CUET Mathematics 2023 22 May Shift 3 PYQs

The value of the determinant $\begin{vmatrix} a\cos\theta & b\sin\theta & 0 \\ -b\sin\theta & a\cos\theta & 0 \\ 0 & 0 & c \end{vmatrix}$ is :

Which of the following are correct?

(A) If A and B are symmetric matrices such that AB = BA, then AB is symmetric.

(B) If A and B are symmetric matrices of the same order, then (A+B) is a symmetric matrix.

(C) If A and B are symmetric matrices of the same order, then (AB-BA) is a symmetric matix.

(D) If A and B are symmetric matrices of the same order, then (AB+BA) is a skew symmetric matrix

Choose the correct answer from the options given below:

If the points $(2, -3)$, $(\lambda, -1)$ and $(0, 4)$ are collinear, then the value of $\lambda$ is