Question

If ${\left[\begin{array}{l l}{x y}&{4}\\ {z+6}&{x+y}\end{array}\right]}\ ={\left[\begin{array}{l l}{8}&{w}\\ {0}&{6}\end{array}\right]},$ write the value of x + y + z.

If A = $\left(\begin{array}{l l }3 & 10 \\ 2 & 7\end{array}\right)$ , then write A⁻¹.

Evaluate $\textstyle\int{\frac{\cos{\sqrt{x}}}{\sqrt{x}}}\,d x\ .$

If $\left(\begin{array}{l l }x-y & 2y \\ 2y+z & x+y\end{array}\right)$ = $\left(\begin{array}{l l }1 & 4 \\ 9 & 5\end{array}\right)$

L and M are two points with position vectors $2\stackrel{\rightarrow}{a}-\stackrel{\rightarrow}{b}$ and $\stackrel{\rightarrow}{a}+2\stackrel{\rightarrow}{b}$ respectively. Write the position vectors of a point N which divides the line segment LM in the ratio 2:1 externally.

If R = {(x, y) : x + 2y = 8} is a relation on N, writethe range of R.

Find : $\int{\frac{\sin^{2}x-\cos^{2}x}{\sin x\cos x}}\,d x$