$A$ capacitor $C_1 = 1.0 \, \mu F$ is charged up to a voltage $V = 60 \, V$ by connecting it to a battery $B$ through switch $(1)$. Now,$C_1$ is disconnected from the battery and connected to a circuit consisting of two uncharged capacitors $C_2 = 3.0 \, \mu F$ and $C_3 = 6.0 \, \mu F$ in series through a switch $(2)$ as shown in the figure. The sum of the final charges on $C_2$ and $C_3$ is ...... $\mu C$.

In the figure,the area of each plate is $A$ and the distance between consecutive plates is $d$. What is the effective capacitance between points $A$ and $B$?

For the shown situation, in the steady state condition, what is the ratio of the charge stored in the first capacitor to the charge stored in the last $(n^{th})$ capacitor?

Two capacitors $C_1 = 4\ \mu F$ and $C_2 = 2\ \mu F$ are charged to the same potential $V = 500\ V$,but with opposite polarity as shown in the figure. The switches $S_1$ and $S_2$ are closed. Determine the correct statement.

In the circuit shown in the figure,the ratio of charges on $5 \mu F$ and $4 \mu F$ capacitors is:

Six point charges are kept at the vertices of a regular hexagon of side $L$ and centre $O$,as shown in the figure. Given that $K = \frac{1}{4 \pi \varepsilon_0} \frac{q}{L^2}$,which of the following statement$(s)$ is (are) correct?
$(A)$ The electric field at $O$ is $6K$ along $OD$
$(B)$ The potential at $O$ is zero
$(C)$ The potential at all points on the line $PR$ is same
$(D)$ The potential at all points on the line $ST$ is same.