(B) mode
The mode gives the value that occurs most frequently. To know the marks obtained by the maximum number of students, the teacher needs the mode.
Mode = value with the highest frequency. The textbook states: "In situations which require establishing the most frequent value or most popular item, the mode is the best choice." Here, "marks obtained by maximum number of students" directly means the most frequently occurring marks, so mode is the correct measure — not mean (average of all) or median (middle value).