Question

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

Find a vector in the direction of $\stackrel{\rightarrow}{a}=\stackrel{\wedge}{i}-2\;\stackrel{\wedge}{j}$ that has magnitude 7 units.

If $\left(\begin{array}{l l }1 & 2 \\ 3 & 4\end{array}\right)$ $\left(\begin{array}{l l }3 & 1 \\ 2 & 5\end{array}\right)$ = $\left(\begin{array}{l l }7 & 11 \\ k & 23\end{array}\right)$ , then write the value of k.

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

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

Write the degree of the differential equation : $\left(\frac{d y}{d x}\right)^{4}+3x\frac{d^{2}y}{d x^{2}}=0.$

Write the value of $\stackrel{\rightarrow}{p}\$ for which the vectors $3\stackrel{\wedge}{i}+2\stackrel{\wedge}{j} +9\stackrel{\wedge}{k}$ and $\stackrel{\wedge}{i}-2p\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$ are parallel vectors.