Is it permissible for me to complete my studies in a mixed engineering technical college, given the small number of girls in it, my ability to lower my gaze, and my parents' desire for me to complete my studies?

Studying in co-educational universities, in the manner common nowadays, is not permissible, as it is a means to discord (fitnah) and corruption. It is obligatory to enroll in a university free from this prohibition, if possible. However, if a student cannot find an alternative and needs to study in a co-educational university, and feels secure from discord, then there is no harm in it, provided they are keen to avoid everything that leads to discord. It is obligatory to associate with the righteous, avoid the corrupt and the wicked, and cooperate with people of uprightness in calling to Allah, enjoining good, and forbidding evil.