Which of the following give the correct representation of Hardy-Weinberg equation?

Options

A. `p+q+2pq=1`
B. `(p+q)^2=1`
C. `p^2+2pq+q^2=1`
D. Both(2) and (3)

Answer

To solve the question regarding the correct representation of the Hardy-Weinberg equation, we can follow these steps:

### Step 1: Understand the Hardy-Weinberg Principle
The Hardy-Weinberg principle states that the genetic variation in a population will remain constant from one generation to the next in the absence of disturbing factors. This principle is mathematically represented through specific equations.

### Step 2: Identify the Components of the Hardy-Weinberg Equation
The Hardy-Weinberg equation involves two alleles, typically designated as:
- **p**: frequency of the dominant allele
- **q**: frequency of the recessive allele

According to the Hardy-Weinberg principle, the sum of the frequencies of the alleles must equal 1:
\[ p + q = 1 \]

### Step 3: Write the Expanded Form of the Hardy-Weinberg Equation
The genotypic frequencies can be expressed as:
\[ p^2 + 2pq + q^2 = 1 \]
Where:
- \( p^2 \): frequency of homozygous dominant individuals
- \( 2pq \): frequency of heterozygous individuals
- \( q^2 \): frequency of homozygous recessive individuals

### Step 4: Analyze the Given Options
Now, let's analyze the options provided in the question:
1. **p + q + 2pq = 1**: This is incorrect because it does not represent the Hardy-Weinberg equation.
2. **(p + q)^2 = 1**: This is correct since squaring the sum of the frequencies gives us the expanded form.
3. **p^2 + 2pq + q^2 = 1**: This is also correct as it is the expanded form of the Hardy-Weinberg equation.
4. **Both second and third**: Since both the second and third options are correct, this option is also correct.

### Step 5: Conclusion
The correct representation of the Hardy-Weinberg equation is given by options 2 and 3. Therefore, the answer is:
**Both second and third.**