JEE Main 2024 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 27 January 2024, Shift 1, Maths Q22

Question 22 of 90 in this shift, Maths question 22 of 30, Section B.

Let

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

AB_1=\begin{bmatrix}1\\0\\0\end{bmatrix}

AB_2=\begin{bmatrix}2\\3\\0\end{bmatrix}

AB_3=\begin{bmatrix}3\\2\\1\end{bmatrix}

\alpha=|B|

and

\beta

is the sum of all the diagonal elements of B, then

\alpha^3+\beta^3

is equal to ________.

Official answer

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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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
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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.