Question

Write the value of $\textstyle\int\!{\frac{\ d x}{x^{2}+16}}$

If matrix A = $[a_{i j}]_{2\times2}$, where $a_{i j}$ = $\left\{\begin{array}{l}{{2,\ i\neq j}}\\ {{0,\ i=j^{\prime}}}\end{array}\right.$ , Write the matrix A.

Find the magnitude of each of the vectors $\stackrel{\rightarrow}{a}$ and $\stackrel{\rightarrow}{b}$,having the same magnitude such that the angle between them is 60° and their scalar product is ${\frac{9}{2}}.$

Write the inverse of the matrix $\left(\begin{array}{l l }cosθ & -sinθ \\ sinθ & cosθ\end{array}\right)$ .

If m and n are the order and degree, respectively of the differential equation $\textstyle y\left({\frac{d y}{d x}}\right)^{3}+x^{3}\left({\frac{d^{2}y}{d x^{2}}}\right)^{2}-x y$= sin x, then write the value of m + n.

Write the projection of the vector $\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ along the vector $\stackrel{\rightarrow}{j}\$.

If a line has direction ratios 2, – 1, – 2, then what are its direction cosines ?