Introduction:
An LR circuit is a circuit that consists of a resistor (R) and an inductor (L) connected in series. When a battery is connected to the circuit, it causes a current to flow through the circuit. In this question, we are given that the LR circuit is connected at t = 0, and we need to determine which quantities are not zero just after the connection.

Explanation:

Current in the circuit:
The current in the circuit is determined by the voltage of the battery and the resistance of the circuit. As soon as the circuit is connected, the battery provides a potential difference, which causes an immediate flow of current in the circuit. Therefore, the current in the circuit is not zero just after the connection. So, option 'a' is incorrect.

Magnetic field energy in the inductor:
The magnetic field energy in the inductor is given by the equation E = (1/2)LI^2, where L is the inductance and I is the current flowing through the inductor. Since the current in the circuit is not zero just after the connection, there will be a non-zero current flowing through the inductor. Therefore, the magnetic field energy in the inductor is also not zero just after the connection. So, option 'b' is incorrect.

Power delivered by the battery:
The power delivered by the battery is given by the equation P = VI, where V is the voltage across the battery and I is the current flowing through the circuit. As we have already established that the current in the circuit is not zero just after the connection, and the battery provides a voltage, the power delivered by the battery is also not zero just after the connection. So, option 'c' is incorrect.

Emf induced in the inductor:
When the circuit is connected or disconnected, there is a change in the current flowing through the inductor. This change in current induces an electromotive force (emf) in the inductor. However, just after the connection, the current in the circuit is not changing, and therefore, there is no change in current through the inductor. Hence, there is no emf induced in the inductor just after the connection. Therefore, option 'd' is correct.

Conclusion:
In an LR circuit connected to a battery, the current in the circuit, the magnetic field energy in the inductor, and the power delivered by the battery are not zero just after the connection. However, the emf induced in the inductor is zero just after the connection.