In the meter bridge shown,the length $AB$ for which the deflection in the galvanometer is zero will be ............. $cm$.

$A$ wire of length $10 \ cm$ and radius $\sqrt{7} \times 10^{-4} \ m$ is connected across the right gap of a meter bridge. When a resistance of $4.5 \ \Omega$ is connected in the left gap using a resistance box,the balance length is found to be at $60 \ cm$ from the left end. If the resistivity of the wire is $R \times 10^{-7} \ \Omega \ m$,then the value of $R$ is:

In a meter bridge,the point $D$ is the neutral point (null point) as shown in the figure.

In a meter bridge,two gaps in the metallic strip are connected by $3 \Omega$ and $9 \Omega$ resistors. What should be the value of the shunt that needs to be added in parallel to the $9 \Omega$ resistor to shift the balancing point by $25 \text{ cm}$ (in $\Omega$)?

$A$ resistance of $20 \Omega$ is connected in the left gap of a metre bridge and an unknown resistance greater than $20 \Omega$ is connected in the right gap. When these resistances are interchanged,the balance point shifts by $20 \text{ cm}$. The unknown resistance is (in $\Omega$)

In a meter bridge experiment,resistances are connected as shown in the figure. The balancing length $l_1$ is $55 \, cm$. Now,an unknown resistance $x$ is connected in series with $P$ and the new balancing length is found to be $75 \, cm$. The value of $x$ is