JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 17 March 2021, Shift 1, Maths Q82

Question 82 of 90 in this shift, Maths question 22 of 30, Section B.

If A

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

, then the value of

\det(A^{4})+\det\left(A^{10}-(\mathrm{Adj}(2A))^{10}\right)

is equal to __________.

Official answer

NTA final key.

Chapter: Determinants
Topic: Matrix Inverse
Idea tested: Cofactor Matrix and Adjoint

Same idea in other shifts

Asked 6× in all

8 Apr 2026, Shift 2 · Q4Let $A = \begin{bmatrix} \alpha & 1 & 2 \\ 2 & 3 & 0 \\ 0 & 4 & 5 \end{bmatrix}$ and…HardSingle correct
5 Apr 2024, Shift 2 · Q5Let $\alpha\beta \neq 0$ and…MediumSingle correct
26 Jul 2022, Shift 1 · Q4Let A be a $2 \times 2$ matrix with $\det\,(\mathrm{A}) = -1$ and…HardSingle correct
4 Aug 2021, Shift 1 · Q63Let $A=\begin{bmatrix}x&3&2\\1&y&4\\2&2&z\end{bmatrix}$ , $xyz=60$ and $8x+4y+3z=20$ . If $A(adj\ A)=k\,I$ , then $k$ is equal toMediumSingle correct
2 Apr 2017 (offline) · Q64If $A=\begin{bmatrix}2&-3\\-4&1\end{bmatrix}$ , then $\mathrm{adj}(3A^2+12A)$ is equal to :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.