Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2017 Q.51)**
**1. Governing Concept & Question Classification**:
- **Section**: BT
- **Question Type**: **MCQ** (2 Marks)
- **Topic**: Recombinant DNA Technology (Partial Restriction Digestion Fragment Combinatorics)
**2. Detailed Step-by-Step Derivation**:
- Consider a linear 10 kb DNA fragment with EcoRI cleavage sites located at coordinates:
$\text{Coordinates (kb)}: \quad 0\text{ kb (end)}, \quad 2\text{ kb}, \quad 4\text{ kb}, \quad 7\text{ kb}, \quad 10\text{ kb (end)}$
- The internal EcoRI cleavage sites are at positions: $x_1 = 2\text{ kb}$, $x_2 = 4\text{ kb}$, and $x_3 = 7\text{ kb}$.
- These three internal sites divide the 10 kb DNA molecule into four elementary segments:
- Segment 1: $[0, 2] \implies \text{length } 2\text{ kb}$
- Segment 2: $[2, 4] \implies \text{length } 2\text{ kb}$
- Segment 3: $[4, 7] \implies \text{length } 3\text{ kb}$
- Segment 4: $[7, 10] \implies \text{length } 3\text{ kb}$
- In a **partial digestion**, each of the internal sites may or may not be cleaved. The resulting fragment lengths correspond to all possible contiguous sub-segments:
- **Single elementary segments**:
- $[0, 2] = 2\text{ kb}$
- $[2, 4] = 2\text{ kb}$
- $[4, 7] = 3\text{ kb}$
- $[7, 10] = 3\text{ kb}$
- Distinct lengths: **2, 3 kb**.
- **Two contiguous segments**:
- $[0, 4] = 2 + 2 = 4\text{ kb}$
- $[2, 7] = 2 + 3 = 5\text{ kb}$
- $[4, 10] = 3 + 3 = 6\text{ kb}$
- Distinct lengths: **4, 5, 6 kb**.
- **Three contiguous segments**:
- $[0, 7] = 2 + 2 + 3 = 7\text{ kb}$
- $[2, 10] = 2 + 3 + 3 = 8\text{ kb}$
- Distinct lengths: **7, 8 kb**.
- **All four segments (uncut fragment)**:
- $[0, 10] = 10\text{ kb}$.
- Compiling all unique fragment lengths obtained upon partial digestion:
$\{2, 3, 4, 5, 6, 7, 8, 10\}\text{ kb}$
- **Option-by-Option Evaluation**:
- **Option (A) [CORRECT]**: Lists the complete, rigorous set of all 8 possible fragment lengths: 2, 3, 4, 5, 6, 7, 8, and 10 kb.
- **Option (B) [INCORRECT]**: Omits 8 kb and the full-length 10 kb fragment.
- **Option (C) [INCORRECT]**: Incomplete list.
- **Option (D) [INCORRECT]**: Lists only the complete digestion fragment sizes (2 and 3 kb), not partial digestion products.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **A**
- **Scoring Criteria**: +2.0 Marks (Negative marking: -0.67 marks).