It is appreciated that you have chosen to discuss in time.
1. Is HR person your employer? In all probabilities: No! He /she at the most be (if empowered by Board in writing) signing authority on offer letter, appointment letter!
Has the establishment supplied soft copy or signed hard copy?
Is there a statement inserted in offer letter like................................" You shall have to sign agreements at the time of joining"?
Has the company provided you the HR policy/Service Rules and Regulations mentioned in appointment letter before signing appointment letter. Usually it is stated that service conditions shall be governed by HR policy/Service Rules and Regulations................................but these are not supplied shown alongwith/before appointment letter. Download these and keep a copy.
Has it been stated that standing orders (certified/model) shall apply? Inquire and obtain the copy.
The agreements/clauses being enforced by company may be violative of standing orders.
Any clause violative of standing orders shall not survive.
2. If accepted appointment letter may supersede offer letter (the language and statements should be examined by your able labor consultant/service lawyer).
Thus you shall be accepting T&C inserted by employer in appointment letter, agreements drafted by employer by your own volition.
Would it be workable for you to submit a gentle and carefully structured representation in writing under proper acknowledgment addressed to appointing authority, MD etc ........................................that you were allured to join........................and T&C envisaged by employer were communicated to you by offer letter dated................................and based on the offer made to you...........................you had resigned the current employment and now............................clauses/agreements have been added for you to sign without any prior opportunity given to you before the submission of notice of resignation to current employer/expiry of notice period................................and having left your current employment you are left with no choice!
If you are able to do so then you shall be building a favorable record that you signed under duress.
3. The Indian courts have consistently been declining to enforce NON Compete Clauses/agreements post termination of employment...................................as it hits right to earn livelihood........................and clauses of Indian Contracts Act.
However the decision by court of law is pleasure of court of law and what it would be down the line from now can not be forcasted although the basic tenets and fabric of law may not change........................
4. IT is advisable to record such meetings/calls (audio/visual) and keep some witness/evidence for use at appropriate time in appropriate forum.
While you represent you must not use cut and paste option and show the job advt., job application, interview call letter, selection letter, offer letter, appointment letter, standing orders, HR policy/service rules and regulations, NON Compete agreement to a competent and experienced Labor Consultant/service lawyer and give inputs in person and let your lawyer draft and structure your representations to suit you in the long run.
If you feel that you shall come across such HR personnel/employers it is advisable to retain access to a competent and experienced Labor Consultant/service lawyer and discuss before hand and do not sign on dotted line in haste.