New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Matrices and Determinants question

2024 · 5 Apr · Shift 2 · Q45

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Matrices and Determinants
2024 · 5 Apr · Shift 2 · Q45

Matrices and Determinants question

2024 · 5 Apr · Shift 2 · Q45

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

Let

\alpha \beta eq 0

and

A=\left[\begin{array}{rrr}\beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alpha & 2 \alpha\end{array}\right]

. If

B=\left[\begin{array}{rrr}3 \alpha & -9 & 3 \alpha \\ -\alpha & 7 & -2 \alpha \\ -2 \alpha & 5 & -2 \beta\end{array}\right]

is the matrix of cofactors of the elements of

A

, then

\operatorname{det}(A B)

is equal to :

A
64
B
343
C
125
D
216

More from Matrices and Determinants

For $α, β \in R$ and a natural number $n$ , let $A_{r} = r 2 r 3 r - 2 123 \frac{n ^{2}}{2} + α n^{2} - β \frac{n ( 3 n - 1 )}{2}$ . Then $2 A_{10} - A_{8}$ …2024 · MCQ
Let $α β γ = 45; α, β, γ \in R$ . If $x (α, 1, 2) + y (1, β, 2) + z (2, 3, γ) = (0, 0, 0)$ for some $x, y, z \in R, x y z e q 0$ , then $6 α + 4 β + γ$ is equal to …2024 · Numerical
If $A$ is a square matrix of order 3 such that $det (A) = 3$ and $det (adj (- 4 adj (- 3 adj (3 adj ((2 A)^{- 1}))))) = 2^{m} 3^{n}$ …2024 · MCQ
If the system of equations $2 x + 7 y + λ z = 3 3 x + 2 y + 5 z = 4 x + μ y + 32 z = - 1$ has infinitely many solutions, then $(λ - μ)$ is equal to :2024 · Numerical
Let $A = 210 a 35 01 b$ . If $A^{3} = 4 A^{2} - A - 21 I$ , where $I$ is the identity matrix of order $3 \times 3$ , then $2 a + 3 b$ is equal to2024 · MCQ
Let $A = [21 - 1 1]$ . If the sum of the diagonal elements of $A^{13}$ is $3^{n}$ , then $n$ is equal to .2024 · Numerical
If $α e q a, β e q b, γ e q c$ and $α a a b β b c c γ = 0$ …2024 · MCQ
If the system of equations $x + 4 y - z = λ, 7 x + 9 y + μ z = - 3, 5 x + y + 2 z = - 1$ has infinitely many solutions, then $(2 μ + 3 λ)$ is equal to :2024 · MCQ