can I break my fast in this day of my exam?
It is not permissible to break the fast for the reason you mention, rather it is haraam, because it is not included in the reasons for which one is allowed not to fast in Ramadaan.
From Fataawa al-Lajnah al-Daa’imah, vol. 10, p. 240
It should be noted that fasting in Ramadaan is an obligation upon every accountable Muslim, and no one is excused from fasting at the time of fasting except for those who have valid excuses, who are granted the concession of being allowed not to fast, such as the sick, travelers, pregnant and breastfeeding women, the very old and those who are forced to break their fast.
Sheikh Muhammed Salih Al-Munajjid