What is the lowest resistance that can be obtained by combining four coils of resistances $4\, \Omega, 8\, \Omega, 12\, \Omega$ and $24\, \Omega$?

$A$ piece of wire having resistance $R$ is cut into four equal parts. $(a)$ How will the resistance of each part compare with the original resistance? $(b)$ If the four parts are placed in parallel,how will the joint resistance compare with the resistance of the original wire?

How can three resistors of resistances $2\, \Omega$,$3\, \Omega$,and $6\, \Omega$ be connected to give a total resistance of $1\, \Omega$?

If three resistors of $5 \Omega$,$10 \Omega$,and $15 \Omega$ are connected in series,the equivalent resistance $R$ is equal to ........ (in $\Omega$)

$(a)$ What is the total resistance of $n$ resistors each of resistance $R$ connected in:
$(i)$ series?
$(ii)$ parallel?
$(b)$ Calculate the resultant resistance of $3$ resistors $3 \ \Omega, 4 \ \Omega$,and $12 \ \Omega$ connected in parallel.

The equivalent resistance between points $A$ and $B$ of the following electric circuit will be $.........$