Engineering Mathematics-I Unit 3 – Differential Calculus-II: AKTU previous year questions
12 AKTU questions from Unit 3 (Differential Calculus-II) asked in 2024–2026, tagged by marks, year and topic. In short: about 25 marks of every paper come from this unit; the most asked topic is Jacobians (12 times); 8 questions came back in a later year. The latest ones are listed below; on the page you can filter them by 2-mark or long questions, topic and repeats.
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)
- Find the volume of the largest rectangular parallelepiped that can be inscribed in the ellipsoid $\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1$. (7 marks, 2025, Lagrange's Method of Multipliers)
- 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)
- Find the maxima and minima of the function $\sin x + \sin y + \sin(x + y)$. (7 marks, 2025, Maxima and Minima of Functions of Several Variables)
- Calculate the error in $R$ if $E=RI$ and possible errors in $E$ and $I$ are 30% and 20% respectively. (2 marks, 2024, Approximation of Errors)
- Expand $f(x,y)=e^x\cos y$ about the point $\left(1,\frac{\pi}{4}\right)$ by Taylor's series. (7 marks, 2024, Taylor's and Maclaurin's Expansions for Functions of One and Two Variables)
- 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)
- The pressure $P$ at any point $(x,y,z)$ in space is $P=400xyz^2$. Find the highest pressure at the surface of a unit sphere $x^2+y^2+z^2=1$ using Lagrange's method. (7 marks, 2024, Lagrange's Method of Multipliers)
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
Unit 3 question pattern
- 2-mark questions: 3 asked in 2024–2026
- 7-mark questions: 9 asked in 2024–2026
- About 25 marks from Unit 3 in every paper
- 8 questions were asked again in a later year
Unit 3 questions year by year
- 2026: 4 Unit 3 questions asked (23 marks across that year's papers)
- 2025: 4 Unit 3 questions asked (23 marks across that year's papers)
- 2024: 4 Unit 3 questions asked (23 marks across that year's papers)