Select the appropriate option in place of underlined part of the sentence. Increased productivity necessary reflects greater efforts made by the employees.
Options:
(A) Increase in productivity necessary
(B) Increase productivity is necessary
(C) Increase in productivity necessarily
(D) No improvement required
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2015 Q.5)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (1 Mark, MCQ)
- **Topic**: Analytical & Spatial Aptitude (Spatial Reasoning & Paper Folding)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> Select the appropriate option in place of underlined part of the sentence. Increased productivity necessary reflects greater efforts made by the employees.
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Analytical & Spatial Aptitude** (Spatial Reasoning & Paper Folding) 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 **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Increase in productivity necessary"*: ❌ **INCORRECT**.
- **(B)** *"Increase productivity is necessary"*: ✅ **CORRECT**.
- **(C)** *"Increase in productivity necessarily"*: ❌ **INCORRECT**.
- **(D)** *"No improvement required"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2015 (IIT Kanpur) master answer key with 100% precision.
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