This Mathematics-I (KAS-103) question paper consists of three sections — A, B, and C — and students must attempt all sections. The paper tests core engineering mathematics concepts including matrices, eigenvalues, vector calculus, differential calculus, integral calculus, multiple integrals, and theorems of calculus. Questions are divided into short, medium, and long-answer formats.
SECTION A — Very Short Answer Questions (20 Marks)
Students must answer all 10 questions, each carrying 2 marks.
Topics include:
Eigenvalues
Linear dependence/independence of vectors
Higher-order derivatives
Asymptotes
Polar coordinates
Error analysis
Differentiation of exponential functions
Volumes bounded by cylinders
Solenoidal vector field condition
Green’s theorem
This section checks fundamental concepts and quick problem-solving ability.
SECTION B — Short Answer Questions (30 Marks)
Students must attempt any three questions, each of 10 marks.
Topics include:
Eigenvalues and eigenvectors
Rolle’s Theorem
Taylor series expansion
Changing order of integration
Irrotational vector fields and scalar potential
This section evaluates understanding of calculus and linear algebra with multi-step calculations.
SECTION C — Long Answer Questions (30 Marks)
Students must answer one question from each subsection (Q3, Q4, Q5, Q6, Q7).
Each question carries 10 marks.
Q3 — Linear Algebra
Conditions for unique/no/infinite solutions of linear equations
Rank reduction to normal form
Q4 — Differential Calculus
Higher derivatives of sin(x)
Mean Value Theorem
Q5 — Optimization & Algebra
Minimum material for open box
Relations between roots of cubic equation
Q6 — Double Integration / Area / C.G.
Area between curves
Centre of gravity of a bounded region
Q7 — Vector Calculus
Directional derivatives
Stokes’ Theorem verification
This Mathematics-I (KAS-103) question paper covers linear algebra, calculus, multiple integration, vector calculus, and optimization. Students answer conceptual, short, and long-form mathematical questions across three mandatory sections.
