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They demonstrate problem solving abilities and analytical thinking.
Education is not a time-waste I can assure you.
I wouldn't have been able to fund the good certifications outside of a college to get a job in infosec.
So i can tell you it's well worth studying hard (well, studying at least).
I'd be really impressed seeing some of your C coding if you learned it over the summer holidays. That's a lot to fit in...
Yes, they can be gained through other avenues, but a lot of employers prefer having it written on a certificate what you can or cannot do instead of you telling them you can do xyz.
...But the chances of you making decent money from being a sportsman is very slim. Play a ball sport - you hit a ball one way, the wind takes it another way, you need to know how to compensate. Thats physics.
You can't change how it is. People want qualifications. You can get work via experience, but going down that route may mean you end up gaining experience further down the chain in a job you don't like.
For example: say you want to be a network administrator, you first have to get a job a network tech to get experience, before that (because you don't have a qualification or experience) you may need to get experience helping the techies out. Failing that they may need someone to make tea :P.
I'm not sure what groups your talking about, there may be conferences around your area where hackers/security professionals meet up. That would be something for you to look up.
Same as sh3llc0de i don't know much about Indian education. But if you want to get a good career in IT you have to stick at your education. They will value your education more than some 'hacking club' you speak of. Also if they see you drop out it shows lack of determination. Start studying for entry level certs that will give you a good step on the ladder and get an entry level part time job.
You need to learn chem to fully understand physics and vice~versa. Also chem is pretty much just how things react to others what properties they have and sometimes blowing S**T up.