Which of the following is correct about Hardy Weinberg's principle ?

Options

A. `p^2` is the number of pure homozygous dominant individuals in the population , `q^2` is the number of pure homozygous recessive individuals in the population.
B. `p^2` is the number of pure homozygous dominant recessive individuals in the population , `q^2` is the number of pure homozygous dominant individuals in the population and 2pq is the number of heterozygous individuals in the population.
C. `p^2` is the proportion of pure homozygous dominant individuals in the population , `q^2` is the proportion of pure homozygous recessive individuals in the population and 2pq is the proportion of heterozygous individuals in the population.
D. `p^2` is the proportion of pure homozygous recessive individuals in the population , `q^2` is the proportion of pure homozygous dominant individuals in the population and 2pq is the proportion of heterozygous individuals in the population.

Answer

To solve the question regarding the Hardy-Weinberg principle, we will analyze each option provided and determine which one correctly describes the principle.

### Step-by-Step Solution:

1. **Understanding the Hardy-Weinberg Principle**:
- The Hardy-Weinberg principle states that in a large, randomly mating population with no evolutionary influences (such as mutation, migration, or selection), the allele and genotype frequencies will remain constant from generation to generation.
- The principle is mathematically represented as:
\[ p^2 + 2pq + q^2 = 1 \]
where:
- \( p^2 \) = frequency of homozygous dominant individuals (AA)
- \( q^2 \) = frequency of homozygous recessive individuals (aa)
- \( 2pq \) = frequency of heterozygous individuals (Aa)

2. **Analyzing the Options**:
- **Option 1**: "p square is number of pure homozygous dominant and q square is number of pure homozygous recessive individuals in the population."
- This is partially correct as it correctly identifies \( p^2 \) and \( q^2 \), but it does not mention \( 2pq \), which is crucial. So, this option is **incorrect**.

- **Option 2**: "p square is the number of pure homozygous dominant recessive individuals and q square is number of pure homozygous dominant in individuals."
- This option is incorrect as it misstates the definitions of \( p^2 \) and \( q^2 \). Thus, this option is **incorrect**.

- **Option 3**: "Q-square is proportional of pure homozygous dominant individuals in the population and Q-square is pure homozygous recessive and 2PQ is proportion of heterozygous individuals in the population."
- This option correctly identifies \( p^2 \) as homozygous dominant, \( q^2 \) as homozygous recessive, and \( 2pq \) as heterozygous individuals. Therefore, this option is **correct**.

- **Option 4**: "P-square is pure homozygous recessive, Q-square is pure homozygous dominant and 2PQ is pure heterozygous individual."
- This option incorrectly assigns the roles of \( p^2 \) and \( q^2 \). Thus, this option is **incorrect**.

3. **Conclusion**:
- After analyzing all options, we find that **Option 3** is the only correct statement regarding the Hardy-Weinberg principle.

### Final Answer:
The correct option about Hardy-Weinberg's principle is **Option 3**.