Troubled by allegations of conflicts of interest against some legislators, a Virginia Senate committee doggedly questioned Gov.-elect Gerald L. Baliles's cabinet nominees yesterday on issues ranging from bank board seats to personal checking accounts.

"The conflict-of-interest law is so far-reaching that any entity of an entity can come back to haunt you," state Sen. William T. Parker (D-Chesapeake) said, noting that in past years he had been questioned about his business dealings.

Parker's warning came as Donald J. Finley, secretary of education-designate, defended his membership on the board of the newly formed Commonwealth Bank in Richmond.

Finley told the Senate Privileges and Elections Committee that he would resign his directorship if any allegations of conflicts arise.

Just down the hall in the House committee, however, questioning was more relaxed, punctuated with jokes rather than serious questions about conflicts.

Minutes before she told senators that she owned little more than a house in Portsmouth, Secretary of Human Resources-designate Eva S. Teig was telling House members about her childhood experiences with government red tape.

When her family was trying to emigrate from Egypt and her father was able to leave before the rest of the family, Teig noted: "It took us eight months to unravel the Egyptian bureaucracy, which makes ours look like nothing!" That has made her determined to cut as much red tape as possible, she said.

Meanwhile, Vivian L. Watts, the Fairfax County delegate who has been tapped as secretary of transportation and public safety, was receiving condolences from senators fearful that she faces an overwhelming task as administrator over two of the state's most controversial agencies.

"There's a certain blessing in an impossible task," quipped Watts. "You can take the slings and arrows a little better."

Rural lawmakers questioned Watts' support for mass transit and other urban-related transportation issues that she has supported as a legislator.

"I'd like for you to say it ain't so," said Sen. John C. Buchanan (D-Wise), prefacing his question to Watts. "Do you have any mission to further the mass transit program?"

"We now need to move people back and forth just as much as we've moved goods back and forth," Watts replied.

Later, as Watts stepped away from the podium, state Sen. William Truban (R-Shenandoah) called out: "Good luck, dear lady."

All six of Baliles' cabinet nominees were questioned today along with his proposed chief of staff David K. McCloud.

None ran into any serious obstacles and all are expected to win easy confirmation, perhaps as early as Friday.