Question

Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} given by f = {(1, 2) (3, 5) (4, 1)} and g = {(1, 3), (2, 3), (5, 1)} Write down gof.

If the determinant of matrix A of order 3 × 3 is of value 4, write the value of |3A|.

Evaluate : $\textstyle\int\!{\frac{\ d x}{\sin^{2}x\cos^{2}x}}$ .

Write the value of : $\textstyle\int{\frac{\sec^{2}x}{\operatorname{cosec}^{2}x}}d x.$

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.

If a matrix has 5 elements, then write all possible orders it can have.

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