The Supreme Court agreed yesterday to decide whether states may seize prison inmates' Social Security or veterans benefits as reimbursement for the costs of keeping them behind bars.

The justices will hear a challenge to an Arkansas law, similar to laws in four other states, under which authorities confiscated one inmate's $275 monthly Social Security retirement check and another prisoner's $626 monthly Veterans Administration benefits.

The court also added 11 more cases to its docket, filling up about three-fourths of its calendar for the 1987-88 term.

The justices said they would try to resolve differing interpretations of the meaning of the 13th Amendment's bar on "involuntary servitude." The court will hear argument early next year in U.S. v. Kozminski, a case from Michigan involving two mentally retarded farmhands who, although not physically detained, were allegedly mistreated, beaten and coerced into working on the farm for more than a decade.

A federal appeals court, adopting a narrow definition of the amendment and related federal laws, said it should only cover coercion by fraud or deceit of minors, immigrants or the mentally incompetent. The appeals court, in contrast to other appeals courts, said its narrower definition of involuntary servitude would not apply to more subtle forms of coercion or to "the day-to-day activities of cult groups, communes and religious orders."

The justices also said they would decide whether the Miranda ruling, which requires police to read suspects their rights, provides adequate constitutional protections for suspects who have been indicted.

The case, Patterson v. Illinois, questions whether the standard warnings police give are sufficient protection of a suspect's rights to legal counsel under the Sixth Amendment.

In another criminal case, Michigan v. Chesternut, the court agreed to decide whether police, with no particular reason to suspect criminal activity, may chase someone who runs after seeing them.

A Michigan trial court said the police chase and subsequent arrest of a man on drug charges violated the Fourth Amendment's prohibition of unreasonable searches and seizures.

The justices said they would decide whether federal labor law overrides state laws aimed at protecting workers from retaliatory firings. The case, Lingle v. Norge Division of Magic Chef Inc., involves an Illinois woman who was fired from her job after filing what her employer said was a false claim for disability benefits under the state's worker compensation program.

The court also agreed to decide what conditions must be met before federal prosecutors can introduce evidence at trial of a defendant's "prior bad acts."

The case, Huddleston v. U.S., involves a Michigan man who was convicted of possession of stolen videotapes. The key issue at trial was whether the defendant, Guy Rufus Huddleston, knew the tapes were stolen. In order to prove that, prosecutors attempted to introduce evidence that Huddleston had engaged in similar sales and attempted sales of stolen televisions to an undercover agent. Huddleston, in his appeal to the high court, argued that such evidence should not have been admitted because the government could not prove the televisions were stolen.

The solicitor general urged the court to take the Arkansas prisoner benefits case, Bennett v. Arkansas, arguing that the Arkansas law was preempted by federal laws that clearly say that Social Security and VA benefits, without exception, may not be garnished or seized for any reason.

Michigan, Ohio, Oklahoma and Tennessee have similar statutes, according to the solicitor general's brief, while another 14 states, including Maryland, provide for some forms of inmate reimbursement in certain circumstances.

In other action, the court, without comment, declined to hear several highly publicized cases, including:South African Airways' appeal of a ban on its U.S. landing rights. The ban was part of economic sanctions imposed on the white-minority government in an attempt to force it to dismantle its system of apartheid. Uranium mine workers' appeal of a ruling that the government cannot be sued for contributing to the deaths and illnesses of uranium miners in Utah even if they were not told of a study outlining the risks of radiation poisoning. An appeal by doctors challenging a Massachusetts law that set limits on payments to doctors for treating Medicare patients.