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

If $$A=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$$, and $$A(\operatorname{adj} A)=k I$$, then the value of $$(k+1)^4$$ is

$$\int \cos ^3 x e^{\log (\sin x)^2} d x=$$