Question

If f(x) = 27x³ and g(x) = $x^{1/3}$, then find gof(x).

Find : $\textstyle\int\!{\frac{1}{x(1+\log x)}}\,d x$

Let R={(a,a³): a is a prime number less than 5} be a relation. Find the range of R.

Find the value of x + y from the following equation : 2 $\left(\begin{array}{l l }x & 5 \\ 7 & y-3\end{array}\right)$ + $\left(\begin{array}{l l }3 & -4 \\ 1 & 2\end{array}\right)$ = $\left(\begin{array}{l l }7 & 6 \\ 15 & 14\end{array}\right)$ .

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

Find $\stackrel{\rightarrow}{a}$.$\stackrel{\rightarrow}{b}$,If $\stackrel{\rightarrow}{a}$ = $-\stackrel{\wedge}{i}+\stackrel{\wedge}{j} -2\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{b}$ = $2\stackrel{\wedge}{i}+3\stackrel{\wedge}{j} -\stackrel{\wedge}{k}$.

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).