$\left|\begin{array}{lll}2 & 3 & 5 \\ 3 & 5 & 2 \\ 5 & 2 & 3\end{array}\right|+\left|\begin{array}{ccc}1 & 1 & 1 \\ 7 & 11 & 13 \\ 49 & 121 & 169\end{array}\right|=$

If $P$ and $Q$ are square matrices such that $P^{2006} = O$ and $PQ = P + Q$,then $\det(Q)$ will be

Match List-$I$ with List-$II$:

List-$I$	List-$II$
a) $A$ matrix which is not a square matrix	i) Symmetric matrix
b) $A$ square matrix $A' = A$	ii) Null matrix
c) The diagonal elements of a diagonal matrix are same	iii) Rectangular matrix
d) $A$ matrix which is both symmetric and skew symmetric	iv) Scalar matrix

Let the numbers $2, b, c$ be in an $A.P.$ and $A = \begin{bmatrix} 1 & 1 & 1 \\ 2 & b & c \\ 4 & b^2 & c^2 \end{bmatrix}$. If $\det(A) \in [2, 16]$,then $c$ lies in the interval:

If $A = \begin{bmatrix} \cos^2 \alpha & \cos \alpha \sin \alpha \\ \cos \alpha \sin \alpha & \sin^2 \alpha \end{bmatrix}$ and $B = \begin{bmatrix} \cos^2 \beta & \cos \beta \sin \beta \\ \cos \beta \sin \beta & \sin^2 \beta \end{bmatrix}$ are two matrices such that the product $AB$ is a null matrix,then $\alpha - \beta$ is:

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	$(s)$ $3$