Which one of the following reactions does not form a gaseous product?

$A$ parallel plate capacitor with oil (dielectric constant $K = 2$) between the plates has capacitance $C$. If the oil is removed,the capacitance of the capacitor becomes:

The correct match of the group reagents in List$-I$ for precipitating the metal ion given in List$-II$ from solutions, is

List$-I$	List$-II$
$(P)$ Passing $H _2 S$ in the presence of $NH _4 OH$	$(1) \ Cu ^{2+}$
$(Q) \ \left( NH _4\right)_2 CO _3$ in the presence of $NH _4 OH$	$(2) \ Al ^{3+}$
$(R) \ NH _4 OH$ in the presence of $NH _4 Cl$	$(3) \ Mn ^{2+}$
$(S)$ Passing $H _2 S$ in the presence of dilute $\text{HCl}$	$(4) \ Ba ^{2+}$
	$(5) \ Mg ^{2+}$

If $x^2+y^2=t+\frac{1}{t}$ and $x^4+y^4=t^2+\frac{1}{t^2}$,then $x^3 y \frac{d y}{d x}$ is equal to

If $z=1+i\sqrt{3}$,then $|\operatorname{Arg} z|+|\operatorname{Arg} \bar{z}|$ is equal to

$A$ cylinder of height $h$ is filled with water and is kept on a block of height $h / 2$. The level of water in the cylinder is kept constant. Four holes numbered $1, 2, 3$ and $4$ are at the side of the cylinder and at heights $0, h / 4, h / 2$ and $3h / 4$ respectively from the base of the cylinder. When all four holes are opened together,the hole from which water will reach the farthest distance on the plane $PQ$ is the hole number