Four dipoles having charge $\pm e$ are placed inside a sphere. The total flux of $\vec{E}$ coming out of the sphere is

Shown in the figure is a shell made of a conductor. It has inner radius $a$ and outer radius $b$,and carries a total charge $Q$. At its centre is a dipole $\vec{P}$ as shown. In this case,

$A$ few electric field lines for a system of two charges $Q_1$ and $Q_2$ fixed at two different points on the $x$-axis are shown in the figure. These lines suggest that:
$(A)$ $|Q_1| > |Q_2|$
$(B)$ $|Q_1| < |Q_2|$
$(C)$ at a finite distance to the left of $Q_1$ the electric field is zero
$(D)$ at a finite distance to the right of $Q_2$ the electric field is zero

Select the correct statement$(s)$.
$(1)$ The tangent drawn at any point on an electric field line gives the direction of the force acting on a positive charge at that point.
$(2)$ The normal drawn at any point on an electric field line gives the direction of the force acting on a positive charge at that point.
$(3)$ Electric field lines start from a negative charge and end on a positive charge.
$(4)$ Electric field lines start from a positive charge and end on a negative charge.

$A$ point charge $+q$ is placed in front of a grounded metal plate. Points $P$ and $Q$ are between the charge $X$ and the plate $Y$ as shown in the figure. Let $E_P$ and $E_Q$ be the magnitudes of the electric fields at points $P$ and $Q$ respectively. Which of the following statements is true?

If an electric field is given by $\vec{E} = 10 \hat{i} + 3 \hat{j} + 4 \hat{k}$,calculate the electric flux through a surface of area $A = 10 \text{ units}$ lying in the $yz$-plane.