Subtopic: Discrete & Continuous Probability Distributions
Question Statement:
A double reciprocal Lineweaver-Burk plot of an uninhibited enzyme catalyzed reaction has a y-intercept of 0.2 (µmol/min)^-1 and an x-intercept of -0.5 mM^-1. The value of Vmax in µmol/min is ________.
Official Answer Key:
25 to 25
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2023 Q.30)**
**1. Governing Concept & Definition**:
- **Topic**: Human Genetics & X-Linked Recessive Inheritance
- Let $X^D$ denote the normal allele and $X^d$ denote the recessive allele causing Fabry disease.
- Phenotypically normal father: Genotype $X^D Y$
- Carrier mother: Genotype $X^D X^d$
**2. Detailed Step-by-Step Calculation**:
- **Parental Cross**:
$X^D Y \times X^D X^d$
- **Possible Offspring Genotypes & Probabilities**:
- $X^D X^D$ (Normal female): $25\%$ ($1/4$)
- $X^D X^d$ (Carrier female): $25\%$ ($1/4$)
- $X^D Y$ (Normal male): $25\%$ ($1/4$)
- $X^d Y$ (Affected male with Fabry disease): $25\%$ ($1/4$)
- **Probability of having a son with Fabry disease**:
- Across all children born to this couple, the probability that a child is both a son and affected ($X^d Y$) is:
$P(\text{affected son}) = \frac{1}{4} = 0.25 = 25\%$
**3. Final Answer**:
- **Calculated Value**: **25%**
- **Official GATE Accepted Range**: **25 to 25**
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