(SEM I) THEORY EXAMINATION 2020-21 ENGINEERING MATHEMATICS

This document contains the official AKTU B.Tech 1st Semester (2020–21) Theory Examination question paper for Engineering Mathematics–I (KAS103T). It is the full 100-mark, 3-hour university exam paper that follows the exact AKTU pattern with Section A, Section B, and Section C. This question paper is extremely important for students preparing for semester exams, competitive exams, internal assessments, and for strengthening core mathematical concepts used throughout engineering.

Engineering Mathematics–I focuses on core foundational areas such as Matrices, Differential Calculus, Partial Derivatives, Vector Calculus, Multiple Integrals, Eigenvalues/Eigenvectors, Theorems of Calculus, Curve Tracing, and Jacobians. This paper perfectly covers all the essential concepts that every first-year B.Tech student must understand.

Detailed Breakdown of the Question Paper

SECTION A – 10 Short Questions (20 Marks)

This section includes 10 questions of 2 marks each, testing quick conceptual understanding. Topics include:

Unitary matrix proof

Rank–Nullity Theorem

Rolle’s Theorem

Symmetry of given curve

Function derivative proofs

Partial derivative transformations

Simple integrals

Volume calculation using triple integration

Solenoidal vector field verification

Green’s Theorem

These questions help students revise essential formulas and theorems.

SECTION B – 3 Medium-Length Questions (30 Marks)

Attempt any 3 out of 5 questions. Topics covered:

Finding matrix inverse

Solving differential equations using substitution

Jacobians and transformation of variables

Double integration with change of variables

Divergence theorem and surface integral evaluation

This section strengthens analytical skills and conceptual clarity.

SECTION C – 5 Long Answer Questions (50 Marks)

Students must attempt one part from each question, each carrying 10 marks. This section includes advanced-level engineering mathematics problems:

Question 3 – Matrices & Eigen Values

Reducing matrix to normal form using PAQ
OR

Finding eigenvalues and eigenvectors

Question 4 – Differential Calculus

Finding envelope of a family of lines
OR

Special trigonometric derivatives

Question 5 – Maxima/Minima & Transformations

Optimization problem using maxima/minima
OR

Derivative transformations and verification

Question 6 – Double Integrals & Mass Calculation

Changing the order of integration
OR

Mass & centre of gravity of lamina with variable density

Question 7 – Vector Calculus

Irrotational motion & velocity potential
OR

Verification of Stokes’ Theorem

This section helps students practice long, detailed mathematical derivations and proofs.