If the speed of a 3-phase, 400 V, 50 Hz synchronous motor is trebled, the efficiency of the machine will _________.

Correct option is C

​$$\text{Given:} \\[4pt]\text{Synchronous speed formula:} \\[6pt]N_s = \dfrac{120f}{P} \\[8pt]\text{where:} \\[4pt]N_s = \text{Synchronous speed} \\[4pt]f = \text{Frequency} \\[4pt]P = \text{Number of poles}$$​​

Formula Used: The efficiency of a motor is independent of the synchronous speed. Therefore, tripling the synchronous speed will not affect the motor's efficiency.
Solution:
As per the given formula, the synchronous speed depends on frequency and the number of poles . The efficiency of the machine is not influenced by the synchronous speed.
Hence, if the speed of the motor is tripled, the efficiency of the machine will remain constant.