When there is a clear notice period in the exit clause of the contract of employment, its waiver or adjustment against accrued leave for early relief is a matter of pure discretion of the employer. The employee can not prevail over the employer's discretion because of any options mentioned in the contract for the employer can always take refuge under the alleged exigencies of work. If the HR is adamant , better approach the CEO and try to convince him politely. Even, if it fails to work, be prepared to serve the entire notice period.
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Also, as per the BECA, Section 37(c), if the employee has worked for more than one year then they need to serve a notice period of 4 weeks and I have agreed to that while as per the Section 14 of Specific Relief Act, the employer cannot force an employee to serve a complete notice period if they are ready to pay the amount.