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

When two resistances $R_1$ and $R_2$ are connected in series and introduced into the left gap of a meter bridge and a resistance of $10 \ \Omega$ is introduced into the right gap,a null point is found at $60 \ cm$ from the left side. When $R_1$ and $R_2$ are connected in parallel and introduced into the left gap,a resistance of $3 \ \Omega$ is introduced into the right gap to get a null point at $40 \ cm$ from the left end. The product $R_1 R_2$ is $............. \ \Omega$.

On interchanging the resistances,the balance point of a meter bridge shifts to the left by $10 \, cm$. The resistance of their series combination is $1 \, k\Omega$. How much was the resistance on the left slot before interchanging the resistances? ................... $\Omega$

When the right gap of a meter bridge consists of two equal resistors in series,the balancing point is at $50 \ cm$. When one of the resistors in the right gap is removed and is connected in parallel to the resistor in the left gap,the balancing point is at: (in $cm$)

The resistance in the left and right gaps of a meter bridge are $10 \Omega$ and $30 \Omega$ respectively. If the bridge is balanced,then the distance of the null point from the center of the wire is (in $cm$)

In the given figure of a meter bridge experiment,the balancing length $AC$ corresponding to null deflection of the galvanometer is $40 \, cm$. What will be the balancing length if the radius of the wire $AB$ is doubled (in $, cm$)?