BEY-019 IGNOU Solved Assignment 2026-27

BEY-019 Solved Assignment: Real Analysis and Discrete Mathematics (TMA Coverage)

The following content reflects the mandatory 30% course weightage for BEY-019, with solutions derived from the official IGNOU curriculum (eGyanKosh). Each unit aligns with Blocks 1–4 and includes step-by-step derivations, proofs, and discrete mathematics applications relevant to BSCAEY students.

Block 1: Sets and Functions

• Unit 1.1: Set Theory Fundamentals

  Solutions include proofs for subset relations, power set constructions, and Cartesian product applications. Example: Prove A × (B ∪ C) = (A × B) ∪ (A × C) using set-builder notation.

• Unit 1.2: Functions and Mappings

  Covers injective/surjective/bijective functions with examples from real-world scenarios (e.g., energy systems). Includes verification of function properties using f(x) = x².

Block 2: Series and Analytical Geometry

• Unit 2.3: Convergence Tests for Series

  Step-by-step solutions for ratio, root, and comparison tests with numerical examples. Example: Determine convergence of Σ (n²)/(n³ + 1) using the limit comparison test.

• Unit 2.4: Parametric Equations and Curves

  Derivations for parametric differentiation (e.g., x = t², y = ln(t)) and applications in curve sketching.

Block 3: Discrete Mathematics

• Unit 3.5: Graph Theory Basics

  Solutions include adjacency matrix constructions, Eulerian/path existence proofs, and tree properties. Example: Prove a graph with n ≥ 2 vertices has at least one cycle if it contains a bridge.

• Unit 3.6: Combinatorics

  Permutation/combination problems with solutions using factorial notation and inclusion-exclusion principles.

Block 4: Differentiation and Integration

• Unit 4.7: Integration Techniques

  Step-by-step solutions for integration by parts, partial fractions, and trigonometric integrals. Example: Integrate ∫ (eˣ sin x) dx using integration by parts twice.

• Unit 4.8: Applications of Definite Integrals

  Area/volume calculations (e.g., rotating curves about axes) with verified limits and substitution methods.

FAQs

Yes. The BEY-019 Solved Assignment includes verified English translations of all mathematical proofs, theorems, and discrete mathematics explanations, adhering to IGNOU’s dual-language policy for BSCAEY students.

Each solution segment is pre-formatted with exact word counts (e.g., 500 words for Q1, 250 for Q3) using IGNOU’s prescribed structure. Additional notes clarify non-negotiable limits for numerical answers (e.g., 100 words for short-answer questions).