How much electric flux will come out through a surface $S = 10\hat{j}$ kept in an electrostatic field $\vec{E} = 2\hat{i} + 4\hat{j} + 7\hat{k}$ units?

Consider three point charges $-2Q$, $Q$ and $-Q$ and three surfaces $S_1$, $S_2$ and $S_3$. Match the entries of List-$I$ with that of List-$II$ using Gauss's Law.

List-$I$	List-$II$
$(a)$ Net flux through $S_1$	$(i)$ $\frac{-2Q}{\epsilon_0}$
$(b)$ Net flux through $S_2$	(ii) $\frac{-Q}{\epsilon_0}$
$(c)$ Net flux through $S_3$	(iii) Zero

The electric flux for Gaussian surface $A$ that encloses the charged particles in free space is (given $q_1 = -14\, nC$,$q_2 = 78.85\, nC$,$q_3 = -56\, nC$):

There exists an electric field of $1 \ N/C$ along the $Y$-direction. The flux passing through a square of $1 \ m^2$ placed in the $XY$-plane inside the electric field is . . . . . . .

The electric field in a region is given by $\vec E = a\hat i + b\hat j$. Here $a$ and $b$ are constants. Find the net flux passing through a square area of side $l$ parallel to the $y-z$ plane.

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 $4 a$ having its center at the origin is