In a meter bridge experiment,the balance point is obtained if the gaps are closed by $2 \Omega$ and $3 \Omega$ resistors. $A$ shunt of $X \Omega$ is added to the $3 \Omega$ resistor to shift the null point by $22.5 \text{ cm}$. The value of $X$ is: (in $\Omega$)

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 the right gap of a meter bridge consists of two equal resistors in series,the balancing point is at $50 \ cm$. When one of the resistors in the right gap is removed and is connected in parallel to the resistor in the left gap,the balancing point is at: (in $cm$)

In a meter bridge,the wire of length $1\, m$ has a non-uniform cross-section such that the variation $\frac{dR}{d\ell}$ of its resistance $R$ with length $\ell$ is $\frac{dR}{d\ell} \propto \frac{1}{\sqrt{\ell}}$. Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point $P$. What is the length $AP$?

In a metre bridge experiment, the resistance in the left gap is $20 \text{ } \Omega$ and in the right gap is $60 \text{ } \Omega$. The bridge is balanced. The distance of the null point from the centre of the wire is (in $\text{ cm}$)

Assertion $(A):$ In a meter bridge experiment,the unknown resistance is placed inside an enclosure maintained at a higher temperature. The null point can be obtained at the same position as before by decreasing the value of the standard resistance.
Reason $(R):$ The resistance of a metal increases with an increase in temperature.