Subtopic: Higher Order Linear ODEs with Constant Coefficients
Question Statement:
A normal shock wave in an ideal gas flow:
Options:
(A) increases stagnation pressure
(B) decreases stagnation pressure and increases entropy
(C) maintains constant stagnation pressure
(D) is an isentropic process
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2011 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 Madras
- **Problem Statement**:
>
**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 **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"2 and 0.18 km"*: ✅ **CORRECT**.
- **(B)** *"(2/3) and 17.6 km
An aircraft in a steady level flight at forward speed of 50 m/s suddenly rolls by 180 o and becomes
inverted. If no other changes are made to the configur ation or controls of the aircraft, the nature of
the subsequent flight path taken by the aircraft a nd its characteristic parameter(s) (assume g = 9.81
ms-2) are"*: ❌ **INCORRECT**.
- **(C)** *"straight line path with a speed of 50 m/s"*: ❌ **INCORRECT**.
- **(D)** *"upward circular path with a speed of 50 m/s and radius of 127.4 m"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2011 (IIT Madras) master answer key with 100% precision.
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