Dear Spandan, yes definitely you can work at GOOGLE. If you are skillful and you have potential that GOOGLE wants then they will surely hire you. You just to master your coding skills. Also the Data Structures and Algorithm part has to be excellent, this is the main requirement. Being a dropper doesn't provide any hindrance to your job. It's your skills and will power that decides your career. If you want to go to Google then you can. 

All the best. 

Feel free to ask for any query