As you asking for require eligibility for appear in GAIL (India) Limited Recruitment exam for Trainee Engineer post, so I am telling require info as per its last recruitment:

Executive Trainee (Chemical):
Degree in Engineering in Chemical/ Petrochemical/ Chemical Technology/ Petrochemical Technology

Executive Trainee (Mechanical):
Degree in Engineering in Mechanical/ Production/ Production & Industrial/ Manufacturing/ Mechanical & Automobile

Executive Trainee (Electrical):
Degree in Engineering in Electrical/ Electrical & Electronics

Executive Trainee (Instrumentation):
Degree in Engineering in Instrumentation/ Instrumentation & Control/ Electronics & Instrumentation/ Electrical &
Instrumentation/ Electronics/ Electrical & Electronics

Executive Trainee (Business Information System):
Degree in Engineering in Computer Science/ Information Technology/ Master Degree in Computer Application (MCA)

Executive Trainee (Telecom/ Telemetry):
Degree in Engineering in Electronics/ Electronics & Communication/ Electronics & Telecommunication/ Telecommunication/ Electrical & Electronics/ Electrical & Telecommunication