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.
