CUET Mathematics 2025 13 May Shift 2 PYQs

If the system of equations

$x - 3y + 5z = 3$

$x - 2y + 4z = 4$

$2x - 7y + \lambda z = 5$

has infinite number of solutions, then the value of $\lambda$ is:

if $A = \begin{bmatrix}1 & 0\\3 & 1\end{bmatrix}$ and $A^4 = \begin{bmatrix}1 & 0\\k & 1\end{bmatrix}$ then value of $k$ is

Let the matrix $A = [a_{ij}]_{3 imes3}$ be defined by

$a_{ij} = \begin{cases} i2i + 3j, & i \leq j \\ 5, & i = j \\ 3i - 2j, & i > j \end{cases}$

The number of elements in the matrix A which are greater than 7, is: