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Dear Gayathri, Go for non-medical or you can opt for Diploma courses after 10th. In my opinion better option would be to join Dual Diploma B.Tech course where you save your one year as well as pressure of entrance tests. After doing a Diploma you get direct admission in second year of B.Tech. There are many universities in India that are offering you these Dual Diploma- B.Tech courses. Some of them are also offering you scholarships based on your percentage in your previous qualification. So, I feel it is better to take admission in an Dual Diploma-B.Tech course. Here are some of the universities, you can visit their websites for more details
NMIMS, Vile Parle West, Mumbai, Maharashtra
Lovely Professional University, get Road, Phagwara, Punjab
Maharishi Markandeshwar Engineering College, Ambala, Haryana
Good luck.

Dear Bhagyanath, You have not mentioned your state. Try for some good private university. Many reputed private universities are offering B.Arch. They have their different criteria for admissions. Some offer admission on basis of JEE scores, some offer admission on basis of NATA and some offer admission on the basis of both. Some even offer direct admission on basis of class 12 marks. Some of the universities also offer scholarships on basis of your performance in class 12 or JEE or NATA. You can check the details of any of the reputed universities like VIT, Lovely, SRM, etc. All these universities have wonderful infrastructure and world-class facilities to offer to students apart from good placements. Good luck.

Hello Shubham, Delhi University changes its rules every year but Mathematics is compulsory if you wish to pursue B.Com (Hons). In 2015, there were few changes made in the admission policy. Mathematics will be compulsory for Students of B.Com hons and Economic Hons. In case if you are opting for B.Com Prog. and if you don't have mathematics your 2 point 5 percent will be deducted Although some colleges might give you leverage on this
Since it is an umbrella degree for all commerce related domains it will open up a wide range of career options for you after graduation
You can look at pursuing different specialist certifications after or along with graduation such as CFA or CS or CA or ICWAI etc. These certifications would allow you to work in areas such as banking investment banking insurance auditing tax consulting private equity and related areas
These are all highly respectable and lucrative career options and if you can manage the relatively tough academic cycle then you can make a highly successful career in this domain
Good luck.