JEE Main 2022 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 28 June 2022, Shift 1, Maths Q4

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

Let

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 __________.

(1) $512\times10^6$ Official answer
(2) $256\times10^6$
(3) $1024\times10^6$
(4) $256\times10^{11}$

Official answer

Option 1

NTA final key.

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

Same idea in other shifts

Asked 5× in all

5 Apr 2024, Shift 1 · Q3Let A and B be two square matrices of order 3 such that $|A|=3$ and $|B|=2$ . Then…MediumSingle correct
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
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.