Yes, there are provisions in India's labor laws that allow for pay deductions due to late arrivals and shortened working hours.
The Shops and Establishment Act, which is applicable in Noida, India, allows for deductions in the case of late arrivals. The specifics of these deductions can vary based on the state's interpretation of the Act.
In terms of shortened working hours, the Payment of Wages Act, 1936, allows for deductions if a worker is absent from duty. The deduction is proportional to the period of absence.
However, it's important to note that these deductions should not exceed 50% of the employee's total wages in a month, as per the Payment of Wages Act.
It's also crucial to remember that any policy regarding pay deductions should be clearly communicated to employees, and ideally, should be part of the employment contract.
For more specific information, you may want to consult the Shops and Establishment Act applicable to Uttar Pradesh and the Payment of Wages Act, 1936.