CUET Mathematics 2022 17 Aug Shift 2 PYQs

The set of all values of $\alpha$ for which the system of linear equations

$x + y + z = 1$

$x + 2y + 4z = \alpha$

$x + 4y + 10z = \alpha^2$

is consistent, is

If matrix $A = \begin{bmatrix} x & 2 & 3 \\ a & y & -5 \\ b & c & 0 \end{bmatrix}$ is a skew-symmetric matrix, then

(A) $x + y + c = 5$

(B) $c = 5$

(C) $a + b + c = 0$

(D) $a + b - c = 10$

Choose the correct answer from the options given below:

If the area of a triangle whose vertices are (-1, 3), (1, -5) and (k, 2) where $k > 0$ is 30 sq. units, then the value of k is