Find the equivalent resistance between point $A$ and $B$ in the following circuit. (The resistance of each resistor is $R$)

What will be the most suitable combination of three resistors $A = 2 \, \Omega$,$B = 4 \, \Omega$,$C = 6 \, \Omega$ so that $\frac{22}{3} \, \Omega$ is the equivalent resistance of the combination?

Eight copper wires of length $l$ and diameter $d$ are joined in parallel to form a single composite conductor of resistance $R$. If a single copper wire of length $2\,l$ has the same resistance $R$,then its diameter will be $.....d$.

Let there be $n$ resistors $R_1, \dots, R_n$ with $R_{\max} = \max \{R_1, \dots, R_n\}$ and $R_{\min} = \min \{R_1, \dots, R_n\}$. Show that when they are connected in parallel,the resultant resistance $R_p < R_{\min}$ and when they are connected in series,the resultant resistance $R_s > R_{\max}$. Interpret the result physically.

In the figure given,the electric current flowing through the $5\, k\Omega$ resistor is $'x' \, mA.$
The value of $x$ to the nearest integer is .........

$A$ student has $10$ resistors of resistance $r$. The minimum resistance made by him from given resistors is