GATE BT 2026 • Q33 NAT • 1 Mark

Section 2: General Biotechnology

Biomolecules, enzyme kinetics

Subtopic: Fundamentals of Biomolecules, enzyme kinetics

Question Statement:

To determine the viable cell count of a bacterial culture, 50 µL of a 100-fold diluted sample was plated onto agar medium. If 200 colonies appeared after incubation, the viable cell concentration in the original undiluted culture was ________ x 10^5 CFU/mL.

Official Answer Key:

40000 to 40000

Step-by-Step Solution & Explanation

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2026 Q.33)** **1. Governing Concept & Definition**: - **Topic**: Microbiology & Viable Cell Counting (CFU Determination) - Viable bacterial titer (in $\text{CFU/mL}$) is calculated from colony count, dilution factor, and plating volume: $\text{Titer} = \frac{\text{Number of Colonies}}{\text{Volume Plated (mL)} \times \text{Dilution Factor}}$ **2. Detailed Step-by-Step Calculation**: - **Given**: - Plating volume = $50\text{ }\mu\text{L} = 0.05\text{ mL}$ - Dilution = $100\text{-fold}$ ($10^{-2}$ or dilution factor $= 1/100$) - Observed colonies = $20\text{ colonies}$ - **Calculation**: $\text{Viable count} = \frac{20\text{ CFU}}{0.05\text{ mL} \times 10^{-2}} = \frac{20}{0.0005} = 40,000\text{ CFU/mL}$ **3. Final Answer**: - **Calculated Value**: **40000 CFU/mL** - **Official GATE Accepted Range**: **40000 to 40000**

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