Mathematics vs Applied Mathematics: which one to take
Two subjects with similar names and very different doors.
What each contains
Mathematics (041) is the full course: sets, relations, calculus, trigonometry, vectors, three-dimensional geometry, probability. Applied Mathematics (241) covers numbers, algebra, statistics, probability, financial mathematics and the calculus needed for business and data interpretation.
Who can take which
CBSE norms allow 041 only after Class 10 Maths Standard. Students with Basic can take 241. Schools sometimes get exceptions, so ask if you took Basic and want 041.
Where each is accepted
041 is required for JEE, NATA, IMU CET, pilot training, ISI and CMI, and most B.Sc Mathematics and Statistics programmes. 241 is accepted for many B.Com, BBA, Economics and data programmes, but not for engineering. Delhi University accepts either for Economics Honours; some other universities do not, so check the programme page.
The decision
Engineering, architecture or physical sciences in view: 041. Commerce or humanities with a quantitative degree in view: 241 is enough unless your target programme says otherwise. No quantitative degree in view: consider whether you need either.
Guidance based on the CBSE scheme of studies and public exam bulletins. Confirm rules with your school and the official sources before deciding.