The plates of a parallel plate capacitor are charged up to $100 \, V$. $A$ $2 \, mm$ thick plate is inserted between the plates. To maintain the same potential difference,the distance between the capacitor plates is increased by $1.6 \, mm$. The dielectric constant of the plate is:

The monomer of $[-C(CH_3)_2 - CH_2-]_n$ is ...

The $P-V$ diagram of a system undergoing thermodynamic transformation is shown in figure. The work done on the system in going from $A$ $\rightarrow B$ $\rightarrow C$ is $50 \ J$ and $20 \ cal$ heat is given to the system. The change in internal energy between $A$ and $C$ is ...... $J$. (Take $1 \ cal = 4.2 \ J$)

The $P-V$ diagram of $2\,g$ of helium gas for a certain process $A \to B$ is shown in the figure. What is the heat given to the gas during the process $A \to B$ (in $P_0V_0$)?

Let $\alpha$ and $\beta$ be the roots of the equation $x^2-x-1=0$. If $p_{k}=(\alpha)^{k}+(\beta)^{k}, k \geq 1$,then which one of the following statements is not true?