GATE AE 2010 • Q27
MCQ • 1 Mark
Propulsion
Thermodynamic Cycles of Gas Turbines
Subtopic: Turbojet, Turbofan & Turboprop Engine Performance
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)
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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