What this set is
This is an original Doubtly set of 24 most important questions for the Mumbai University FE Semester 1 Applied Mathematics-I (BSC101, NEP 2020 scheme, introduced in 2024-25) exam in Winter 2026. It is not an official university paper and does not predict the actual paper. Questions are grouped module by module, four per module, and every question has a full step-by-step solution. Marks (3, 4, 5 or 6) follow the way such questions are marked in recent MU papers.
How the questions were chosen
We went through the last three Applied Mathematics-I papers (December 2024, June 2025 KT and December 2025) and listed the question type behind every sub-question. Types that came in two or three of these papers, or that carry 5 to 6 marks, were picked. For each type we wrote fresh questions in the same style. Per module, at most one question is taken as-is from those papers, and its stem says which paper it came from.
| Module and question type | Dec 2024 | June 2025 KT | Dec 2025 |
|---|---|---|---|
| 1. Roots of a complex number / solving \(x^n\) equations | Yes | Yes | Yes |
| 1. Expansion of \(\sin^m\theta\cos^n\theta\) in multiple angles | Yes | Yes | Yes |
| 2. Separating real and imaginary parts (tan, tanh, sin of \(x+iy\)) | No | Yes | Yes |
| 2. Logarithm of a complex number | Yes | Yes | Yes |
| 3. Euler's theorem and its second-order corollary | Yes | Yes | Yes |
| 3. Composite functions (chain rule), e.g. \(f(y-z,z-x,x-y)\) | Yes | Yes | Yes |
| 4. Maxima and minima of \(f(x,y)\) | Yes | Yes | Yes |
| 4. \(n^{th}\) derivative and Leibniz's theorem | Yes | Yes | Yes |
| 5. Consistency with \(\lambda,\mu\) (the same system each time) | Yes | Yes | Yes |
| 5. Rank by normal form / PAQ | Yes | Yes | Yes |
| 5. Unitary / orthogonal / Hermitian matrices | Yes | Yes | Yes |
| 6. Newton–Raphson method | Yes | Yes | Yes |
| 6. Gauss–Seidel and Gauss–Jacobi iterations | Yes | Yes | Yes |
One pattern stands out: the \(\lambda,\mu\) system \(x+y+z=6,\ x+2y+3z=10,\ x+2y+\lambda z=\mu\) appeared word for word in all three papers, and the Euler's theorem problem with \(\sin^{-1}\frac{x+y}{\sqrt x+\sqrt y}\) came twice. Those are included as-is (Q.20 and Q.12). Expansion of functions (Taylor and Maclaurin series) is in the Module 6 syllabus but was not asked in these three papers, so revise it from your notes as well.
How to use this set
Try each question on paper first, under time: roughly 1.5 to 2 minutes per mark, the pace of the real 60-mark, 2-hour exam. Then compare your working with the solution, line by line. In MU papers the method carries most of the marks, so practise writing the formula you use, the substitution and the final boxed result, as the solutions do. Every numerical answer and identity here was checked with a computer algebra system. If you can do all 24 confidently, you have covered the question types that came most often in the last three papers.
FAQs
Are these the questions that will come in the Winter 2026 exam?
No one can promise that. These are the question types that repeated most across the last three papers, so they are the best use of revision time, but study the full syllabus too.
Why are some questions marked "asked in MU"?
For each module, one question that the university has already set (some more than once) is included as-is so you can see the exact exam wording. All other questions are new ones of the same type.
What is the actual exam pattern?
The recent papers are 60 marks in 2 hours. Q.1 has short 3-mark questions (attempt any five), and Q.2 to Q.6 each have three parts worth 4, 5 and 6 marks, of which you answer any three questions.