Ph.D

Yes, you are eligible for UGC NET exam. But make sure you fulfil all the eligibility criteria of the exam. You should have minimum 55% aggregate marks in post graduation if you are from the general category or if you belong to SC/ST/OBC/PWD category then you should have at least 50% aggregate marks. As you say you have 70% marks in MCA so you are definitely eligible for the exam. If you want to apply for JRF your age must not more than 30 years but for assistant professor no restriction on age. You can appear for that when you want to do.

From which college are you pursuing your integrated Ph.D. in chemistry? I would suggest you to try to solve all the GATE previous year questions and collect all the standard textbooks. Some of the books you can refer for preparation are The Pearson Guide to UGC-CSIR Chemical Sciences by Dr. Sanjay Singh Rawal, CSIR UGC NET Chemical Sciences (Part A, B & C) by R. Gupta's and Trueman's UGC-CSIR JRF/NET Chemical Sciences (Chemistry) by B. Roy, M. Gagan.

Hi Sakshi,
You can give IIT JAM exam and for this you have to clear maths exam in +2 class if not so because IIT provides M.Sc.
Good luck.

Yes, you have to clear GATE for PhD.

Refer the link for details: https://www.shiksha.com/engineering/course/ph-d-shri-jagdishprasad-jhabarmal-tibrewala-university-rajasthan-other-190998

Yes, you are eligible after passing OUCET exam. After completion of your PG, you can go for PhD as well.

I'm assuming that you wanted to write about JEST (Joint Entrance screening test) and the answer is Yes, you can give JEST after B.Sc. To get integrated Ph.D. in many institutes you can check that on the site of JEST also there is integrated PhD. in TIFR where you've to give their own entrance exam GS also both of these entrance exams will be followed up by an interview. So best of luck and you actually should have potential to pursue for an integrated course.

As you are already a Post Graduate in the form of MBA, you need to go for NET to do Ph.D. But if you want to have two things-
1. Priority in getting Admission in Ph.D. then NET qualified Candidature will help a lot.
2. If you want to have a Job in Higher Education after Ph.D. then NET is the way. UGC NET is the basic requirement to apply for a job as Assistant Professor. You can join Ph.D. first and keep the NET Preparation on.