Question

When AABBcc is crossed with AaBbCc then the ratio of hybrid for all the three genes is
A) $\dfrac{1}{8}$
B) $\dfrac{1}{4}$
C) $\dfrac{1}{{16}}$
D) $\dfrac{1}{{32}}$

Answer 1

Mendel observed that the heredity results in the discrete units of inheritance and every unique unit was independent in its actions on a single genome. The inheritance of traits depends on passing on these units.

Complete answer:
Genetic cross is a purposeful mating of two individuals leading in the combination of genetic materials in the offspring. Types of genetic cross are monohybrid cross, dihybrid cross test cross, back cross, Punnett cross which allows geneticists to predict the possible genotype and phenotypes of offspring.
In the above question the parents genotype is given AABBcc $\times$ AaBbCc. The cross is made between them after the cross the three genes formed will be AaBbCc heterozygous regarding three genes. Hence the genome of the spring should be AaBbCc regarding three genes.
Parent Generation$\to$ AABBcc $\times$ AaBbCc
All the genes assort independently. Therefore, after taking single genes one by one to know the frequency then,

1. Gene A-

Parents	AA	Aa
A(Homozygous)	Aa(heterozygous)
Offspring	AA	Aa

So the offspring has a combination of homozygous and heterozygous. Hence the offspring genotype is Aa and AA which is heterozygous and homozygous so that frequency will be $\dfrac{1}{2}$and $\dfrac{1}{2}$.
Hence, the frequency of Aa is $\dfrac{1}{2}$.

2. Gene B-

Parents	BB	Bb
B(Homozygous)	Bb(heterozygous)
Offspring	BB	Bb

So the offspring has a combination of homozygous and heterozygous. Hence the offspring genotype is Bb and BB which is heterozygous and homozygous so that frequency will be $\dfrac{1}{2}$and $\dfrac{1}{2}$.
Hence, the frequency of Bb is $\dfrac{1}{2}$.

3. Gene C-

Parents	cc	Cc
c(Homozygous)	Cc(heterozygous)
Offspring	cc	Cc

So the offspring has a combination of homozygous and heterozygous. Hence the offspring genotype is cc and Cc which is heterozygous and homozygous so that frequency will be $\dfrac{1}{2}$and $\dfrac{1}{2}$.
Hence, the frequency of Cc is $\dfrac{1}{2}$.

Parent generation $\to$ AABBcc $\times$ AaBbCc
Gametes are of different types $\to$ ABC, Abc, ABc, AbC, abc, aBC, aBc, abC
AABBCc, AABbcc, AABBcc, AABbCc, AaBbcc, AaBBCc, AaBBcc, AaBbCc.
The ratio of hybrid for all three genes for AaBbCc is $\dfrac{1}{8}$.

Hence, the correct answer is option (A).

Note: The genetic cross is the purposeful mating of two individuals resulting in the combination of genetic material in the offspring. The two of them during the mating will result in the production of a diploid offspring with two homologous copies of each chromosome.