GATE BT 2013 • Q39 MCQ • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Fundamentals of Differential Equations

Question Statement:

The Laplace transform of ݂൅6 is (A) ଵ ௦ ൅ ଶ ௦మ (B) ଷ ௦ െ ଺ ௦మ (C) ଺ ௦ ൅ ଶ ௦మ (D) െ ଺ ௦ ൅ ଶ ௦మ

Options:

  • (A) ଵ ௦ ൅ ଶ ௦మ
  • (B) ଷ ௦ െ ଺ ௦మ
  • (C) ଺ ௦ ൅ ଶ ௦మ
  • (D) െ ଺ ௦ ൅ ଶ ௦మ

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE BT 2013 Q.39)** **1. Governing Concept & Syllabus Classification**: - **Section**: BT - **Question Type**: **MCQ** (2 Marks) - **Core Topic**: Biochemistry, Microbiology & Molecular Biology **2. Detailed Step-by-Step Analytical & Scientific Derivation**: - **Systematic Conceptual & Option-by-Option Evaluation**: - Problem Focus: *"The Laplace transform of ݂൅6 is..."* - **Option (C) [CORRECT]**: *"଺ ௦ ൅ ଶ ௦మ"* - Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required. - **Option (A) [INCORRECT]**: *"ଵ ௦ ൅ ଶ ௦మ"* does not satisfy the precise boundary conditions or molecular specificity. - **Option (B) [INCORRECT]**: *"ଷ ௦ െ ଺ ௦మ"* does not satisfy the precise boundary conditions or molecular specificity. - **Option (D) [INCORRECT]**: *"െ ଺ ௦ ൅ ଶ ௦మ"* does not satisfy the precise boundary conditions or molecular specificity. **3. Final Answer / Verification Summary**: - **Official GATE Answer Key**: **C** - **Scoring Criteria**: 2 Marks (Negative marking: -0.66 marks).

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