John W. Hinckley Jr., accused of the attempted assassination of President Reagan and the shooting of three other persons last March 30, will stand trial Nov. 30, a U.S. judge said yesterday.

Hinckley, who is in custody in the Army stockade at Fort Meade, Md., has been undergoing psychiatric examination by doctors for both the prosecution and the defense since his arrest the day of the shootings. His lawyers have admitted in court papers that Hinckley shot Reagan, his press secretary, a U.S. Secret Service agent and a D.C. police officer. They have told the court that Hinckley will contend that he was insane at the time and should not be held criminally responsible.

Meanwhile, the Justice Department is conducting an investigation to determine who leaked transcripts of telephone conversations between Hinckley and actress Jodie Foster to United Press International, which published segments of the transcripts in a recent news article. Foster previously had denied that she had ever talked to Hinckley.

Law enforcement sources, who confiscated an unmailed letter -- apparently written for Foster -- from Hinckley's hotel room on the day of the shootings, believe that Hinckley may have attacked the President in an attempt to impress the young actress.

Judge Barrington D. Parker, who will preside at Hinckley's trial, said the leak to UPI appeared to be a "flagrant violation" of another federal judge's order which warned lawyers and law enforcement officials against making any statements about the Hinckley case. Parker made the statement during a hearing on various issues in the case that was held in his chambers last week. A copy of a transcript of that proceeding, which was closed to the public, was made available later.

According to the transcript, U.S. Attorney Charles F.C. Ruff told Parker that there was no dispute that the transcripts probably were given to UPI by a federal agent, "that it is entirely improper . . . I have begun to take steps to try to determine who it was."