Question

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

The two vectors $:{\hat{j}}+{\hat{k}}$ and $3\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$ represent the two sides AB and AC, respectively of $\Delta A B C.$ Find the length of the median through A.

If A is a 3 × 3 matrix, $|A|\neq0$ and $|3A|\,=\,k|A|,$ then write the value of k.

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

Write fog, if f : R → R and g : R → R are given by f(x) = |x| and g(x) = |5x - 2|.

If $\left(\begin{array}{l l }x-y & z \\ 2x-y & w\end{array}\right)$ = $\left(\begin{array}{l l }-1 & 4 \\ 0 & 5\end{array}\right)$ , find the value of x + y.

Find : $\textstyle\int{\frac{\sin^{6}x}{\cos^{8}x}}\,d x.$