(SEM I) THEORY EXAMINATION 2017-18 ENGINEERING MATHE MATICS

This document contains a comprehensive Engineering Mathematics question paper designed as per B.Tech university examination standards. The paper is divided into Section A, B, and C, covering a complete range of topics from calculus, matrices, vector calculus, multiple integrals, curve tracing, and differential equations.

It is ideal for AKTU, VTU, JNTU, BTU, MAKAUT, CU, DU, RTU, and all B.Tech first-year students.

SECTION A – Short Answer Questions (2 × 7 = 14 Marks)

Includes fundamental questions from:

nth derivatives of algebraic–logarithmic functions

Double integrals

Jacobians and partial derivatives

Area bounded by curves

Error propagation

Solenoidal vector conditions

Matrix reduction & rank determination

These questions test theoretical understanding and quick calculation skills.

SECTION B – Analytical Questions (7 × 3 = 21 Marks)

Covers medium-level problems from:

Higher Order Derivatives

Differential coefficients of trigonometric combinations

Euler-type derivative identities

Matrices and Determinants

Rank of matrices using row transformations

Matrix inverse using elementary operations

Jacobian & Partial Derivatives

Transformation of variables

Functional relations among variables

Multiple Integrals

Change of order of integration

Beta & Gamma function properties

Vector Calculus

Irrotational fields

Line integral evaluation

These questions strengthen concept clarity and procedural methods.

SECTION C – Long Answer Questions (7 × 5 = 35 Marks)

Includes advanced, exam-focused topics:

1. Differential Calculus & Differential Equations

Recurrence relations for higher derivatives

Mixed partial derivative identities

Curve tracing techniques

2. Maxima, Minima & Approximation

Lagrange multipliers

Differentials in geometrical applications

Multivariable Taylor's expansion

3. Linear Algebra

System of equations with parameters (λ, μ)

Cayley–Hamilton theorem

Unitary matrices & complex numbers

4. Multiple & Triple Integrals

Mass of a 3D solid

Improper integrals

Triple integrals over rectangular regions

5. Vector Theorems

Green’s theorem

Stokes’ theorem

Identities: curl(grad φ) = 0, div(curl V) = 0

These problems build strong foundations for engineering mathematics, competitive exams, and semester finals.