Select the incorrect statement.

If $u=\sin ^{-1}\left(\frac{x}{y}\right)+\tan ^{-1}\left(\frac{y}{x}\right)$,then the value of $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is

$A$ minimum value of $\int_0^x t e^{t^2} d t$ is

Eubacteria is an example of which domain?

As shown in the figure,a block of mass $10 \, kg$ lying on a horizontal surface is pulled by a force $F$ acting at an angle of $30^{\circ}$ with the horizontal. For $\mu_{s} = 0.25$,the block will just start to move for the value of $F$ in $N$ is: [Given $g = 10 \, ms^{-2}$]

Along the $x$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at a point $P$ located at a distance $r$ from the charge $-q$ (where $r > a$) is ($\varepsilon_0$ is the permittivity of free space):