Minor is used after these nouns:
undergraduate

be, seem

extremely, fairly, very, etc.
This is a very minor operation and there is very little risk involved.

comparatively, relatively
That's a relatively minor matter—we can leave it till later.

apparently, seemingly

Minor is used with these nouns:
accident, adjustment, ailment, alteration, amendment, annoyance, blemish, breach, bruise, bug, bump, burn, catastrophe, celebrity, change, character, chord, classic, complaint, complication, component, composer, concession, concussion, consideration, contribution, correction, crime, criticism, cut, damage, defect, deity, depression, detail, difference, disagreement, disappointment, discomfort, discrepancy, dispute, distraction, disturbance, diversion, drawback, earthquake, error, eruption, exception, explosion, fault, flaw, fluctuation, graze, heart attack, hiccup, illness, imperfection, importance, improvement, incident, inconvenience, indiscretion, infection, infringement, injury, irregularity, irritation, issue, key, knock, lapse, league, leak, masterpiece, miracle, mishap, modification, mystery, nuisance, offence, office, official, operation, panic, part, poet, point, problem, rebellion, reduction, reform, repair, reservation, revision, revolution, road, role, royalty, scale, scratch, scuffle, setback, shortcoming, side effect, significance, skirmish, snag, sport, squabble, stroke, surgery, symptom, technicality, tremor, triumph, upset, vandalism, variation, violation, wound