No such data available but as far as your purpose is concerned - yeah, It seems like a general trend that girls avoid engineering and only a handful of girl aspirants apply for IITJEE exam.

I personally believe that more girls must pursue PROFESSIONAL courses and it is good news that with each passing year, the JEE exam also has seen more women applying. Also as per growing trends, more and more women are being accepted into the job market and their competitive spirit is improving. So there is greater chance for them to fare better in the top ranks in upcoming years.

In 2014, there were only five girls in the top 100. Girls comprised 12.49% of the 36,566 students who qualified to join IITs from the 1,47,678 appeared, better than that of year 2013- 11.54%. Also, their representation in 2016 further got better: 23.16% of those who appeared for the JEE-Advanced were girls, compared with 17.35% in 2015- total of 1,17,237 students.

There are different reasons for this-

1 – No Encouragement, No expectation, no effort, No Emphasis

In most middle-class families, a lot of times, the expectations from boy child & girl child differ.

In case of a boy, there is general emphasis is on study, and get into a good professional college.

But in the subconscious of a lot of families, the expectation from a girl is to study, have a decent job and get married.

A lot of my female students agree that their parents didn’t really expect them to crack JEE, but get good marks in Board exam or at best get admission into a good engineering or medical college.

2 – Women generally are not trained to be as focussed hence don’t do that well in standardised problem-orientated aptitude tests. Girls are generally made to be active in socialising, household works in addition to their school studies.

Some say Genetically, women are very good at multi-tasking which men find difficult to manage. Entrance Tests like IIT, GATE and CAT requires complete focus and single-minded dedication to succeed.

Obviously, I understand that with more awareness, more girls are being encouraged now & very soon, i wish Girls do as well in various Competitions.

JEE Advanced 2016—

The Joint Entrance Examination (Advanced) for 2016 sprung quite a few surprises as More girls qualified this year to join the prestigious Indian Institutes of Technology, but none made it to the top-100 ranks

In JEE advanced 2016, Riya Singh of Kota, Rajasthan had ranked 1st in the Common Rank List (CRL) in Female category. Her All India Rank (AIR) was 133.

Total number of Female candidates who registered for the JEE Advanced 2016 was 30,020. Out of them 27,778 Female candidates sat for the test, of them only 4,570 female candidates had been declared successful.

JEE Advanced 2015—

Total 26456 students (3049 girls) have qualified out of total 117238 students actually appeared for JEE Advanced 2015. Girl’s topper was Krati Tiwari (AIR 47).

JEE Advanced 2013—

Two young girls Aditi Ladha (AIR 6, score 320 out of 360) rom the Delhi Zone and Sibala Madhuri (AIR 8, score 314 out of 360) from Madras zone are the first girls ever to have secured a position in the top 10 ranks of the IIT-JEE (advanced).

Of the 21,110 candidates qualifying the examinations 2,392 were girls.

In 2013, only five girls made it to the top 100 qualifying students.

Girls formed only 11 per cent of the total qualifying students

A total of 27,151 aspirants out of the registered 1,26,997 qualified in the examination.

The prominent reason for poor performance of girls in the exam is lack of encouragement to girls by either their parents or the social system to get into engineering. Most girl students opt for medical, arts or commerce subjects. However, it does not mean girls cannot become good engineers.

NOTE About JEE advanced-

From the academic year 2016-17, ISM, Dhanbad started to admit female candidates into Mining Engineering or Mining Machinery Engineering related courses.

Admissions to IIT Chhattisgarh, IIT Goa, IIT Jammu and IIT Karnataka were also started from the academic year 2016 - 17.

Apart from 23 IITs (including the four new ones), admissions on the basis of JEE advanced are granted to institutes like Rajiv Gandhi Institute of Petroleum Technology; Rae Bareli Indian Institute of Petroleum and Energy, Visakhapatnam; Indian Institute of Space Science and Technology (IIST), Thiruvananthapuram etc.

There are altogether 9784 seats available in all these institutes- 16 IITs and also Indian School of Mines in Dhanbad.