Subtopic: Higher Order Linear ODEs with Constant Coefficients
Question Statement:
The approximate ratio of mass flow rates of the primary air stream to the secondary air stream required to achieve the turbine inlet total temperature of 1550 K is:
Options:
(A) 2:1
(B) 1:2
(C) 1:1.5
(D) 1:1
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2009 Q.38)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (2 Mark, MCQ)
- **Topic**: Differential Equations (Higher Order Linear ODEs with Constant Coefficients)
- **Organizing Institute**: IIT Roorkee
- **Problem Statement**:
> K is
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Differential Equations** (Higher Order Linear ODEs with Constant Coefficients) under *Engineering Mathematics*. 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 **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"2:1"*: ❌ **INCORRECT**.
- **(B)** *"1:2"*: ❌ **INCORRECT**.
- **(C)** *"1:1.5"*: ✅ **CORRECT**.
- **(D)** *"1:1"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2009 (IIT Roorkee) master answer key with 100% precision.
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