Two known resistances are connected in two gaps of a meter bridge. The null point is obtained at $20 \ cm$ 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 smaller resistance is (in $Omega$)

$A$ meter bridge is set up as shown,to determine an unknown resistance '$X$' using a standard $10 \ \Omega$ resistor. The galvanometer shows a null point when the tapping key is at the $52 \ cm$ mark. The end corrections are $1 \ cm$ and $2 \ cm$ respectively for the ends $A$ and $B$. The determined value of '$X$' is (in $Omega$)

Two wires $A$ and $B$ of equal lengths are connected in the left and right gaps of a metre bridge. The null point is obtained at $40 \ cm$ from the left end. If the diameters of the wires $A$ and $B$ are in the ratio $3:1$,what is the ratio of the specific resistance (resistivity) of $A$ to that of $B$ (in $:$)?

$A$ wire of length $3 \, m$ connected in the left gap of a meter-bridge balances $8 \, \Omega$ resistance in the right gap at a point, which divides the bridge wire in the ratio $3:2$. The length of the wire corresponding to a resistance of $1 \, \Omega$ is: (in $ \, m$)

In the meter bridge experiment,the length $AB$ of the wire is $1 \ m$. The resistors $X$ and $Y$ have values $5 \ \Omega$ and $2 \ \Omega$ respectively. When a shunt resistance $S$ is connected in parallel to $X$,the balancing point is found to be $0.625 \ m$ from $A$. Then,the resistance of the shunt $S$ is (in $Omega$)

Consider a $72\, cm$ long wire $AB$ as shown in the figure. The galvanometer jockey is placed at $P$ on $AB$ at a distance $x\, cm$ from $A$. The galvanometer shows zero deflection. The value of $x$,to the nearest integer,is ..... $cm$.