Engineering Mathematics-I Unit 3 – Differential Calculus-II: important questions for AKTU
Unit 3 (Differential Calculus-II) questions that AKTU repeats most often. This unit carries about 25 marks per paper. Start with the repeated questions, then the most asked topics.
Most repeated Unit 3 questions
- 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
- If $u^3+v^3+w^3=x+y+z$, $u^2+v^2+w^2=x^3+y^3+z^3$, and $u+v+w=x^2+y^2+z^2$, show that $\frac{\partial(u,v,w)}{\partial(x,y,z)}=\frac{(x-y)(y-z)(z-x)}{(u-v)(v-w)(w-u)}$. (10 marks, 2020, Jacobians) – also asked in 2019, 2021, 2022, 2023, 2024, 2025
- If $u^3+v^3=x+y$, $u^2+v^2=x^3+y^3$, then show $ \frac{\partial(u,v)}{\partial(x,y)}=\frac{y^2-x^2}{2uv(u-v)}. $ (7 marks, 2024, Jacobians) – also asked in 2020, 2021, 2022, 2025, 2026
Most important Unit 3 topic
- Jacobians (Unit 3: Differential Calculus-II) – asked 12 times in 2019, 2020, 2021, 2022, 2023, 2024, 2025, 2026
Most asked Unit 3 topics
- Jacobians – asked 12 times
- Lagrange's Method of Multipliers – asked 8 times
- Taylor's and Maclaurin's Expansions for Functions of One and Two Variables – asked 5 times
More Unit 3 previous year questions
- If $x=r\cos\theta$, $y=r\sin\theta$, find $\frac{\partial(r,\theta)}{\partial(x,y)}$. (2 marks, 2026, Jacobians)
- Expand $x^2y + 3y - 2$ in powers of $(x-1)$ and $(y+2)$ up to 3rd degree using Taylor’s series. (7 marks, 2026, Taylor's and Maclaurin's Expansions for Functions of One and Two Variables)
- Find the minimum distance from the point (1,2,0) to the cone $z^2 = x^2 + y^2$. (7 marks, 2026, Lagrange's Method of Multipliers)
- Find approximate value of $[(0.98)^2 + (2.01)^2 + (1.94)^2]^{1/2}$. (7 marks, 2026, Approximation of Errors)
- What are the applications of Jacobians (2 marks, 2025, Jacobians)
Unit 3 syllabus topics
- Taylor's and Maclaurin's Expansions for Functions of One and Two Variables
- Maxima and Minima of Functions of Several Variables
- Lagrange's Method of Multipliers
- Jacobians
- Approximation of Errors