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

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 $............. \ \Omega$.

The resistances in the left and right gaps of a balanced metre bridge are $12 \Omega$ and $36 \Omega$ respectively. If the resistances are interchanged,the balance point shifts by:

In a meter bridge (Figure), the null point is found at a distance of $33.7 \; cm$ from $A$. If now a resistance of $12 \; \Omega$ is connected in parallel with $S$, the null point occurs at $51.9 \; cm$. Determine the values of $R$ and $S$.

In a meter bridge,the two gaps contain resistances of $10 \, \Omega$ and $30 \, \Omega$ respectively. If these resistances are interchanged,the null point shifts by ..... cm.

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