JEE Main 2022 · 30 Jun · Shift 1 · Mathematics Q5

← JEE Main 2022 · 30 Jun · Shift 1

MathematicsSingle correct+4 / -1Question 5 of 90

Let A and B be two square matrices of order 2. If $\det(A)=2$ , $\det(B)=3$ and $\det\left(\left(\det\left(5(\det A)B\right)\right)A^2\right)=2^a3^b5^c$ for some $a,b,c\in\mathbf N$ , then $a+b+c$ is equal to :

Answer and worked solution

Official answer: B

Order 2. $\det(10B)=100\times3=300$ , then $\det(300A^2)=300^2\times4=2^6\,3^2\,5^4$ .

$a+b+c=12$ .

(B)

Topics:Determinants and properties

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JEE Main 2022 · 30 Jun · Shift 1, Mathematics question 5