The equation of a line with slope $$-\frac{1}{\sqrt{2}}$$ and makes an intercept of $$2 \sqrt{2}$$ units on negative direction of $$y$$-axis is

If $$\mathrm{\frac{3+2i}{1+i}=\frac{1}{2}(x+iy)}$$, then x $$-$$ y =

If the angle between the vectors $$\overline{\mathrm{a}}=2 \lambda^2 \hat{\mathrm{i}}+4 \lambda \hat{\mathrm{j}}+\hat{\mathrm{k}}$$ and $$\overline{\mathrm{b}}=7 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}$$ is obtuse, then $$\lambda \in$$

A population P grew at the rate given by the equation $$\frac{dP}{dt}=0.5P$$, then the population will become double in