$$\lim _\limits{x \rightarrow 0} \frac{9^x-4^x}{x\left(9^x+4^x\right)}=$$

If the length of the perpendicular to a line from the origin is $2 \sqrt{2}$ units, which makes an angle of $135^{\circ}$ with the X -axis, then the equation of line is

A spherical rain drop evaporates at a rate proportional to its surface area. If initially its radius is 3 mm and after 1 second it is reduced to 2 mm , then at any time t its radius is (where $0 \leq \mathrm{t}<3$)

If $\overline{\mathrm{a}}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \bar{b}=-\hat{i}+2 \hat{j}+\hat{k}$ and $\bar{c}=3 \hat{i}+\hat{j}$ such that $\overline{\mathrm{b}}+\lambda \overline{\mathrm{a}}$ is perpendicular to $\overline{\mathrm{c}}$, then $\lambda$ is