The population of a town increases at a rate proportional to the population at that time. If the population increases from forty thousand to eighty thousand in 20 years, then the population in another 40 years will be

If the vectors $m \hat{i}+m \hat{j}+n \hat{k}, \hat{i}+\hat{k}, n \hat{i}+n \hat{j}+p \hat{k}$ lie in a plane then…

The value of

$$ \begin{aligned} \sin ^2 5^{\circ}+\sin ^2 10^{\circ} & +\sin ^2 15 +\ldots \ldots \ldots \ldots \ldots \ldots+\sin ^2 85^{\circ}+\sin ^2 90^{\circ}= \end{aligned} $$

The area bounded by the curve $x=2-y-y^2$ and the Y -axis is