When zeolite (hydrated sodium aluminium silicate) is treated with hard water,the sodium ions are exchanged with:

$z=\tan (y+a x)+\sqrt{y-a x} \Rightarrow z_{x x}-a^2 z_{y y}$ is equal to

$300 \, g$ of water at $25^{\circ} C$ is added to $100 \, g$ of ice at $0^{\circ} C$. The final temperature of the mixture is ........... $^{\circ} C$.

If $A$ and $B$ are any two sets,then $A \cup (A \cap B)$ is equal to

$A$ baby has been born with a small tail. It is a case exhibiting:

The sensitivity of a galvanometer is $60 \text{ div/A}$. When a shunt is used,its sensitivity becomes $10 \text{ div/A}$. If the resistance of the galvanometer is $20 \ \Omega$,then the value of the shunt used is: (in $\Omega$)