WASHINGTON (AP) _ The Supreme Court agreed Monday to decide whether abused children may sue public officials for failing to protect them from their parents.

The justices said they will hear an appeal on behalf of a Wisconsin boy who suffered serious and permanent brain damage from beatings by his father. Social workers and officials are accused of gross negligence in ignoring evidence the boy was being brutally victimized.

The court's study of the case, expected to yield a ruling sometime in 1989, comes amid growing concern nationwide over child abuse.

In other actions, the court:

-Left intact a ruling that forces school officials in New Mexico to defend themselves at trial against allegations they violated a young girl's constitutional rights by paddling her.

-Left intact a federal law requiring broadcasters to give equal time to opposing candidates for public office.

-Agreed to consider killing a key provision of a law designed to promote competitive bidding on government contracts. At issue is the proper boundary between presidential and congressional power.

-Agreed to decide in a case from Texas whether states may impose sales taxes on most books, newspapers and magazines while exempting religious publications.

-Refused to let states and local governments regulate the prices most of the nation's cable television operators charge for basic service.

In the child-abuse case, the court will consider reinstating a suit against the Winnebago County, Wis., Department of Social Services and two of its employees.

The agency was accused of violating the rights of Joshua DeShaney because it failed to rescue him from his father's beatings. The department was charged with knowing about the beatings since 1983 when Joshua was four.

He has been institutionalized since 1984, suffering from injuries that destroyed half his brain and left him profoundly retarded.

The boy's father, Randy DeShaney, since has been convicted of child abuse and sentenced to two years to four years in prison.

A social worker, Ann Kemmeter, was assigned to the DeShaney case in 1983 after Joshua was brought to a hospital with various cuts and bruises.

Ms. Kemmeter visited the DeShaney home several times but allegedly failed to take any steps to remove him from the home or protect him.

DeShaney's ex-wife, Melody, sued the social services officials on grounds they violated the child's constitutional right not to be deprived of liberty without due process.

Mrs. DeShaney was divorced from her husband and living in Cheyenne, Wyo., when she was informed her son had suffered serious brain damage. DeShaney had custody of his son.

The 7th U.S. Circuit Court of Appeals threw out Mrs. DeShaney's suit. The appeals court said the social welfare agency and its employees ''though blameworthy, did not cause Joshua's injuries.'' The appeals court said Ms. Kemmeter ''merely failed to protect him from his bestial father.''

The appeals court also said welfare agencies should not be placed in the predicament of removing a child from home and facing suit by the parent or leaving the child there and risk being sued by the child.

Putting officials in that position ''is unlikely to improve the welfare of American families and is not grounded in constitutional text or principle,'' the appeals court said.

In other developments, the court:

-Agreed in a case from Pennsylvania to consider shielding states from having to help pay for cleaning up hazardous waste sites when the federal government sues businesses under the ''Superfund'' law.

-Refused to hold Hustler magazine financially liable for the death of a 14- year old Texas boy who died during a sexual experiment that was the subject of an article in the magazine.

-Refused to allow the manufacturer of the Dalkon Shield to set up a $15 million emergency fund to help women who say the contraceptive device left them infertile.

-Refused to give a Pasadena, Calif., shopping mall owner more power to restrict such activities as distribution of leaflets and solicitation of signatures for petitions.

-Refused to kill a 13-year-old lawsuit against former federal and military officials stemming from an armed confrontation between Indians and federal agents at Wounded Knee, S.D., in 1973.