Question

Evaluate: $\textstyle\int\cot{x}(cosec x-1)e^{x}d x$ .

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

State the reason why the Relation R = {(a, b) : a ≤ b²} on the set R of real numbers is not reflexive.

Find the sum of the vectors : $\stackrel{\rightarrow}{a}=\hat{i}-3\hat{k},$ ${\vec{b}}=2{\hat{j}}-{\hat{k}},$ $\stackrel{\rightarrow}{c}=2\hat{i}-3\hat{j}+2\hat{k}.$

If A = $[a_{i j}]$ is is a matrix of order 2 × 2, such that |A| = –15, and $C_{i j}$ represents the cofactor of $a_{i j}$ , then find $a_{21}c_{21}+a_{22}c_{22}$

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.

Find the scalar components of the vector $\stackrel{\rightarrow}{A B}$ with initial point A(2,1) and terminal point B (– 5, 7).