The correct answer is $\boxed{\text{C. 750 r.p.m.}}$.
The speed of a synchronous motor is given by the following equation:
$$n = \frac{120f}{p}$$
where $n$ is the speed in revolutions per minute (rpm), $f$ is the frequency in hertz (Hz), and $p$ is the number of poles.
In this case, the frequency is halved, the pole number is halved, and the load torque is halved. This means that the speed of the motor will be halved, or 750 rpm.
Option A is incorrect because the frequency is halved, so the speed should also be halved. Option B is incorrect because the pole number is halved, so the speed should also be halved. Option D is incorrect because the speed is calculated using the frequency, pole number, and load torque, and all of these values have been halved.