In a metre bridge experiment, the resistance in the left gap is $15 \text{ } \Omega$ and in the right gap is $45 \text{ } \Omega$. The bridge is balanced. The distance of the null point from the centre of the wire is (in $\text{ cm}$)

The resistance per centimeter of a meter bridge wire is $r$. $A$ resistance of $X \ \Omega$ is placed in the left gap and a resistance of $25 \ \Omega$ is placed in the right gap. The balancing length from the left end is $40 \ cm$. Now,the wire is replaced by another wire of $2r$ resistance per centimeter. The new balancing length for the same settings will be at: (in $cm$)

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 $cm$)

In a meter bridge,a $30 \Omega$ resistance is connected in the left gap and a pair of resistances $P$ and $Q$ in the right gap. Measured from the left,the balance point is $37.5 \text{ cm}$ when $P$ and $Q$ are in series,and $71.4 \text{ cm}$ when they are in parallel. The values of $P$ and $Q$ (in $\Omega$) are:

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 figure shows a rough sketch of a meter bridge. The galvanometer $(G)$ shows zero deflection at a length $l \, cm$. Now,$R_1$ and $R_2$ are interchanged,and the balancing length increases by $25 \, cm$. Find the ratio $R_1/R_2$.