JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 5 April 2024, Shift 1, Maths Q3

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

Let A and B be two square matrices of order 3 such that

|A|=3

and

|B|=2

. Then

|A^{T}A(\mathrm{adj}(2A))^{-1}(\mathrm{adj}(4B))(\mathrm{adj}(AB))^{-1}AA^{T}|

is equal to :

(1) $32$
(2) $64$ Official answer
(3) $81$
(4) $108$

Official answer

Option 2

NTA final key.

Chapter: Determinants
Topic: Matrix Inverse
Idea tested: Determinant of Adjoint of Inverse

Same idea in other shifts

Asked 5× in all

27 Jun 2022, Shift 2 · Q4Let $A$ and $B$ be two $3\times3$ matrices such that $AB=I$ and $|A|=\frac{1}{8}$ . Then $|adj\,(B\,adj(2A))|$ is equal toMediumSingle correct
28 Jun 2022, Shift 1 · Q4Let $A$ be a matrix of order $3\times3$ and $\det(A)=2$ . Then $\det(\det(A)\,\mathrm{adj}(5\,\mathrm{adj}(A^3)))$ is equal to __________.MediumSingle correct
3 Aug 2021, Shift 1 · Q63Let A be a square matrix of order 3 and $|A| = 3$ . If $|\mathrm{Adj}\,(3\,\mathrm{Adj}\,(4A))| = 2^m \cdot 3^n$ , then the ordered pair…MediumSingle correct
4 Aug 2021, Shift 2 · Q62If A is a $3\times3$ matrix and $|A|=\frac{1}{36}$ , then the value of $|2\cdot adj(3\cdot adj(6A))|$ isMediumSingle 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.