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:

$A$ wire of length $3 \, m$ connected in the left gap of a meter-bridge balances $8 \, \Omega$ resistance in the right gap at a point, which divides the bridge wire in the ratio $3:2$. The length of the wire corresponding to a resistance of $1 \, \Omega$ is: (in $ \, m$)

In a metre-bridge,when a resistance in the left gap is $2 \ \Omega$ and an unknown resistance is in the right gap,the balance length is found to be $40 \ cm$. On shunting the unknown resistance with $2 \ \Omega$,the balance length changes by: (in $cm$)

Resistances in the left gap and right gap of a meter bridge are $10 \Omega$ and $30 \Omega$ respectively. If the resistances in the two gaps are interchanged, the balance point will shift to the right by: (in $\text{cm}$)

The resistances in the two gaps of a balanced meter bridge are $X \ \Omega$ and $3X \ \Omega$ respectively. If the resistances are interchanged, the balance point shifts by: (in $\text{ cm}$)

$A$ meter bridge setup is shown in the figure. It is used to determine an unknown resistance $R$ using a given resistor of $15\,\Omega$. The galvanometer $(G)$ shows null deflection when the tapping key is at the $43\,cm$ mark from end $A$. If the end correction for end $A$ is $2\,cm$ and for end $B$ is $1\,cm$,then the determined value of $R$ will be . . . . . . $\Omega$.