Resistors of $1\, \Omega$, $2\, \Omega$, and $3\, \Omega$ are connected in the form of a triangle. If a $1.5\, V$ cell of negligible internal resistance is connected across the $3\, \Omega$ resistor, the current flowing through this resistance will be ................ $A$.

Four resistances $10 \ \Omega$,$5 \ \Omega$,$7 \ \Omega$ and $3 \ \Omega$ are connected to form the sides of a rectangle $AB$,$BC$,$CD$,and $DA$ respectively. Another resistance of $10 \ \Omega$ is connected across the diagonal $AC$. The equivalent resistance between $A$ and $B$ is ............. $\Omega$.

The ammeter $A$ reads $2\, A$ and the voltmeter $V$ reads $20\, V$. The value of resistance $R$ is (Assuming finite resistances of ammeter and voltmeter).

Under what condition can the current passing through the resistance $R$ be increased by short-circuiting the battery of emf $E_2$? The internal resistances of the two batteries are $r_1$ and $r_2$ respectively.

Given below are two statements:
Statement $I:$ The equivalent resistance of resistors in a series combination is smaller than the least resistance used in the combination.
Statement $II:$ The resistivity of the material is independent of temperature.
In the light of the above statements,choose the correct answer from the options given below:

An electrical circuit consists of ten $100 \,\Omega$ resistors. Out of these $10$ resistors,a group of $n_1$ resistors are connected in parallel and another group of $n_2$ resistors are separately connected in parallel. These two groups are then connected in series and this combination is connected to a voltage source of $100 \,V$. If the net current through the circuit is $2.5 \,A$,the values of $n_1$ and $n_2$ are: