bmatrix}

\alpha \in \mathbf{C}

. Then the absolute value of the sum of all values of

\alpha

for which

\det(AB) = 0

is :

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

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

1 Feb 2024, Shift 1 · Q3If $A=\begin{bmatrix}\sqrt{2}&1\\-1&\sqrt{2}\end{bmatrix}$ , $B=\begin{bmatrix}1&0\\1&1\end{bmatrix}$ , $C=ABA^T$ and $X=A^TC^2A$ , then…EasySingle correct
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 · Q5Let A and B be two square matrices of order 2. If $\det(A) = 2$ , $\det(B) = 3$ and…MediumSingle correct
17 Mar 2021, Shift 1 · Q63If 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…EasySingle 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.