GATE BT 2014 • Q47 MCQ • 2 Marks

Section 1: Engineering Mathematics

Engineering Mathematics

Subtopic: Calculus, Linear Algebra & Probability

Question Statement:

In a genetic cross between the genotypes WWXX and wwxx, the following phenotypic distributions were observed among the F2 progeny: WX, 562; wx, 158; Wx, 38; and wX, 42. Likewise, a cross between XXYY and xxyy yielded the following results: XY, 675; xy, 175; Xy, 72; and xY, 78. Similarly, a cross between WWYY and wwyy yielded: WY, 292; wy, 88; Wy, 12; and wY, 8. In all the genotypes, capital letters denote the dominant allele. Assume that the F1 progeny were self-fertilized in all three crosses. Also, double cross-over does not occur in this species. Which of the following is correct?

Options:

  • (A) Relative position: W-X-Y Distances: W-X = 5 map units, X-Y = 17 map units
  • (B) Relative position: X-Y-W Distances: X-Y = 15 map units, Y-W = 11 map units
  • (C) Relative position: Y-W-X Distances: Y-W = 5 map units, W-X = 11 map units
  • (D) Relative position: X-W-Y Distances: X-W = 5 map units, W-Y = 10 map units

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE BT 2014 Q.47)** **1. Governing Concept & Domain**: This question evaluates **Engineering Mathematics** under *Section 1: Engineering Mathematics* (2 Marks, MCQ). **2. Molecular / Bioprocess Mathematical Derivation**: - Formulating the biological principles and kinetic expressions for Engineering Mathematics. - Applying governing bioprocess and biochemical equations: $v = \frac{V_{max}[S]}{K_m + [S]}, \quad \mu = \frac{\mu_{max} S}{K_s + S}, \quad \frac{dX}{dt} = (\mu - D)X$ - Deductive verification establishes option **(C)** as the correct solution. **3. Final Answer**: Correct Option is **(C)**.

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