Question

Write value of $\textstyle\int$ sec x(sec x + tan x) dx

Find $|\stackrel{\rightarrow}{x}|\$, if for a unit vector $\stackrel{\rightarrow}{a}\$ and ($\stackrel{\rightarrow}{x}\$ + $\stackrel{\rightarrow}{a}\$ )($\stackrel{\rightarrow}{x}\$ -$\stackrel{\rightarrow}{a}\$ ) = 15.

If matrix A = $\left(\begin{array}{l l }1 & -1 \\ -1 & 1\end{array}\right)$ and A² = kA, then write the value of k.

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

If A = $\left(\begin{array}{l l }4 & 6 \\ 7 & 5\end{array}\right)$ , then what is the value of $\ A{\cdot}(a d j A)$ ?

Write the value of $\textstyle\int\!{\frac{2-3\sin x}{\cos^{2}x}}\,d x$.

Find ‘λ’ when the projection of $\stackrel{\rightarrow}{a}\$ = $λ\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$ on $\stackrel{\rightarrow}{b}\$ = $2\stackrel{\wedge}{i}+6\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$ is 4 units.