GATE BT 2014 • Q36 MCQ • 2 Marks

Section 2: General Biotechnology

Biomolecules, enzyme kinetics

Subtopic: Fundamentals of Biomolecules, enzyme kinetics

Question Statement:

The concentration profile of a chemical at a location x and time t, denoted by 𝑐𝑐(𝑥𝑥, 𝑡𝑡), changes as per the following equation, 𝑐𝑐(𝑥𝑥, 𝑡𝑡) = 𝑐𝑐0 √2 𝜋𝜋 𝐷𝐷 𝑡𝑡 𝑒𝑒𝑒𝑒𝑒𝑒[−𝑥𝑥2 2 𝐷𝐷 𝑡𝑡] where 𝐷𝐷 𝑎𝑎𝑛𝑛𝑛𝑛 𝑐𝑐0 are assumed to be constant. Which of the following is correct?

Options:

  • (A) 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕= 𝐷𝐷 𝜕𝜕2𝑐𝑐 𝜕𝜕𝑥𝑥2
  • (B) 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕= 𝐷𝐷 2 𝜕𝜕2𝑐𝑐 𝜕𝜕𝑥𝑥2
  • (C) 𝜕𝜕2𝑐𝑐 𝜕𝜕𝑡𝑡2 = 𝐷𝐷 𝜕𝜕2𝑐𝑐 𝜕𝜕𝑥𝑥2 (E) 𝜕𝜕2𝑐𝑐 𝜕𝜕𝑡𝑡2 = 𝐷𝐷 2 𝜕𝜕2𝑐𝑐 𝜕𝜕𝑥𝑥2

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE BT 2014 Q.36)** **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 concentration profile of a chemical at a location x and time t, denoted by 𝑐𝑐(𝑥𝑥, 𝑡𝑡), changes as per the following equation, 𝑐𝑐(𝑥𝑥, 𝑡𝑡) = 𝑐𝑐0 √2 𝜋𝜋 𝐷𝐷 𝑡𝑡 𝑒𝑒𝑒𝑒𝑒𝑒[−𝑥𝑥2 2 𝐷𝐷 𝑡𝑡] where 𝐷𝐷 𝑎𝑎𝑛𝑛𝑛𝑛 𝑐𝑐0 are assumed..."* - **Option (B) [CORRECT]**: *"𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕= 𝐷𝐷 2 𝜕𝜕2𝑐𝑐 𝜕𝜕𝑥𝑥2"* - Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required. - **Option (A) [INCORRECT]**: *"𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕= 𝐷𝐷 𝜕𝜕2𝑐𝑐 𝜕𝜕𝑥𝑥2"* does not satisfy the precise boundary conditions or molecular specificity. - **Option (C) [INCORRECT]**: *"𝜕𝜕2𝑐𝑐 𝜕𝜕𝑡𝑡2 = 𝐷𝐷 𝜕𝜕2𝑐𝑐 𝜕𝜕𝑥𝑥2 (E) 𝜕𝜕2𝑐𝑐 𝜕𝜕𝑡𝑡2 = 𝐷𝐷 2 𝜕𝜕2𝑐𝑐 𝜕𝜕𝑥𝑥2"* does not satisfy the precise boundary conditions or molecular specificity. **3. Final Answer / Verification Summary**: - **Official GATE Answer Key**: **B** - **Scoring Criteria**: 2 Marks (Negative marking: -0.66 marks).

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