The correct answer is option 3, which states that Indians were never admitted to the British Indian Medical Service (IMS). This statement is not correct as Indians were indeed admitted to the IMS.

Option 1 states that the IMS began in 1764, which is correct. The British Indian Medical Service was established in 1764 to provide medical care primarily to the British troops stationed in India.

Option 2 states that the IMS recruited health professionals through a competitive examination, and this is also correct. The IMS implemented a competitive examination system to recruit qualified individuals for various positions within the service.

Option 4 states that the IMS was initially meant to look after the troops, and this is also correct. The main purpose of establishing the IMS was to provide medical care to the British soldiers stationed in India, although its scope later expanded to serve the civilian population as well.

Overall, the British Indian Medical Service (IMS) began in 1764 and recruited health professionals through a competitive examination. Indians were also admitted to the IMS, making option 3 incorrect.