If A and B are symmetric matrices of the same order, then which one of the following is true?

If A and B are symmetric matrices of same order, then which of the following are correct?

(A) AB-BA is a skew-symmetric matrix.

(B) AB+BA is a skew-symmetric matrix.

(C) $AB^T-BA^T$ is a skew-symmetric matrix.

(D) AB+BA is a symmetric matrix.

Choose the correct answer from the options given below:

If $\begin{vmatrix} m! & (m+1)! & (m+2)! \\ (m+1)! & (m+2)! & (m+3)! \\ (m+2)! & (m+3)! & (m+4)! \end{vmatrix} = 2k$, where $m$ is a positive integer then which of the following are factors of $k$?

A. $m!$

B. $(m+1)!$

C. $(m+2)!$

D. $(m+3)!$

Choose the correct answer from the options given below:

The value of $\begin{vmatrix} 1 & x & y \\ 1 & x+y & y \\ 1 & x & x+y \end{vmatrix}$ is

If $A = \begin{bmatrix} 2 & -3 & 4 \\ -3 & 5 & x \\ 4 & 3 & 0 \end{bmatrix}$ is a symmetric matrix and $B = \begin{bmatrix} 0 & 2 & -10 \\ -2 & z & 6 \\ y & -6 & 0 \end{bmatrix}$ is a skew-symmetric matrix, then the value of $(xy + yz + zx)$ is

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

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 :