In a meter bridge experiment,when resistance $X$ is in the left gap and $Y$ is in the right gap,the null point is found at $20 \ cm$ from the left end. If $X < Y$,what will be the new position of the null point from the same end if a resistance of $4X$ is placed in the left gap instead of $X$?

Two resistances are connected in two gaps of a meter bridge. The balance point is $20 \ cm$ from the zero end. $A$ resistance of $15 \ \Omega$ is connected in series with the smaller of the two. The null point shifts to $40 \ cm$. The value of the smaller resistance in $\Omega$ is

In order to measure the internal resistance $r_1$ of a cell of emf $E$,a meter bridge of wire resistance $R_0=50 \Omega$,a resistance $R_0/2$,another cell of emf $E/2$ (internal resistance $r$) and a galvanometer $G$ are used in a circuit,as shown in the figure. If the null point is found at $l=72 \text{ cm}$,then the value of $r_1$ is . . . . $\Omega$.

In a metre bridge experiment, the balance point is obtained if the gaps are closed by $2 \text{ } \Omega$ and $3 \text{ } \Omega$. $A$ shunt of $X \text{ } \Omega$ is added to $3 \text{ } \Omega$ resistor to shift the balancing point by $22.5 \text{ cm}$. The value of $X$ is

In a meter-bridge experiment,a resistance of $18 \Omega$ is connected in the left gap and an unknown resistance $R$ is connected in the right gap. The null point is obtained at $\ell_{1}$ from the left end. If the unknown resistance is replaced by $(\frac{R}{3}) \Omega$,the null point is obtained at $1.5 \ell_{1}$. The unknown resistance $R$ is: (in $\Omega$)

$STATEMENT-1$: In a Meter Bridge experiment,a null point for an unknown resistance is measured. Now,the unknown resistance is placed inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.
$STATEMENT-2$: The resistance of a metal increases with an increase in temperature.