New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Matrices and Determinants question

2025 · 2 Apr · Shift 1 · Q39

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

PYQ Library
JEE Main
Mathematics
Matrices and Determinants
2025 · 2 Apr · Shift 1 · Q39

Matrices and Determinants question

2025 · 2 Apr · Shift 1 · Q39

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

If the system of linear equations

\begin{aligned} & 3 x+y+\beta z=3 \\ & 2 x+\alpha y-z=-3 \\ & x+2 y+z=4 \end{aligned}

has infinitely many solutions, then the value of

22 \beta-9 \alpha

is :

A
31
B
37
C
43
D
49

More from Matrices and Determinants

If the system of equations $2 x + λ y + 3 z = 5 3 x + 2 y - z = 7 4 x + 5 y + μ z = 9$ has infinitely many solutions, then $(λ^{2} + μ^{2})$ is equal to :2025 · MCQ
Let $A$ be a $3 \times 3$ real matrix such that $A^{2} (A - 2 I) - 4 (A - I) = O$ , where $I$ and $O$ are the identity and null matrices, respectively. If $A^{5} = α A^{2} + β A + γ I$ , where $α, β$ , and $γ$ are real constants, then $α + β + γ$ …2025 · MCQ
Let $A$ be a matrix of order $3 \times 3$ and $∣ A ∣ = 5$ . If $∣2 adj (3 A adj (2 A)) ∣ = 2^{α} \cdot 3^{β} \cdot 5^{γ}, α, β, γ \in N$ , then $α + β + γ$ is equal to2025 · MCQ
Let $I$ be the identity matrix of order $3 \times 3$ and for the matrix $A = λ 47 25 - 1 362, ∣ A ∣ = - 1$ . Let $B$ be the inverse of the matrix $adj (Aadj (A^{2}))$ …2025 · Numerical
Let $A = cos θ 0 sin θ 010 - sin θ 0 cos θ$ . If for some $θ \in (0, π), A^{2} = A^{T}$ , then the sum of the diagonal elements of the…2025 · Numerical
Let the matrix $A = 110001010$ satisfy $A^{n} = A^{n - 2} + A^{2} - I$ for $n ⩾ 3$ . Then the sum of all the elements of $A^{50}$ is :2025 · MCQ
Let $A$ be a $3 \times 3$ matrix such that $∣ adj (adj (adj A)) ∣ = 81$ . If $S = {n \in Z : (∣ adj (adj A) ∣)^{\frac{( n - 1 ) ^{2}}{2}} = ∣ A ∣^{(3 n^{2} - 5 n - 4)}}$ …2025 · MCQ
Let the system of equations : $2 x + 3 y + 5 z = 9 7 x + 3 y - 2 z = 8 12 x + 3 y - (4 + λ) z = 16 - μ$ have infinitely many solutions. Then the radius of the circle centred at $(λ, μ)$ and…2025 · MCQ