The metre bridge wire is made of alloys such as nichrome because they have:

The correct option is: low temperature coefficient of resistance and high resistivity.

A metre bridge (or slide wire bridge) is an electrical apparatus used to measure an unknown resistance based on the principle of a Wheatstone bridge. The wire used in a metre bridge must have specific electrical properties to ensure precision and accuracy during experiments. Alloys like nichrome, constantan, or manganin are chosen for this wire due to the following reasons:

1. High Resistivity:
The resistance of a wire is given by the relation:
$$R=\rho \frac{l}{A}$$
where $\rho$ represents the resistivity of the material, $l$ is the length of the wire, and $A$ is its cross-sectional area. Since the wire in a metre bridge is limited to a length of exactly 1 metre, it must have high resistivity to provide a sufficiently large and measurable resistance without requiring an impractically thin wire.

2. Low Temperature Coefficient of Resistance:
When electric current flows through the wire during measurement, heat is generated due to Joule heating:
$$H=I^{2}Rt$$
This heating causes the temperature of the wire to rise. The resistance of a conductor changes with temperature according to the formula:
$$R_T=R_0(1+\alpha \Delta T)$$
where $\alpha$ is the temperature coefficient of resistance and $\Delta$T is the temperature change. If the wire has a high value of $\alpha$, its resistance will fluctuate during the experiment, leading to significant errors. Using an alloy with a very low temperature coefficient of resistance ensures that its resistance remains constant and unaffected by temperature changes during operation.