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

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

The probability distribution of a random variable X is

then Var(X) =