$A$ bimetallic strip consists of metals $A$ and $B$. It is mounted rigidly at the base as shown. The metal $A$ has a higher coefficient of expansion compared to that of metal $B$. When the bimetallic strip is placed in a cold bath,it will:

A positive ion $A$ and a negative ion $B$ has charges $6.67 \times 10^{-19}\ {C}$ and $9.6 \times 10^{-10}\ {C}$, and masses $19.2 \times 10^{-27}\ {kg}$ and $9 \times 10^{-27}\ {kg}$ respectively. At an instant, the ions are separated by a certain distance $r$. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is ${P} \times 10^{-13}$, where the value of $P$ is _________ .
(Take $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\ {Nm}^2 {C}^{-1}$ and universal gravitational constant as $6.67 \times 10^{-11}\ {Nm}^2 {kg}^{-2}$)

The rate of the reaction $2N_2O_5 \to 4NO_2 + O_2$ can be written in three ways:
$-\frac{d[N_2O_5]}{dt} = k[N_2O_5]$
$\frac{d[NO_2]}{dt} = k'[N_2O_5]$
$\frac{d[O_2]}{dt} = k''[N_2O_5]$
The relationship between $k$ and $k'$ and between $k$ and $k''$ are:

Let $O$ be the origin and $A$ be a point on the curve $y^2=4x$. Then the locus of the midpoint of $OA$ is:

What is $Y$ in the following reaction?
$C_2H_5I + NaOC_2H_5 \longrightarrow X + NaI$
$X + 2HI \xrightarrow{\Delta} 2Y + H_2O$

Two equally charged metal spheres $A$ and $B$ repel each other with a force of $4 \times 10^{-5} ~N$. Another identical uncharged sphere $C$ is touched to $A$ and then placed at the midpoint of the line joining the spheres $A$ and $B$. The net electric force on the sphere $C$ is