Engineering Mathematics-I Unit 2 – Differential Calculus-I: AKTU previous year questions
12 AKTU questions from Unit 2 (Differential Calculus-I) asked in 2024–2026, tagged by marks, year and topic. In short: about 34 marks of every paper come from this unit; the most asked topic is Successive Differentiation (nth-Order Derivatives) (12 times); 11 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 2 previous year questions
- If $y = x^3 \log_e x$, prove that $\frac{d^4y}{dx^4} = \frac{6}{x}$. (2 marks, 2026, Successive Differentiation (nth-Order Derivatives))
- If $u(x, y) = (\sqrt{x} + \sqrt{y})^5$, then find the degree of the function $u(x, y)$. (2 marks, 2026, Euler's Theorem for Homogeneous Functions)
- Find the $n^{th}$ derivative of $\frac{2x+1}{(2x-1)(2x+3)}$. (7 marks, 2026, Successive Differentiation (nth-Order Derivatives))
- 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)
- Trace the curve: $y^2(a+x) = x^2(3a-x)$. (7 marks, 2026, Curve Tracing)
- If $u = \frac{x^2+y^2}{x+y}$, find the value of $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}$. (2 marks, 2025, Euler's Theorem for Homogeneous Functions)
- What is the difference between total derivatives and partial derivatives? (2 marks, 2025, Total Derivative)
- Find the $n^{th}$ derivative of $\tan^{-1}(\frac{x}{a})$. (7 marks, 2025, Successive Differentiation (nth-Order Derivatives))
- Trace the curve $y^2(a+x) = x^2(3a - x)$. (7 marks, 2025, Curve Tracing)
- If $u = f(r)$, where $r^2 = x^2 + y^2$, prove that $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = f''(r) + \frac{1}{r} f'(r)$. (7 marks, 2025, Change of Variables)
- Find all symmetry in the curve $y^2(a^2+x^2)=x^2(a^2-x^2)$. (2 marks, 2024, Curve Tracing)
- If $u=y^2e^{y/x}+x^2\tan^{-1}\left(\frac{x}{y}\right)$, show that (i) $x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=2u$. (ii) $x^2\frac{\partial^2u}{\partial x^2}+2xy\frac{\partial^2u}{\partial x\partial y}+y^2\frac{\partial^2u}{\partial y^2}=2u$. (7 marks, 2024, Euler's Theorem for Homogeneous Functions)
Most asked Unit 2 topics
- Successive Differentiation (nth-Order Derivatives) – asked 12 times
- Euler's Theorem for Homogeneous Functions – asked 10 times
- Rolle's, Lagrange's and Cauchy's Mean Value Theorems – asked 7 times
Unit 2 question pattern
- 2-mark questions: 5 asked in 2024–2026
- 7-mark questions: 7 asked in 2024–2026
- About 34 marks from Unit 2 in every paper
- 11 questions were asked again in a later year
Unit 2 questions year by year
- 2026: 5 Unit 2 questions asked (25 marks across that year's papers)
- 2025: 5 Unit 2 questions asked (25 marks across that year's papers)
- 2024: 2 Unit 2 questions asked (9 marks across that year's papers)