GATE AE 2013 • Q27
MCQ • 1 Mark
Propulsion
Thermodynamic Cycles of Gas Turbines
Subtopic: Turbojet, Turbofan & Turboprop Engine Performance
Question Statement:
Given that the Laplace transform, ࣦ1() ate s a then ࣦ
53s i n h 5tet =
Options:
-
(A) 2
3
10
s
s s
-
(B) 2
15
10s s
-
(C) 2
3
10
s
s s
-
(D) 2
15
10s s
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2013 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 Bombay
- **Problem Statement**:
> Given that the Laplace transform, ࣦ1() ate s a then ࣦ 53s i n h 5tet =
**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 **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"2
3
10
s
s s"*: ❌ **INCORRECT**.
- **(B)** *"2
15
10s s"*: ✅ **CORRECT**.
- **(C)** *"2
3
10
s
s s"*: ❌ **INCORRECT**.
- **(D)** *"2
15
10s s"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2013 (IIT Bombay) master answer key with 100% precision.
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