When a metal conductor connected to the left gap of a meter bridge is heated,the balancing point

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 two arms of a 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,the gaps are enclosed by resistances of $2 \ \Omega$ and $3 \ \Omega$. The value of shunt to be added to the $3 \ \Omega$ resistor to shift the balancing point by $22.5 \ cm$ is (in $\Omega$)

In a meter bridge or Wheatstone bridge for the measurement of resistance,the known and the unknown resistances are interchanged. The error so removed is

$A$ resistance of $20 \Omega$ is connected in the left gap of a metre bridge and an unknown resistance greater than $20 \Omega$ is connected in the right gap. When these resistances are interchanged,the balance point shifts by $20 \text{ cm}$. The unknown resistance is (in $\Omega$)