If $\begin{bmatrix} x & 4 & -1 \end{bmatrix} \begin{bmatrix} 2 & 1 & 0 \\ 1 & 0 & 2 \\ 0 & 2 & 4 \end{bmatrix} \begin{bmatrix} x \\ 4 \\ -1 \end{bmatrix} = 0$,then $x=$

Let $A = \begin{pmatrix} 1 & 2 & 7 \\ 4 & -2 & 8 \\ 3 & 8 & -7 \end{pmatrix}$ and $\det(A - \alpha I) = 0$, where $\alpha$ is a real number. If the largest possible value of $\alpha$ is $p$, then the circle $(x - p)^2 + (y - 2p)^2 = 320$ intersects the coordinate axes at

Match the Statements / Expressions in Column $I$ with the Statements / Expressions in Column $II$.

Column $I$	Column $II$
$(A)$ The minimum value of $\frac{x^2+2x+4}{x+2}$ for $x > -2$ is	$(p)$ $0$
$(B)$ Let $A$ and $B$ be $3 \times 3$ matrices of real numbers,where $A$ is symmetric,$B$ is skew-symmetric,and $(A+B)(A-B)=(A-B)(A+B)$. If $(AB)^t=(-1)^k AB$,where $(AB)^t$ is the transpose of the matrix $AB$,then the possible values of $k$ are	$(q)$ $1$
$(C)$ Let $a=\log_3 \log_3 2$. An integer $k$ satisfying $1 < 2^{(-k+3^{-a})} < 2$,must be less than	$(r)$ $2$
$(D)$ If $\sin \theta = \cos \phi$,then the possible values of $\frac{1}{\pi}(\theta \pm \phi - \frac{\pi}{2})$ are	$(s)$ $3$

How many $3 \times 3$ matrices $M$ with entries from $\{0, 1, 2\}$ are there,for which the sum of the diagonal entries of $M^T M$ is $5$?

If the matrix $A = \begin{bmatrix} 4 & 1 \\ 3 & 2 \end{bmatrix}$ is expressed as the sum of a symmetric matrix $B$ and a skew-symmetric matrix $C$, then which of the following relations is correct?

If $A$ is a square matrix such that $A^2=A$,then $(I-A)^3$ is