In an electrical circuit, a fuse is connected. 

A fuse is a tool used to safeguard electrical circuits and devices from harm. Its job is to find any type of short circuit and cut off the current to that circuit.
We are aware that a fuse consists of a thin wire with a high resistance and low melting point that is typically made of copper, zinc, aluminium, silver, or an alloy to give the fuse the properties it requires.
Let's examine choice A: near a live wire
A live wire is a wire that first conducts current when it enters the circuit and the appliance, creating a potential difference and allowing for the connection of a fuse to the live wire.

Therefore, choice A is right.
When analysing choice B: around the neutral wire
If we connect a fuse to a neutral wire, it is impossible to save any valuable electric appliance because the current has already flowed through half of the circuit and the appliance. Through a neutral wire, current flow while exiting the circuit or the appliance so it does not have a potential difference. Therefore, a neutral wire cannot be used to connect a fuse.

Option B is thus untrue.

If option C is chosen, the earth wire.

To protect an electrical equipment from short circuit current, an earth line is often provided. This is done so that if the fuse does not melt with the short circuit current, the excess current will travel via the ground wire and be neutralised. If, however, a fuse is placed there, the circuit will be broken, harming both the appliance and the circuit.
This is the incorrect choice.
Option D: Any of these, is something to think about.
This is the incorrect choice.

Hence, the correct answer is option A.