Suppose evolution on earth has occurred in such a way that there are 96 amino acids instead of 20. DNA has 12 different types of bases and DNA synthesis occur in the same way as today. The minimum number of bases per DNA codon would be `:`

Options

A. 12
B. 8
C. 2
D. 3

Explanation

To solve the problem of determining the minimum number of bases per DNA codon needed to code for 96 amino acids, given that there are 12 different types of DNA bases, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Current Codon Structure**:
In the current genetic code, one codon is made up of 3 bases and can code for 20 different amino acids.

2. **Identify the New Parameters**:
In this scenario, we have:
- 12 different types of DNA bases (instead of the usual 4: A, T, G, C).
- 96 different amino acids (instead of the usual 20).

3. **Determine the Formula for Codons**:
The number of different combinations of codons that can be formed with 'n' bases per codon is given by the formula:
\[ \text{Number of combinations} = (\text{Number of bases})^{n} \]
In this case, it will be:
\[ 12^n \]
where 'n' is the number of bases per codon.

4. **Set Up the Equation**:
We need to find the minimum value of 'n' such that:
\[ 12^n \geq 96 \]

5. **Calculate Values of 'n'**:
- For \( n = 1 \):
\[ 12^1 = 12 \quad (\text{not sufficient}) \]
- For \( n = 2 \):
\[ 12^2 = 144 \quad (\text{sufficient, as } 144 \geq 96) \]
- For \( n = 3 \):
\[ 12^3 = 1728 \quad (\text{more than sufficient}) \]

6. **Conclusion**:
The minimum number of bases per DNA codon required to code for 96 different amino acids is 2, since \( 12^2 = 144 \) is the smallest power of 12 that meets or exceeds 96.

### Final Answer:
The minimum number of bases per DNA codon would be **2**.

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