Engineering Mathematics-I (BAS103) important questions and topics for AKTU
These are ranked by how often AKTU repeats them across 8 papers. Repeated questions and "very likely" topics are the safest marks in the exam.
Most repeated Engineering Mathematics-I questions
- Change the order of integration and hence evaluate $\int_0^a\int_{\sqrt{ax}}^a\frac{y^2}{\sqrt{y^4-a^2x^2}}\,dy\,dx$. (7 marks, 2026, Change of Order of Integration) – also asked in 2019, 2020, 2021, 2022, 2023, 2025
- If $z = x^4y^2 \sin^{-1}(\frac{x}{y}) + \log x - \log y$, show that $x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y} = 6x^4y^2 \sin^{-1}(\frac{x}{y})$. (7 marks, 2026, Euler's Theorem for Homogeneous Functions) – also asked in 2019, 2020, 2021, 2023, 2024, 2025
- If $y = e^{\tan^{-1}x}$, prove that $(1 + x^2)y_{n+2} + [(2n+2)x - 1]y_{n+1} + n(n+1)y_n = 0$. (10 marks, 2021, Successive Differentiation (nth-Order Derivatives)) – also asked in 2019, 2020, 2022, 2023, 2024, 2025, 2026
- Show that the vector $f(r)\vec{r}$ is irrotational. Where $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$. (7 marks, 2025, Gradient, Curl, Divergence and Their Physical Interpretations) – also asked in 2019, 2020, 2021, 2022, 2024, 2026
- If $u = xyz, v = x^2 + y^2 + z^2$ and $w = x + y + z$. Find the jacobian $\frac{\partial(x, y, z)}{\partial(u, v, w)}$. (7 marks, 2025, Jacobians) – also asked in 2019, 2020, 2021, 2022, 2024, 2026
High-probability Engineering Mathematics-I topics
- Gradient, Curl, Divergence and Their Physical Interpretations (Unit 5: Vector Calculus) – asked 15 times in 2019, 2020, 2021, 2022, 2023, 2024, 2025, 2026
- Successive Differentiation (nth-Order Derivatives) (Unit 2: Differential Calculus-I) – asked 12 times in 2019, 2020, 2021, 2022, 2023, 2024, 2025, 2026
- Jacobians (Unit 3: Differential Calculus-II) – asked 12 times in 2019, 2020, 2021, 2022, 2023, 2024, 2025, 2026