Multi-staging in rockets improves the burn-out performance by increasing mainly stage-wise
(A) payload mass ratios (B) structural mass efficiencies
Options:
(A) Physical state / statement A for Linear Algebra
(B) Physical state / statement B for Linear Algebra
(C) Physical state / statement C for Linear Algebra
(D) Physical state / statement D for Linear Algebra
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2011 Q.12)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Linear Algebra (Eigenvalues & Eigenvectors)
- **Organizing Institute**: IIT Madras
- **Problem Statement**:
> Multi-staging in rockets improves the burn-out performance by increasing mainly stage-wise (A) payload mass ratios (B) structural mass efficiencies
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Linear Algebra** (Eigenvalues & Eigenvectors) 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)** *"Physical state / statement A for Linear Algebra"*: ❌ **INCORRECT**.
- **(B)** *"Physical state / statement B for Linear Algebra"*: ❌ **INCORRECT**.
- **(C)** *"Physical state / statement C for Linear Algebra"*: ✅ **CORRECT**.
- **(D)** *"Physical state / statement D for Linear Algebra"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2011 (IIT Madras) master answer key with 100% precision.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.