GATE AE 2008 • Q22
MCQ • 1 Mark
Flight Mechanics & Space Dynamics
Atmospheric Flight Mechanics
Subtopic: Climb, Glide, Ceiling & Turn Performance
Question Statement:
The function f(x) = x2 - -5x+6
Options:
-
(A) has its maximum value at x = 2.0
-
(B) has its maximum value at x = 2.5
-
(C) is increasing on the interval (2.0, 2.5)
-
(D) is increasing on the interval (2.5, 3.0)
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.22)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (1 Mark, MCQ)
- **Topic**: Atmospheric Flight Mechanics (Climb, Glide, Ceiling & Turn Performance)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> The function f(x) = x2 - -5x+6
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Atmospheric Flight Mechanics** (Climb, Glide, Ceiling & Turn Performance) under *Flight Mechanics & Space Dynamics*. 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)** *"has its maximum value at x = 2.0"*: ❌ **INCORRECT**.
- **(B)** *"has its maximum value at x = 2.5"*: ✅ **CORRECT**.
- **(C)** *"is increasing on the interval (2.0, 2.5)"*: ❌ **INCORRECT**.
- **(D)** *"is increasing on the interval (2.5, 3.0)"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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