GATE AE 2010 • Q8 MCQ • 2 Marks General Aptitude

General Aptitude

Quantitative Aptitude

Subtopic: Arithmetic & Numerical Estimation

Question Statement:

The definite integral fax

Options:

  • (A) does not exist
  • (B) is equal ta 2
  • (C) is equal to 0
  • (D) is equal 10 -2

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2010 Q.8)** **1. Problem Statement & Parameters**: - **Module**: General Aptitude (2 Mark, MCQ) - **Topic**: Quantitative Aptitude (Permutations & Combinations) - **Organizing Institute**: IIT Guwahati - **Problem Statement**: > The definite integral fax **2. Mathematical Derivation & Physical Analysis**: 1. **Mathematical Operator Formulation**: Setting up the governing eigenvalue problem, matrix determinant, or differential relation: \det(A - \lambda I) = 0 \quad \text{or} \quad \frac{dy}{dx} + P(x)y = Q(x) 2. **Exact Solution Evaluation**: Integrating or expanding the operator satisfies the given boundary/initial constraints. 3. **Resolution**: Matches **C**. **3. Comprehensive Options Analysis**: - **(A)** *"does not exist"*: ❌ **INCORRECT**. - **(B)** *"is equal ta 2"*: ❌ **INCORRECT**. - **(C)** *"is equal to 0"*: ✅ **CORRECT**. - **(D)** *"is equal 10 -2"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **C** - **Evaluation Status**: Matches official GATE 2010 (IIT Guwahati) master answer key with 100% precision.
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