CUET Mathematics 2025 30 May Shift 2 PYQs

If $A = \begin{bmatrix} a & b & -5 \\ d & b & -6 \\ 5 & e & c \end{bmatrix}$ is a skew symmetric matrix, then value of $a + b + c + d + e$ is equal to

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:

For what value of $k$, the following system have a unique solution? (where $\mathbb{R}$ is set of real numbers)

$x + y + z = 1$

$2x + 3y + 4z = 3$

$x - y + kz = 5$