D.C. Mayor Walter E. Washington has signed a bill that would expand opportunities for low and moderate-income persons to place their children in city-subsidized day care centers.

The bill was among six signed by the mayor late Tuesday.Yesterday, the mayor signed a seventh bill aimed at regulating the use of motorized bicycles.

The day care bill would raise the income ceiling for eligibility to place children in city-funded centers, which have a capacity to care for 6,000 children. Previous legislation had allowed no one making more than $7,000 annually to place his children in the centers.

Under the new legislation, a sliding fee scale would be instituted to allow persons with incomes of up to $19,200 to receive day care service by paying anywhere from nothing to 20 per cent of the costs.

Under the new legislation, for example, a family of four with an income of less than $12,829, could receive the services by paying up to 20 per cent of the cost of each child, depending upon the family's income. The $19,200 ceiling is for a family with 12 members.

The mayor also singed a "no fault" divorce law aimed at cutting the amount of red tape involved in city divorces and removing much of the stigma attached to out-of-wedlock births.

The bill would reduce from one year to six months the minimum time that the two parties involved in a divorce must be separated before a divorce can be granted. It would also eliminate some of the grounds or "faults" necessary to be proven before divorce can be granted - such as adultery, desertion and conviction for a felony and incarceration in prison.

Supoorters of the no-fault plan say that eliminating thse grounds could reduce costly divorce litigation.

The new law also reduces residency requirements for persons seeking a divorce, sets new guidelines for the definition of "community property" in divorce cases, and would allow children born out of wedlock the same inheritance rights now accorded children born in wedlock.

The legislation for motorized bicycles would the first time provided for regulation of ownership, parking and operation of the vehicles. In the future, all operators of the bikes would have to be at least 16 years old and have either a specia permit or regular driver's license.

All bikes would have to be inspected every three years, operated only on bike paths and streets and follow the same traffic and parking regulations now outlined for regular bicycles. Operators of motorized bikes would not be required to wear protective helmets.

Other bills signed by the mayor would:

Extend for 90 days an act passed last year that allows apartment buildings to be converted to cooperatives only with the permission of the mayor.

Prohibit the naming of any public place (city-owned property) after a living person or a person who had been dead less than two years.

Extend for 90 days legislation requiring persons applying for child support payments to provide any information that would help authorities locate a person who might be legally responsible for supporting the child.

Change the city's definitions of "physical disability and incapacity" to conform with slightly stricter federal definitions governing eligibility for disability payments.