If the electric field is given by $\vec{E} = (5 \hat{i} + 4 \hat{j} + 9 \hat{k})$. The electric flux through a surface of area $20$ units lying in the $Y-Z$ plane will be (in units):

Two point charges $2q$ and $q$ are placed at vertex $A$ and the centre of face $CDEF$ of the cube, respectively, as shown in the figure. The electric flux passing through the cube is:

Four charges $2 \mu C, -3 \mu C, 4 \mu C, -4 \mu C$ and $-1 \mu C$ are enclosed by a Gaussian surface of radius $2 \ m$. The net outward flux through the Gaussian surface is (in $\mu V-m$):

$A$ 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?
$[A]$ The electric flux passing through the curved surface of the hemisphere is $-\frac{Q}{2 \varepsilon_0}\left(1-\frac{1}{\sqrt{2}}\right)$
$[B]$ Total flux through the curved and the flat surfaces is $\frac{Q}{\varepsilon_0}$
$[C]$ The component of the electric field normal to the flat surface is constant over the surface
$[D]$ The circumference of the flat surface is an equipotential

$A$ charge $q$ is placed at one corner of a cube as shown in the figure. The flux of the electrostatic field $\overrightarrow{E}$ through the shaded area is ...... .

The given figure shows the electric field lines due to two charges $q_1$ and $q_2$. What are the signs of the two charges?