In the gaps of a meter bridge,two unknown resistances $A$ and $B$ are connected. $A$ null point is obtained when the wire is divided in the ratio $3:4$. When each resistance is increased by $40 \Omega$,the null point divides the wire in the ratio $7:8$. The values of resistances $A$ and $B$ are respectively:

In an experiment to determine the temperature coefficient of resistance of a conductor,a coil of wire $X$ is immersed in a liquid. It is heated by an external agent. $A$ meter bridge setup is used to determine the resistance of the coil $X$ at different temperatures. The balancing points measured at temperatures $t_1=0^{\circ} C$ and $t_2=100^{\circ} C$ are $50 \ cm$ and $60 \ cm$ respectively. If the standard resistance taken out is $S=4 \ \Omega$ in both trials,the temperature coefficient of the coil is

In the meter bridge experiment,for given values of $R_1$ and $R_2$,the balance point is $20 \ cm$ from point $A$. When $R_2$ is shunted by a $20 \ \Omega$ resistance,the balancing point shifts to $50 \ cm$ from point $A$. Find the value of $R_2$ in $\Omega$.

Resistances are connected in a meter bridge circuit as shown in the figure. The balancing length $l_{1}$ is $40\,cm$. Now an unknown resistance $x$ is connected in series with $P$ and the new balancing length is found to be $80\,cm$ measured from the same end. Then the value of $x$ will be $.......\Omega$.

The resistances in the two arms of the meter bridge are $5 \,\Omega$ and $R \,\Omega$ respectively. When the resistance $R$ is shunted with an equal resistance,the new balance point is at $1.6\,l_1$. The resistance $R$ is .................. $\Omega$.

In a meter bridge experiment,the ratio of the left gap resistance to the right gap resistance is $2:3$. The balance length from the left end is (in $\,cm$)