As per the age eligibility the upper age limit is 22 years as on 01.07.2019 for General/ OBC and 25 years as SC/ ST category.

If you meet the eligibility you can apply for the exam. You can check the complete eligibility with the given below link.

https://hospitality.careers360.com/articles/nchm-jee-eligibility-criteria

You can not do both degree together, If you are already doing the Graduation why you again want to do it, If you are interested for Hospitality Management then after Graduation you can go for Management programme like MBA, PGDM.

Good Luck!