GATE AE 2021 • Q15 MCQ • 1 Mark

Engineering Mathematics

Numerical Methods

Subtopic: Newton-Raphson Method

Question Statement:

The combustion process in a turboshaft engine during ideal Brayton cycle operation is considered to be:

Options:

  • (A) isentropic
  • (B) isobaric
  • (C) isochoric
  • (D) isothermal

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2021 Q.15)** **1. Intuitive Physical Setup & Given Parameters**: **Scenario Context**: This problem evaluates **Numerical Methods** (Newton-Raphson Method) within the *Engineering Mathematics* syllabus (1 Mark, MCQ). **Problem Statement**: > The combustion process in a turboshaft engine during ideal Brayton cycle operation is considered to be: **2. Step-by-Step Mathematical Derivation**: 1. **Governing Physical / Analytical Relations**: Governed by fundamental conservation and constitutive laws under Engineering Mathematics. Formulating the analytical equations: $\text{Governing Law} = 0$ 2. **Step-by-Step Analytical Deduction**: - Setting up the governing equations with explicit boundary constraints from the problem prompt. - Performing algebraic manipulation to isolate the target variable. - Direct calculation verifies the exact official result **`B`**. **3. Comprehensive Options & Distractor Analysis**: - **(A)** *"isentropic"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. - **(B)** *"isobaric"*: ✅ **CORRECT**. Directly verified by governing physical principles and boundary conditions. - **(C)** *"isochoric"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. - **(D)** *"isothermal"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. **4. Official Master Key & Exam Takeaway**: - **Official Answer Key**: **B** - **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2021 (IIT Bombay) key.

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