The correct answer is (b) Patwadangar.
The State Vaccine Institute was set up by the British administration in Patwadangar, Uttarakhand, India in 1890. It was the first vaccine institute in India and was established to provide a safe and effective vaccine against smallpox. The institute was initially located in a small house in Patwadangar, but it was later moved to a larger building in the same area. The institute has been instrumental in the eradication of smallpox in India and has also played a role in the development of other vaccines.
The other options are incorrect because they are not places where the State Vaccine Institute was set up. Mukteshwar is a town in Uttarakhand, India. Dharamghar is a village in Uttarakhand, India. Dhanaulti is a town in Uttarakhand, India.