In the CBSE board exam system, the criteria for declaring a student as a topper can be a bit nuanced, especially when considering performance across subjects. If a student fails in mathematics but achieves full marks in all other subjects, including any additional subjects, their overall standing in terms of grades will depend on specific guidelines set by the board.

Under the CBSE grading system, a student must secure a grade above 'E' to be considered as having passed. For Class 10, while there isn't a strict overall division, merit is typically calculated based on the grades received across subjects. If the failing subject is not a core requirement (like a language), and the student excels in other subjects, they might still be eligible for merit recognition, although they would not receive a passing status in mathematics.

However, due to the cumulative nature of grading and the specific mention of merit certificates awarded to top-performing students, it’s crucial to note that having a failing subject may affect their chances of being recognized as a topper, despite outstanding performance elsewhere. Ultimately, the grading policy might not allow for a straightforward determination of being a topper without passing all core subjects.

For more detailed information, you can refer to the official guidelines provided by CBSE.