Question

Write the value of the determinant : $\begin{vmatrix}102 & 18 & 36 \\ 1 & 3 & 4 \\ 17 & 3 & 6\end{vmatrix}$

If $\left(\begin{array}{l l l }2 & 1 & 3\end{array}\right)$ $\left(\begin{array}{l l l }-1 & 0 & -1 \\ -1 & 1 & 0 \\ 0 & 1 & 1\end{array}\right)$ $\left(\begin{array}{l }1 \\ 0 \\ -1\end{array}\right)$ = A , then write the order of matrix A.

Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.

If A = $\left(\begin{array}{l l }cosα & sinα \\ -sinα & cosα\end{array}\right)$ , find α satisfying $0\leq\alpha\leq{\frac{\pi}{4}}$ when $A+A^{T}=\sqrt{2}I$ where $A^{T}$ is transpose of A.

Write the degree of the differential equation : $x\left(\frac{d^{2}y}{d x^{2}}\right)^{3}+y\left(\frac{d y}{d x}\right)^{4}+x^{3}=0$

Evaluate : $\textstyle\int\!{\frac{\ d x}{\sin^{2}x\cos^{2}x}}$ .

If A = $[a_{i j}]$ is is a matrix of order 2 × 2, such that |A| = –15, and $C_{i j}$ represents the cofactor of $a_{i j}$ , then find $a_{21}c_{21}+a_{22}c_{22}$