IIT Delhi - Indian Institute of Technology Answered Questions

CAT score doesn't matter for admission to executive MBA.
Please check out the below procedure and website for more details:
Desirous candidates should apply online along with online payment of Rs. Two Thousand Five Hundred (Rs. 2,500/-) towards application fees. For more information and filling of application form visit: www.iitd.ac.in or http://dms.iitd.ac.in/mba-part-admission.html.
Computer based Written Test, Group Discussion and Personal Interview will be conducted by I.I.T. Delhi. While filling the form, candidates should ensure that they fulfill the eligibility criteria. The online link for application will be available at http://dms.iitd.ac.in/mba-part-admission.html

The list for the batch of 2018-20 is already out. If you have applied please check here:
http://dms.iitd.ac.in/mba-full-admission.html
Also, 78% is a low percentile but the ultimate convert depends on the SI score which takes into consideration a lot of other parameters as well.

You have to firstly apply for JEE Mains and have to score good marks in the exam then you have to appear in JEE advance exam and have to score more than cutoff of IIT Delhi and having more than 75% in class 12th exam or be in top 20 percentile of your board then only you can get admission in IIT Delhi.

The bachelor's degree or equivalent qualification obtained by the candidate must entail a minimum of three years of education after completing higher secondary schooling (10+2) or equivalent.
A minimum of 60% marks in aggregate (of all the years/semesters) or 6.00 CGPA on a 10 point scale or equivalent in the qualifying degree.
So you are definitely eligible for applying. Along with this, you need to score at least 90 percentile to apply. To be the final covert you have to score around 98 in CAT. Also, do mention the extra-curricular activities you have participated in. They do consider it. To know more about the eligibility criteria please visit the below website - http://dms.iitd.ac.in/mba-full-admission.html.