Biomolecules, enzyme kinetics

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2019 Q.29)** **1. Governing Concept & Definition**: - **Topic**: Bioinformatics & Phylogenetic Tree Topologies - For $n$ distinct taxa/species, the number of distinct rooted bifurcating phylogenetic trees ($N_R$) is given by: $N_R = (2n - 3)!! = (2n - 3) \times (2n - 5) \times \dots \times 3 \times 1$ **2. Detailed Step-by-Step Calculation**: - **Given**: - Number of species $n = 3$ - **Formula Evaluation**: $N_R = (2(3) - 3)!! = (6 - 3)!! = 3!! = 3$ - The 3 rooted topologies correspond to: 1. $((A, B), C)$ 2. $((A, C), B)$ 3. $((B, C), A)$ **3. Final Answer**: - **Calculated Value**: **3** - **Official GATE Accepted Range**: **3 to 3**