(SEM I) THEORY EXAMINATION 2021-22 MATHEMATICS-I

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.