$15$ charges, each of value $q$, are placed on the $X$-axis at an equal distance of $0.5R$. The electric flux associated with a spherical closed surface of radius $1.5R$, which has one of the charges at its center, is:

An infinite line of charge with uniform line charge density of $\lambda = 1 \ C \ m^{-1}$ is placed along the $y$-axis. $A$ point charge $q = 1 \ C$ is placed on the $x$-axis at a distance of $d = 3 \ m$ from the origin. At what distance $r$ from the origin on the $x$-axis,between the origin and the point charge,is the total electric field zero (in $m$)?

$A$ long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral. Then

Two long thin charged rods with charge density $\lambda$ each are placed parallel to each other at a distance $d$ apart. The force per unit length exerted on one rod by the other will be (where $k = \frac{1}{4 \pi \varepsilon_0}$)

Two large,thin metal plates are parallel and close to each other. On their inner faces,the plates have surface charge densities of opposite signs and of magnitude $17.0 \times 10^{-22} \; C/m^2$. What is $E$:
$(a)$ in the outer region of the first plate,
$(b)$ in the outer region of the second plate,and
$(c)$ between the plates?

$A$ non-conducting solid sphere of radius $R$ is uniformly charged. The magnitude of the electric field due to the sphere at a distance $r$ from its center is:
$(1) \text{ Increases with increase in } r \text{ for } r < R$
$(2) \text{ Decreases with increase in } r \text{ for } 0 < r < \infty$
$(3) \text{ Decreases with increase in } r \text{ for } R < r < \infty$
$(4) \text{ Is continuous at } r = R$