Question

Write the value of $\textstyle\int\!{\frac{1-\sin x}{\cos^{2}x}}\,d x\,.$

If A = $\left(\begin{array}{l l l }1 & 2 & 2 \\ 2 & 1 & x \\ -2 & 2 & -1\end{array}\right)$ is a matrix satisfying AA’ = 9I, find x.

If $\left(\begin{array}{l l }1 & 0 \\ y & 5\end{array}\right)$ + 2 $\left(\begin{array}{l l }x & 0 \\ 1 & -2\end{array}\right)$ = , where I is a 2×2 unit matrix, find (x – y).

Write the value of x - y + z from following equation. $\left(\begin{array}{l }x+y+z \\ x+z \\ y+z\end{array}\right)$ = $\left(\begin{array}{l }9 \\ 5 \\ 7\end{array}\right)$

Evaluate $\textstyle\int\!{\frac{x^{3}-x^{2}+x-1}{x-1}}\,d x\,.$

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

Find x from the matrix equation $\left(\begin{array}{l l }1 & 3 \\ 4 & 5\end{array}\right)$ $\left(\begin{array}{l }x \\ 2\end{array}\right)$ = $\left(\begin{array}{l }5 \\ 6\end{array}\right)$ .