Write Gauss’s law and give its expression.

If the number of electric lines of force emerging out of a closed surface is $1000$ , then the charge enclosed by the surface is ………. $C$

A cubical region of side a has its centre at the origin. It encloses three fixed point charges, $-q$ at $(0,-a / 4,0),+$ $3 q$ at $(0,0,0)$ and $-q$ at $(0,+a / 4,0)$. Choose the correct option$(s)$.

$(A)$ The net electric flux crossing the plane $x=+a / 2$ is equal to the net electric flux crossing the plane $x=-a / 2$.

$(B)$ The net electric flux crossing the plane $y=+a / 2$ is more than the net electric flux crossing the plane $y=-a / 2$

$(C)$ The net electric flux crossing the entire region is $\frac{q}{\varepsilon_0}$.

$(D)$ The net electric flux crossing the plane $z=+a / 2$ is equal to the net electric flux crossing the plane $x=+a / 2$.

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:-

Two charges of $5 Q$ and $-2 Q$ are situated at the points $(3 a, 0)$ and $(-5 a, 0)$ respectively. The electric flux through a sphere of radius $4a$ having center at origin is