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Hi Preeti,Yes, you are eligible for the exam. Here is the BITSAT 2019 Eligibility criteria for reference. For admission to any of the First Degree programmes of BITS except B.Pharma (Hons.):
Aspirants should have passed class 12th examination of 10+2 system from a recognized Central or State board or its equivalent with Physics, Chemistry, and Mathematics and adequate proficiency in English. For admission to B.Pharma (Hons.):
Aspirants should have passed class 12th examination of 10+2 system from a recognized Central or State board, or it is equivalent with Physics, Chemistry, and Biology and adequate proficiency in English. However, candidates with PCM may also apply for Pharmacy programme. Admission to all the programmes is subject to the conditions given below:
Aspirants should have obtained a minimum of aggregate 75% marks in Physics, Chemistry and Mathematics subjects (if he/she has taken Mathematics in BITSAT or a minimum of aggregate 75% marks in Physics, Chemistry and Biology subjects (if he/she has taken Biology in BITSAT subjects in class 12th examination, with at least 60% marks in each of the Physics, Chemistry, and Mathematics / Biology subjects. Only students who have appeared for 12th class examination in 2019 or who have passed class 12th class Examination in 2018 are eligible to appear in the BITSAT-2019 test. If a candidate has taken more than one attempt in class 12th or its equivalent, only his/her the latest performance was considered, provided this attempt had been for the full component of subjects/courses prescribed. Students who have passed class 12th examination in 2015 or earlier are not eligible to appear in BITSAT-2019. Students who are presently studying in BITSAT any of its campuses too are not eligible to appear in BITSAT-2019. Admissions will be made purely on merit. The merit position of the candidate for admission is based on the score obtained by the candidate in the BITSAT-2019. However, their eligibility for admission is subject to fulfilling the requirement of minimum marks in class 12th examination, as mentioned above. All the best.

Yes, it does offer BA Economics hons. The Department of Economics, established in 1961, is one of the oldest departments of Mithibai College. It offers a 3-year integrated B.A. Programme in Economics covering a total of 9 papers (Microeconomics, Macroeconomics, Indian Economy, Advanced Economic Theory, Growth and Development Economics, Indian Financial Economics, Elementary Mathematics and Statistics for Economic Analysis, International Economics, and Export Management). The college also offers M.A. Economics (CBCS)
The objectives of the course -
Provides a solid background in advanced economics and upgrades the skill sets required in applied economic analysis. Formulating hypotheses in social sciences and testing them. Conduct research to evaluate significant questions in social sciences by reviewing academic literature, collecting data, and applying econometric methods. Beneficial for students wishing to do Ph.D programme.

Now, for the first year. Download your GATE syllabus and previous year paper for mathematics and any other subject which is there in your first year. Now, don't be tensed much. Just keep doing your college on a regular basis and keep learning the concepts, even the smallest one especially for mathematics and if any other subject you have in your first year according to GATE syllabus. Practice Maths for 1 hour daily for a whole year along with previous year questions also. This will save you the trouble for studying mathematics later, and will give you ample time to study your core subjects. Also, in the first year, you should make habit of reading other books like literature, magazines and watch English movies and English tv serials. Increase your vocabulary, grammar status and communication skill. But, don't get too involved in TV Series or movies, don't get addicted. Try to complete your Maths syllabus in first year only. So, in first year, except for time in college you are giving one hour daily to Maths, reading is your new hobby, learning communication skills. Still, you will have ample time for sports and other hobbies and entertainment. You have to enjoy what you are doing. Now for 2nd, 3rd year. Apply the same strategy for the core subject of your GATE syllabus. Try to understand every concept and fundamentals through questioning everything by why or how etc. Make good rapport with teachers and clear your doubts at fundamental levels. In the meantime keep practicing the prev. Year question papers and analyze your mistakes for each question in every subject.
4th year, since all your subjects except few have a solid rock base. Start revising them vigorously and prepare 4th year subjects and any other subjects if you have left them. Also do not forget but keep practicing your math for an hour daily for all 4 years. You can also now give some time to aptitude. Like 1 hour at weekends will be enough. Complete your syllabus by 15th November in your 4th year (strictly). Start revising vigorously from 15th November and complete it by 15th December. 30 days, 10 subjects, 3 days each. Now from 15th DEC to 31st Jan, mock test and test series should be practiced and every mistake analyzed. This will be enough to get you in top rankers for GATE and ESE will also be easy. But, remember not to break your routine, self-determination and the will to be successful.