$\int_{0}^{1000} e^{x - [x]} \, dx$ is equal to:

Who discovered viroids?

If $z = \sec^{-1}\left(\frac{x^4+y^4-8x^2y^2}{x^2+y^2}\right)$,then $x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y}$ is equal to

$A$ star initially has $10^{40}$ deuterons. It produces energy via the processes:
${}_1H^2 + {}_1H^2 \to {}_1H^3 + p$
${}_1H^2 + {}_1H^3 \to {}_2He^4 + n$
The masses of the nuclei are as follows: $M(H^2) = 2.014 \, amu$,$M(p) = 1.007 \, amu$,$M(n) = 1.008 \, amu$,$M(He^4) = 4.001 \, amu$. If the average power radiated by the star is $10^{16} \, W$,the deuteron supply of the star is exhausted in a time of the order of:

If $\overrightarrow{u}=\overrightarrow{a}-\overrightarrow{b}$, $\overrightarrow{v}=\overrightarrow{a}+\overrightarrow{b}$, $|\overrightarrow{a}|=|\overrightarrow{b}|=2$, then $|\overrightarrow{u} \times \overrightarrow{v}|$ is equal to

If the line joining $A(1, 3, 4)$ and $B$ is divided by the point $P(-2, 3, 5)$ in the ratio $1: 3$, then the coordinates of $B$ are: