The figure shows a neutral metallic sphere with a point charge $+Q$ placed near its surface. Electrostatic equilibrium conditions exist on metallic sphere. Mark the correct statements.

            

An infinitely long thin non-conducting wire is parallel to the $z$-axis and carries a uniform line charge density $\lambda$. It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $PQ$ subtends an angle $120°$ at the centre $O$ of the spherical shell, as shown in the figure. The permittivity of free space is ${\epsilon }_0$. Which of the following statements (are) true?

Two non-conducting spheres of radii $R_1$ and $R_2$ and carrying uniform volume charge densities $+\mathrm{\rho }$ and $-\mathrm{\rho }$, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region

A point charge $+Q$ is placed just outside an imaginary hemispherical surface of radius $R$ as shown in the figure. Which of the following statements is/are correct? 

Two small particles $A$ and $B$ having masses $\mathrm{m}=0.5 \mathrm{kg}$ each and charge $q_1=\left(-\frac{155}{18}\mu C\right) and q_2=\left(+100\mu C\right)$ respectively, are connected at the ends of a non-conducting, flexible and inextensible string of length $\mathrm{r}=0.5 \mathrm{m}$. Particle A is fixed and $B$ is whirled along a vertical circle with centre at A. If a vertically upward electric field of strength $E=1.1\times {10}^{5}N{C}^{-1}$ exists in the space, the minimum velocity of the particle $B$ at the highest position is (in $\mathrm{m}/\mathrm{s}$ ) so that it may just complete the circle. $\left(g=10{ ms}^{-2}\right)$ (Approximate the answer to the nearest integer.)

Two charged particles $\left(m,q\right)$ and $\left(2m,-2q\right)$ are placed in a gravity free space where a uniform electric field $E$ exists as shown in figure. After the particles are released they stay at a constant distance from each other. What is the square of distance between them in meter-square? (Neglected the gravitational interaction, take $\frac{q}{4\pi {\epsilon }_{0}E}=200$ metre-square)