The value of $$\int \mathrm{e}^x\left(\frac{x^2+4 x+4}{(x+4)^2}\right) \mathrm{d} x$$ is :

The diagonal of a square is changing at the rate of $$0.5 \mathrm{~cm} / \mathrm{sec}$$. Then the rate of change of area when the area is $$400 \mathrm{~cm}^2$$ is equal to

Let $$\bar{a}=\hat{i}+2 \hat{j}-\hat{k}$$ and $$\bar{b}=\hat{i}+\hat{j}-\hat{k}$$ be two vectors. If $$\bar{c}$$ is a vector such that $$\bar{b} \times \bar{c}=\bar{b} \times \bar{a}$$ and $$\overline{\mathrm{c}} \cdot \overline{\mathrm{a}}=0$$, then $$\overline{\mathrm{c}} \cdot \overline{\mathrm{b}}$$ is

Let $$P \equiv(-3,0), Q \equiv(0,0)$$ and $$R \equiv(3,3 \sqrt{3})$$ be three points. Then the equation of the bisector of the angle $$\mathrm{PQR}$$ is