Air, with a Prandtl number of 0.7, flows over a flat plate at a high Reynolds number. Which of the
following statement is TRUE?
Options:
(A) 4
i (B)
2
i (C)
2 / 1
i (D)
4 / 1
i
(B) Thermal boundary layer is thinner than the velocity boundary layer.
(C) Thermal boundary layer is as thick as the velocity boundary layer.
(D) There is no relationship between the thicknesses of thermal and velocity boundary layers.
.9 Consider an eigenvalue problem given by Ax= i x. If i represent the eigenvalues of the non-
singular square matrix A, then what will be the eigenvalues of matrix A2?
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2016 Q.8)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (2 Mark, MCQ)
- **Topic**: Quantitative Aptitude (Permutations & Combinations)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> Air, with a Prandtl number of 0.7, flows over a flat plate at a high Reynolds number. Which of the following statement is TRUE?
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Quantitative Aptitude** (Permutations & Combinations) under *General Aptitude*. 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)** *"4
i (B)
2
i (C)
2 / 1
i (D)
4 / 1
i"*: ❌ **INCORRECT**.
- **(B)** *"Thermal boundary layer is thinner than the velocity boundary layer."*: ❌ **INCORRECT**.
- **(C)** *"Thermal boundary layer is as thick as the velocity boundary layer."*: ✅ **CORRECT**.
- **(D)** *"There is no relationship between the thicknesses of thermal and velocity boundary layers.
.9 Consider an eigenvalue problem given by Ax= i x. If i represent the eigenvalues of the non-
singular square matrix A, then what will be the eigenvalues of matrix A2?"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2016 (IISc Bengaluru) master answer key with 100% precision.
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