$H^{+}$,$D^{+}$,and $T^{+}$ differ in all of the following $EXCEPT$ one. Identify it.

If $u=f(r)$,where $r^2=x^2+y^2$,then $\left(\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}\right)$ is equal to

At $25 \ ^\circ C,$ the solubility product of $Mg(OH)_2$ is $1.0 \times 10^{-11}.$ At which $pH$ will $Mg^{2+}$ ions start precipitating in the form of $Mg(OH)_2$ from a solution of $0.001 \ M \ Mg^{2+}$ ions?

Four massless springs whose force constants are $2k, 2k, k$ and $2k$ respectively are attached to a mass $M$ kept on a frictionless plane (as shown in the figure). If the mass $M$ is displaced in the horizontal direction,then the frequency of oscillation of the system is:

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

The coordinate axes are rotated through an angle of $135^o$. If the coordinates of a point $P$ in the new system are $(4, -3)$,then the coordinates of $P$ in the original system are: