HelpDesk

HBTU KANPUR · PYQ LIBRARY

Engineering Mathematics 1 PYQs

89 previous-year questions for Engineering Mathematics 1. Use Practice Mode to filter by unit, topic, academic year or examination and open the available solutions.

Practise Engineering Mathematics 1Find notes & lectures →
A college student revising from notebooks with chai by their side

Available question papers

Topics in the question bank

Sample previous-year questions

2026-2027 · mid sem · 3 marks

Functions of One Real Variable

Find the nthn^{\text{th}} derivative of y=tan⁡−1(2x1−x2)y = \tan^{-1}\left(\frac{2x}{1-x^2}\right).
Open the full question bank and solutions →

2026-2027 · mid sem · 3 marks

Functions of Several Real Variables

Given that f(x,y)=sin⁡−1(yx)f(x, y) = \sin^{-1}\left(\frac{y}{x}\right). Using partial differentiation, show that x∂f∂x+y∂f∂y=0x \frac{\partial f}{\partial x} + y \frac{\partial f}{\partial y} = 0.
Open the full question bank and solutions →

2025-26 · end sem · 5 marks

Vector Calculus

Find the directional derivative of f(x,y,z)=x2yz+4xz2f(x,y,z) = x^2yz + 4xz^2 at the point (1,−2,−1)(1, -2, -1) in the direction of the vector 2i^−j^−2k^2\hat{i} - \hat{j} - 2\hat{k}.
Open the full question bank and solutions →

2025-26 · end sem · 5 marks

Matrices and Linear Algebra

Find the rank of the matrix: A=[123−1−2−1−3−11011011−1]A = \begin{bmatrix} 1 & 2 & 3 & -1 \\ -2 & -1 & -3 & -1 \\ 1 & 0 & 1 & 1 \\ 0 & 1 & 1 & -1 \end{bmatrix}
Open the full question bank and solutions →

2026-2027 · mid sem · 3 marks

Functions of One Real Variable

If y=(x2−1)ny = (x^2 - 1)^n, using Leibnitz's Theorem, show that (x2−1)yn+2+2xyn+1−n(n+1)yn=0(x^2 - 1)y_{n+2} + 2xy_{n+1} - n(n+1)y_n = 0
Open the full question bank and solutions →

2026-2027 · mid sem · 3 marks

Functions of One Real Variable

State the mean value theorem applicable to the equation (b−a)f′(c)=f(b)−f(a)(b-a)f'(c) = f(b) - f(a). Verify Lagrange's Mean value theorem for f(x)=(x−1)(x−2)(x−3)f(x) = (x-1)(x-2)(x-3) for x∈[0,4]x \in [0,4].
Open the full question bank and solutions →

2026-2027 · mid sem · 3 marks

Functions of One Real Variable

Verify Cauchy's Mean value theorem for sin⁡x\sin x and cos⁡x\cos x for x∈[−π2,0]x \in \left[-\frac{\pi}{2}, 0\right].
Open the full question bank and solutions →

Imported solutions may contain errors. Check calculations against your notes and official syllabus.