Question

Match List-I with List-II

List-I (Particulars) & List-II (Formula used)
(A) Number of individuals in a perfect $F_2$ population & (III) $4^n$
(B) Number of perfect homozygous individuals in an $F_2$ population & (I) $2^n$
(C) Number of different heterozygous genotypes in an $F_2$ population & (IV) $3^n - 2^n$
(D) Number of different kinds of genotypes in an $F_2$ population & (II) $3^n$

• (A) - (I), (B) - (III), (C) - (II), (D) - (IV)
• (A) - (IV), (B) - (I), (C) - (III), (D) - (II)
• (A) - (III), (B) - (I), (C) - (IV), (D) - (II)
• (A) - (III), (B) - (IV), (C) - (I), (D) - (II)

Hint:

For $n$ segregating genes:
- Number of $F_2$ genotypes = $3^n$
- Number of homozygous genotypes = $2^n$
- Number of heterozygous genotypes = Total $-$ Homozygous = $3^n - 2^n$
- Minimum $F_2$ population size = $4^n$

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Mendelian genetics allows us to predict the genotypic and phenotypic ratios in the segregating $F_2$ generation of a cross involving $n$ independently assorting gene loci.

Step 2: Detailed Explanation:
Let us analyze the mathematical formulas for a cross with $n$ segregating heterozygous genes:
- (A) Number of individuals in a perfect $F_2$ population $\rightarrow$ (III) $4^n$:
Each segregating gene locus has 4 possible combinations of gametes in the $F_2$ generation.
For $n$ loci, the total number of individuals required to represent a perfect $F_2$ population is $4^n$.
- (B) Number of perfect homozygous individuals in an $F_2$ population $\rightarrow$ (I) $2^n$:
At each locus, there are 2 homozygous genotypes ($AA$ and $aa$).
For $n$ loci, the number of completely homozygous genotypes is $2^n$.
- (D) Number of different kinds of genotypes in an $F_2$ population $\rightarrow$ (II) $3^n$:
At each locus, there are 3 possible genotypes ($AA$, $Aa$, and $aa$).
For $n$ loci, the total number of different genotypes possible is $3^n$.
- (C) Number of different heterozygous genotypes in an $F_2$ population $\rightarrow$ (IV) $3^n - 2^n$:
The number of heterozygous genotypes is calculated by subtracting the number of completely homozygous genotypes ($2^n$) from the total number of possible genotypes ($3^n$), yielding $3^n - 2^n$.
This results in the sequence: (A)-(III), (B)-(I), (C)-(IV), (D)-(II).

Step 3: Final Answer:
The correct matching sequence is (A) - (III), (B) - (I), (C) - (IV), (D) - (II).