JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 24 February 2021, Shift 1, Maths Q83

Question 83 of 90 in this shift, Maths question 23 of 30, Section B.

Let

P = \begin{bmatrix} 3 & -1 & -2 \\ 2 & 0 & \alpha \\ 3 & -5 & 0 \end{bmatrix}

, where

\alpha \in \mathbf{R}

. Suppose

Q = [q_{ij}]

is a matrix satisfying

PQ = kI_3

for some non-zero

k \in \mathbf{R}

. If

q_{23} = -\frac{k}{8}

and

|Q| = \frac{k^2}{2}

, then

\alpha^2 + k^2

is equal to ___________.

Official answer

NTA final key.

Chapter: Matrices
Topic: Matrix Inverse
Idea tested: Inverse via Adjoint Formula

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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.