Question Statement:
Given digits 2, 2. 3, 3, 3,4, 4. 4, 4 how many distinct 4 digit numbers greater than 3000 can be
formed?
Options:
-
(A) 50
-
(B) S1
-
(C) 52
-
(D) 54
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2010 Q.64)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: General Aptitude
- **Question Type**: **MCQ** (2 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Systematic Conceptual & Option-by-Option Evaluation**:
- Problem Focus: *"Given digits 2, 2. 3, 3, 3,4, 4. 4, 4 how many distinct 4 digit numbers greater than 3000 can be
formed?..."*
- **Option (B) [CORRECT]**: *"S1"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
- **Option (A) [INCORRECT]**: *"50"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (C) [INCORRECT]**: *"52"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (D) [INCORRECT]**: *"54"* does not satisfy the precise boundary conditions or molecular specificity.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **B**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.66 marks).
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