Question

If $\left(\begin{array}{l l }2x+y & 3y \\ 0 & 4\end{array}\right)$ = $\left(\begin{array}{l l }6 & 0 \\ 0 & 4\end{array}\right)$ then find the value of x.

Write fog, if f : R → R and g : R → R are given by f(x) = 8x³ and g(x) = $x^{1/3}.$

Find the position vector of a point which divides the join of points with position vectors $\;\stackrel{\rightarrow}{(a}-2\stackrel{\rightarrow}{b})$ and $\;\stackrel{\rightarrow}{(2a}+\stackrel{\rightarrow}{b})$ externally in the ratio 2 : 1.

If f : R → R is defined by f(x) = 3x + 2, then define f [f(x)].

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.

Give an example of a skew symmetric matrix of order 3.

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