B M Sharma Solutions for Chapter: Electric Potential, Exercise 2: DPP

The electrostatic potential on the surface of a charged conducting sphere is $100 \mathrm{V}$. Two statements are made in this regard
$S_1:$ at any point inside the sphere, the electric field intensity is zero.
$S_2:$ at any point inside the sphere, the electrostatic potential is $100 \mathrm{V}$.

Which of the following is a correct statement?

If uniform electric field, $\overrightarrow{\mathrm{E}}=E_0\hat{\mathrm{i}}+2E_0\hat{\mathrm{j}}$ where $E_0$ is a constant existing in a region of space and at $\left(0, 0\right)$ the electric potential $V$ is zero, then the potential at $\left(x_0, 0\right)$ will be?

There exists a uniform electric field in the space as shown. Four points $A$, $B$, $C$ and $D$ are marked which are equidistant from the origin. If $V_{\mathrm{A}}$, $V_{\mathrm{B}}$, $V_{\mathrm{C}}$ and $V_{\mathrm{D}}$ are their potentials respectively, then

The potential of an electric field $\overrightarrow{E}=\left(y\hat{i}+x\hat{j}\right)$ is

A uniform electric field exists in the $xy$ plane. The potential of points $\mathrm{A} \left(-2,2\right)$, $\mathrm{B} \left(2,2\right)$ and $\mathrm{C} \left(2,4\right)$ are $16 \mathrm{V}$, $4 \mathrm{V}$ and $12 \mathrm{V}$ respectively. The electric field is (all distances are in $\mathrm{m}$)

Four similar charges each of charge $+q$ are placed at the four corners of a square of side $a$. Find the value of the integral $-{\int }_{\infty }^{a/\sqrt{2}}\overrightarrow{E}·\overrightarrow{dr}$ (in $\mathrm{Volts}$) if the value of  the integral,

$-{\int }_{a/\sqrt{2}}^0\overrightarrow{E}·\overrightarrow{dr}=\frac{\sqrt{2}Kq}{a}$ (where $K=\frac{1}{4\pi {\epsilon }_0}$)

Two infinite, parallel, non-conducting sheets carry equal positive charge density $\sigma$. One is placed in the $yz$ plane and the other at distance $x=a$. Take potential $V=0$ at $x=0$.

About an electric field, which of the following statements are not true?