JEE MAIN Matrices Previous Year Questions (PYQs) – Page 4 of 15

If the system of equations $2x - y + z = 4$, $5x + \lambda y + 3z = 12$, $100x - 47y + \mu z = 212$ has infinitely many solutions, then $\mu - 2\lambda$ is equal to

The values of a and b, for which the system of equations 2x + 3y + 6z = 8, x + 2y + az = 5, 3x + 5y + 9z = b, has no solution, are :

Let $A = [a_{ij}]$ be a square matrix of order $2$ with entries either $0$ or $1$. Let $E$ be the event that $A$ is an invertible matrix. Then the probability $\mathrm{P}(E)$ is

Two fair dice are thrown. The numbers on them are taken as $\lambda$ and $\mu$, and a system of linear equations, x + y + z = 5, x + 2y + 3z = $\mu$ ,x + 3y + $\lambda$z = 1, is constructed. If p is the probability that the system has a unique solution and q is the probability that the system has no solution, then :

$ \text{Let } I(x)=\int \frac{x+1}{x,(1+x e^{x})^{2}},dx,; x>0.\ \text{If } \lim_{x\to\infty} I(x)=0,\ \text{then } I(1) \text{ is equal to:} $

If the system of equations $x+2y-3z=2$, $2x+\lambda y+5z=5$, $14x+3y+\mu z=33$ has infinitely many solutions, then $\lambda+\mu$ is equal to:

Let the system of equations

x + 5y - z = 1

4x + 3y - 3z = 7

24x + y + λz = μ

λ, μ ∈ ℝ, have infinitely many solutions. Then the number of the solutions of this system,

if x, y, z are integers and satisfy 7 ≤ x + y + z ≤ 77, is :

$ \text{Let } A \text{ and } B \text{ be any two } 3\times 3 \text{ symmetric and skew-symmetric matrices respectively. Then which of the following is NOT true?} $

Let A be a 3 $\times$ 3 matrix with det(A) = 4. Let R_i denote the i^th row of A. If a matrix B is obtained by performing the operation R₂ $ \to $ 2R₂ + 5R₃ on 2A, then det(B) is equal to :

Let $P=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right], A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$ and $Q=P A P^{T}$. If $P^{T} Q^{2007} P=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$, then $2 a+b-3 c-4 d$ equal to :