Neetu makes an arrangement of a circuit to study electromagnetic induction: 

She changes the arrangement in 4 different ways as follows:

Trials-

1. Moves the coil to the left away from the magnet.
2. Moves the magnet to the right away from the coil.
3. Moves both coil and magnet towards each other.
4. Moves both coil and magnet in the same direction at the same speed.

In which trial would the galvanometer remain undeflected?

When a conductor is moved inside a magnetic field, a potential difference is induced which sets up an induced electric current in the circuit.

Trials 1, 2 and 3, will generate current as the magnetic field is changing with the respect to the conductor as either the coil or magnet or both are moving with respect to each other. Therefore, the galvanometer would show some deflection.

In trial 4, when both the coil and magnet are moved in the same direction at the same speed, the galvanometer remains undeflected because the magnetic field is not changing with respect to the conductor or coil.

Hence trial 4 is the correct answer.