Subtopic: Discrete & Continuous Probability Distributions
Question Statement:
A cell has five molecules of a rare mRNA. Each cell contains 10^-12 g of total RNA, of which 2% is mRNA. The average molecular weight of an mRNA molecule is 3 × 10^5 g/mol. What fraction of total mRNA does this rare mRNA represent?
Options:
(A) 4.50 × 10^-7
(B) 3.50 × 10^-5
(C) 4.20 × 10^-7
(D) 4.05 × 10^-9
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2010 Q.42)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: Biotechnology
- **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: *"A cell has five molecules of a rare MRNA. Each cell contains 4 × 10* mRNA molecules. How
DNA of the rare mRNA. after making cDNA library from such cell?
nany clones one will need to screen to have 99% probability of find..."*
- **Option (B) [CORRECT]**: *"3.50 × 105"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
- **Option (A) [INCORRECT]**: *"4.50 × 10'"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (C) [INCORRECT]**: *"4.20 × 10'"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (D) [INCORRECT]**: *"4.05 × 109
BT
3/16
--- PAGE 8 ---
2010
BT"* 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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