If the balance point is obtained at the $35^{th} cm$ in a meter bridge,the resistances in the left and right gaps are in the ratio of:

$A$ meter bridge is set up as shown to determine the end corrections at $A$ and $B$. When a resistance of $15\,\Omega$ is used in the left gap and $20\,\Omega$ in the right gap,the null point is obtained at a distance of $42\,cm$ from $A$. When these resistances are interchanged,the null point is obtained at a distance of $57\,cm$ from $A$. The values of the end corrections are:

The resistances in the two arms of the meter bridge are $5 \,\Omega$ and $R \,\Omega$ respectively. When the resistance $R$ is shunted with an equal resistance,the new balance point is at $1.6\,l_1$. The resistance $R$ is .................. $\Omega$.

In a meter bridge experiment,the null point is obtained at $20 \ cm$ from one end of the wire when resistance $X$ is balanced against resistance $Y$. If $X < Y$,then the distance of the new null point from the same end when a resistance of $4X$ is balanced against $Y$ will be ............ $cm$.

In a meter bridge,as shown in the figure,it is given that resistance $Y = 12.5 \, \Omega$ and the balance point is obtained at a distance $l_1 = 39.5 \, cm$ from end $A$ (by jockey $J$). After interchanging the resistances $X$ and $Y$,a new balance point is found at a distance $l_2$ from end $A$. What are the values of $X$ and $l_2$?

$A$ meter bridge with two resistances $R_{1}$ and $R_{2}$ as shown in the figure was balanced (null point) at $40 \text{ cm}$ from the point $P$. The null point changed to $50 \text{ cm}$ from the point $P$, when a $16 \ \Omega$ resistance is connected in parallel to $R_{2}$. The values of resistances $R_{1}$ and $R_{2}$ are . . . . . . .