Engineering Mathematics-I (BAS103) AKTU predicted paper 2026-27
AI-predicted paper for Engineering Mathematics-I based on 8 past papers (2019, 2020, 2021, 2022, 2023, 2024, 2025, 2026). NOT an official AKTU paper. Use as a revision tool only.
Paper pattern
- Section A: Attempt all questions. (14 marks)
- Section B: Attempt any THREE questions out of five. (21 marks)
- Section C: Attempt ONE question from each pair (a or b). (35 marks)
Why these questions
- Unit 2 (Differential Calculus-I) dominates — 23% avg weightage
- Asked every year: Successive Differentiation (nth-Order Derivatives), Euler's Theorem for Homogeneous Functions
- Due for comeback: Cayley-Hamilton Theorem and Its Applications, Complex Matrices: Hermitian, Skew-Hermitian and Unitary
- Low priority (never asked): Characteristic Equation, Applications of Matrices to Engineering Problems
- Most repeated topic: Gradient, Curl, Divergence and Their Physical Interpretations
Section A – 2-mark questions
- If $A=\begin{pmatrix}-1&2&3\\0&3&5\\0&0&-2\end{pmatrix}$, find the eigen values of $A^3+5A+8I$.
- If $u = \frac{x^2+y^2}{x+y}$, find the value of $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}$.
- If $x=r\cos\theta$, $y=r\sin\theta$, find $\frac{\partial(r,\theta)}{\partial(x,y)}$.
- Evaluate $\int_1^2\int_1^3 x^2y^2\,dx\,dy$.
- Prove that $\vec A=(6xy+z^3)\hat i+(3x^2-z)\hat j+(3xz^2-y)\hat k$ is irrotational.
- If $y = \cos^{-1} x$, prove that $(1-x^2)y_2 - xy_1 = 0$.
- Write a short note on Change of Order of Integration.
Section B – sample questions
- If $z = x^4y^2 \sin^{-1}(\frac{x}{y}) + \log x - \log y$, show that $x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y} = 6x^4y^2 \sin^{-1}(\frac{x}{y})$.
- Find the eigen values and eigen vectors of the following Matrix A: $A = \begin{bmatrix} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix}$.
- If $y = e^{\tan^{-1}x}$, prove that $(1 + x^2)y_{n+2} + [(2n+2)x - 1]y_{n+1} + n(n+1)y_n = 0$.