A "letter of appointment" is a legally enforceable document in a court of law. The terms of "termination and notice" are binding on an employee if they are stated expressly in an appointment letter and are acknowledged by their signature.
It is the employee's responsibility to serve the full notice period in order to receive his full salary as well as the relieving letter; no employer may compel an employee to serve the full notice period.
If an employee quits/leaves before the notice period has officially ended, the employer is only legally entitled to the notice pay.
According to the "specific relief act," a contract for personal service can't be upheld in court.You are bound by law (and as per your offer letter) to serve notice or notice pay.
If you are not joining a competitor company, you can still leave the company immediately, which means that companies may not initiate legal proceedings against you.