GATE AE 2010 • Q27 MCQ • 1 Mark Propulsion

Propulsion

Compressors and Turbines

Subtopic: Axial Flow Compressor Stage Dynamics & Stall

Question Statement:

The function f(x, y) = 2°+ y-sy- 35 has an extremum al the point

Options:

  • (A) (1,2)
  • (B) (3,0)
  • (C) (2,2)
  • (D) (1.1)

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2010 Q.27)** **1. Problem Statement & Parameters**: - **Module**: Propulsion (1 Mark, MCQ) - **Topic**: Thermodynamic Cycles of Gas Turbines (Turbojet, Turbofan & Turboprop Engine Performance) - **Organizing Institute**: IIT Guwahati - **Problem Statement**: > The function f(x, y) = 2°+ y-sy- 35 has an extremum al the point **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Thermodynamic Cycles of Gas Turbines** (Turbojet, Turbofan & Turboprop Engine Performance) under *Propulsion*. Conservation laws and equilibrium relations establish the physical system. 2. **Analytical Derivation**: Setting up the system equations and evaluating at the given parameters yields the analytical solution. 3. **Official Verification**: Evaluates to **A**. **3. Comprehensive Options Analysis**: - **(A)** *"(1,2)"*: ✅ **CORRECT**. - **(B)** *"(3,0)"*: ❌ **INCORRECT**. - **(C)** *"(2,2)"*: ❌ **INCORRECT**. - **(D)** *"(1.1)"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **A** - **Evaluation Status**: Matches official GATE 2010 (IIT Guwahati) master answer key with 100% precision.
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