Match the LIST-I with LIST-II

LIST-I	LIST-II
A. $\begin{vmatrix} x+2 & 3 \\ x+5 & 4 \end{vmatrix} = 3$	I. $x = 10$
B. $\begin{vmatrix} x+2 & x+5 \\ 3 & 4 \end{vmatrix} = 13$	II. $x = 60$
C. $\begin{vmatrix} x+4 & x-4 \\ 8 & 7 \end{vmatrix} = 0$	III. $x = 0$
D. $\begin{vmatrix} x+4 & 8 \\ x-4 & 7 \end{vmatrix} = 60$	IV. $x = 20$

Choose the correct answer from the options given below:

The value of $\begin{vmatrix} 2^x & 1 & 6^x \\ 4^x & 1 & 3^x \\ 2^x & 1 & 6^x \end{vmatrix}$, where $x \neq 0$ is:

Which of the following statements are correct?

A. If $P$ and $Q$ are square matrices of same order, then $(PQ^T-QP^T)$ is a skew symmetric matrix.

B. The number of all possible matrices of order $3\times2$ with each entry either –1 or 1, is 64.

C. If $P$ is an invertible matrix, then $P^T$ is also invertible.

D. If $P$ and $Q$ are square matrices of the same order, then $|PQ|=|P|+|Q|$.

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$ and $I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, then the value of $A^2 - 5A + 6I$ is

The minimum value of $\begin{vmatrix}2 & 2 & 2 \\ 2 & 2+x & 2 \\ 2 & 2 & 2+x\end{vmatrix}$, $x \in R$ is

If matrix $A_p = \begin{bmatrix} p & p+1 \\ p-1 & p \end{bmatrix}_{p \in N}$ (where N is the set of natural numbers), then the value of $|A_1| + |A_2| + |A_3| + \dots + |A_{2025}|$ is:

If a, b and c are all different from zero and $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix} = 0$, then the value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$ is :