Question

Evaluate $\textstyle\int$ sec² (7 – 4x) dx.

If 3A – B = $\left(\begin{array}{l l }5 & 0 \\ 1 & 1\end{array}\right)$ and B = $\left(\begin{array}{l l }4 & 3 \\ 2 & 5\end{array}\right)$ , then find the matrix A.

If $\begin{vmatrix} \sin\alpha & \cos\beta \\ \cos\alpha & \sin\beta \end{vmatrix} =-\ {\begin{array}{l}{1}\\ {2}\end{array}}\$ , write the value of x.

Find the projection of vector $\stackrel{\wedge}{i}+3\stackrel{\wedge}{j} +7\stackrel{\wedge}{k}$ on the vector $2\stackrel{\wedge}{i}-3\stackrel{\wedge}{j} +6\stackrel{\wedge}{k}$.

If A = $\left(\begin{array}{l l}{{0}}&{{3}}\\ {{2}}&{{-5}}\end{array}\right)$ and $K A\ =\ {\left(\begin{array}{l l}{0}&{4a}\\ {-8}&{5b}\end{array}\right)}$ find the values of k and a.

If A = {1, 2, 3}, B = {4, 5, 6, 7} and f = {(1, 4), (2, 5),(3, 6)} is a function from A to B. State whether f is one-one or not.

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