Hotel Management

You don't need to give NCHMCT from any institute. You only need to fill the form directly and appear for the exam.

If you are a fresher, you cannot go for an Executive MBA, as they require a minimum work experience of 2 years (in case of IIM's) and pretty much in case of every b-school.
You can go for a regular MBA from a good B-school or you can get a job and start preparation for an executive MBA from a good B-school. Both will give you fruitful results only if you do it from top 30 b-schools in India.

Dear Sourav Biswas,
There are good courses like MBA in tourism and travel management, MBA in hospitality management, etc.
All the best.

Depending on your field of interest, both courses are amazing with equally worth job opportunities. However, with my personal experience, I feel that hospitality sector is not only enticing, but also provides amazing job opportunities.
This sector is one of the fastest growing one and the academics are extremely interesting. My cousin and I pursued an Internship in the hospitality sector and grew overall as a person. She is currently pursuing BBA in hospitality, travel and tourism. You should give it a shot as well.

RS Agarwal for quantitative aptitude, verbal reasoning and logic is most recommended.

You can do distance MBA or if you want to do full time MBA then you have to give priority to that.

Join a good job in your interested department and take a distance MBA course in either hotel management, if you want, or I would suggest you to take some other MBA specialization like travel and tourism or marketing management in which you will get high level jobs in the hotel industry.