This is the 14944th most frequent Russian word.
подлежащими
The word "подлежащими" means "subjects" (in grammar, the doers of the action in a sentence).
In this sentence, 'подлежащие' is used to describe the students who are due to take the exam, functioning as a participle to indicate this obligation.
Студенты, подлежащие экзамену, подготовили свои материалы.
The students who are subject to the exam have prepared their materials.
Here, 'подлежащими' is part of a participial phrase modifying 'слова', emphasizing the subject's claimed adherence to truth.
Его слова подлежащими истине трудно было поверить.
His words, being supposedly truthful, were hard to believe.
In this example, 'подлежащие' establishes the individuals as those who are subject to the responsibility of registration.