CBSE

Hello Tisha,
No, class 6th subject or optional subject won't make a difference.
*It depends on the college too, if you are applying for a course which is based on an entrance test then optional subject won't matter at all.
*Merit based Bachelor's courses are less in India. Terms of each college vary here too. For example, most of the courses of DU are merit-based, but you can't include the marks of 6th subject in the 'Best Four Subjects' (BFS) just like that. Terms vary from course to course. You may face deduction of 2-3% from your BFS% if you include your class 6th subject.
#Above all, It doesn't really matters. You are allotted the 6th subject by your school just so that your overall percentage increases and so does their own reputation.
#Overall percentage also is not important you see Tisha, why? (1) It won't matter if you are giving an entrance test (2) It may or may not matter in DU because BFS% is considered and some % is deducted upon including 6th subject (3) Policies of other merit-based colleges vary and little can be said about them. For example, Fergusson Pune checks just your class 12th mark sheet and then releases merit lists without you even knowing how they selected or rejected students. Hence, you can't say if they checked your optional subject's marks or not.

JEE MAIN-
Eligibility criteria related to Date of Birth
1. Students who are born on or after October 1, 1992 are eligible to apply-
Candidates belonging to Scheduled Caste (SC), Scheduled Tribe (ST) and Persons with Disabilities (PwD), should have been born on or after October 1, 1987. Candidates of these categories have been given a relaxation of 5 years. Note: Date of birth will be considered as per the Secondary Education Board/University certificate.
2. Eligibility criteria related to qualifying exam-
Aspirants should have passed 12th class or qualifying exam in 2015 or 2016. Students, who are appearing in class 12th or qualifying exam in 2017 can also apply.
3. Eligibility criteria related to total subjects/subject combination-
It is mandatory for aspiring candidates to have taken 5 subjects in 12th or qualifying exam. The 5 subjects for B.Tech/B.E. Are:
1-Language, 2-Physics, 3-Mathematics,
4-Any one of (Chemistry, Biology, Biotechnology, Technical Vocational Subject), 5-Any other subject
According to MHRD, apart from admissions to IITs, the qualifying marks for admission to NITs, IIITs and GFTIs have also been revised. As per the notification, for candidates to qualify for admissions to NITs/IIITs/GFTIs, they should have secured at least 75% marks in class 12th exam or be in the top 20 percentile in the class 12th exam conducted by the respective boards. For SC/ST candidates, the eligibility criteria is 65% marks in class 12th.
4. Eligibility related to total number of attempts-
A JEE Main aspirant can avail 3 attempts for the national level undergraduate engineering entrance exam.