The cut off for admission in Engineering colleges or institutes in India as your cousin wants to take admission accordingly are as follows:

JEE Main 2014 Cutoff:
Cut-off score for appearing in JEE (Advanced) – 2014 for following categories:

Category Cut-off Score
Common Merit List (CML) 115
Other Backward Class (OBC - NCL) 74
Scheduled Caste (SC) 53
Scheduled Tribe (ST) 47

GATE 2014 Expected Cutoff

Branch General SC/ST/PD OBC (Non-Creamy) Total
Appeared

Computer Sc. & IT 25.74 17.16 23.17 1,55,190
Civil Engineering 27.13 18.09 24.42 90,872
Electronics &
Communication 25 16.67 22.5 2,16,367
Electrical Engineering 25.74 17.16 23.17 1,41,799
Mechanical Engineering 25 16.67 22.25 1,85,578

10,33,625 students registered for GATE 2014 exam.
8,89,156 students appeared for GATE 2014 exam.
30.17% Female studenta appeared in GATE 2014 and 31,431 qualified
Total Qualified in GATE 2014
85,063 (General) + 42,287 (OBC) + 17,085 (SC)+ 4224 (ST) + 1035 (PwD) = 1,49,694