The city Sanitation Department will have to trash its recent supervisor’s exam because of suspected rampant cheating, The Post has learned.

A document with 121 questions and multiple-choice answers — with the correct answers marked by asterisks — was shared in a Facebook study group and widely circulated, sources said.

Up to 100 of the queries appeared on the agency’s April 13 “promotion to supervisor” civil-service exam — the first given by the city in five years.

“It’s a huge deal” a worker said of the breach. “There’s no way they can use this test. They’re going to have to make everyone re-take it.”

More than 2,300 sanitation workers vying to become bosses — and make a minimum $80,812 salary — took the test, said the city Department of Citywide Administrative Services, which administered it.

DCAS has referred the case to the city Department of Investigation. If DOI finds the exam was “compromised,” a do-over will be called.

“The City of New York has zero tolerance for misconduct. Any allegation of wrongdoing is and will be thoroughly investigated to ensure the integrity of the testing process,” said DCAS spokesman Nick Benson.

He added, “Anyone who discloses the contents of a civil service exam could be subject to termination of employment and even prosecution.”

Possible criminal charges include official misconduct, or bribery if anything of value was given or received, officials said.

A panel of 10 to 12 current Sanitation supervisors helped craft the questions, based on skills needed for the position, DCAS said.

Anyone involved had to sign a DOI warning to keep all testing materials confidential before, during and after the exam.

The 121 questions and answers, obtained by The Post, gauge how supervisors would manage workers doing trash pickups and snow removal.

Some questions deal with ethics. One asks what supervisors should do if their boss, a superintendent, orders them to void a summons issued to a chief’s mother. Three possible answers list various ways to toss the summons. The fourth answer — the right one — is to defy the order.

City Councilman Joseph Borelli (R-Staten Isand) also received a copy of the 121 questions and answers. He left a message with the Sanitation Department’s Inspector General in the DOI Tuesday. Later in the week, Borelli tweeted that his call wasn’t returned. The IG finally returned his call Friday, Borelli said, after The Post asked DOI about his complaint.

The following questions and answers were among the 121 test items widely circulated among sanitation workers before the recent promotion test.

As of Jan. 5, 2015, DSNY no longer collects Electronic Waste (E-Waste) placed out by residents for collection with curbside recycling materials. Which of the following is not considered E-Waste and should continue to be collected by recycling crews?

A) Computers

B) Fax Machines

C) *Microwaves

D) Keyboards

Garage Supervisors are responsible for the inspection of tires on all motor equipment housed at their respective locations. How often should Department vehicle tires be inspected?

A) Weekly

B) *Bi-weekly

C) Monthly

D) Quarterly

Wreckers must be dispatched immediately as a time limit has been established by The New Jersey Turnpike Authority for towing equipment off the Turnpike. What is the time limit?

A) 1 hour

B)*2hours

C)3 hours

D)4 hours

*denotes correct answer