In polygenic inheritance, a particular trait is controlled by 3 different genes. The given problem is of polygenic inheritance. In this, phenotypic ratio is 1:6:15:20:15:6:1 instead of 27:9:9:9:3:3:3:1 in F$ _2$ generation. In the given example, the genotype of parents is AaBbCc and AaBbCc. They will produce gametes ABC, ABc, Abc, abc, aBC, aBc, abC, AbC. The phenotypic ratio will be 1:6:15:20:`15:6:1.

Genotype AABBCC can produce only one type of gamete, i.e., ABC. The frequency for production of ABC gamete is 1.
Genotype AaBbCc can produce 8 types of gametes, i.e., ABC, Abc, ABc, AbC, abc, aBC, aBc and abC.
The frequency of production of one of these gametes is 1/8.
According to the question, a perfect heterozygous cross will occur only when abc gamete from AaBbCc parent fertilises with ABC gamete from AABBCC parent.
Thus, the frequency for this = 1/8X1 = 1/8.

A trihybrid plant YyRrTt during fertilization produces 27 types of genotypes.

It is calculated as 3ⁿ , n= number of contrasting pairs of characters/traits.

In YyRrTt, 3 contrasting pairs of characters are present. So 3³ = 27.

So, the correct option is ‘27’.

A cross is made between the two parents on the basis of 3 contrasting characters is called Trihybrid cross. Mendel conducted trihybrid cross by three characters height of the stem, form of seed, and colour of the cotyledons. In the F2 generation, he obtained, 27:9:9:9:3:3:3:1.

So, the correct option is ‘27:9:9:9:3:3:3:1’.

A plant with genotype AABbCC, is subjected to self pollination, in the F2 generation 3:1 ratio of progeny are formed, because the parent show only one pair of contrasting characters.

So, the correct option is ‘3:1’.

When a cross is made between AaBbCc with AaBbCc, in the next generation 8 types of phenotypes appear, because this cross involves 3 pairs of contrasting characters 2ⁿ, n means number of pairs of characters.

Here 3 pairs of characters are present, 2³ = 8.

So, the correct option is ‘8’.

The plant with genotype AABbcc produces only two types of namely ABc, Abc, because it shows one pair of contrasting characters.

So, the correct option is ‘Two’.

AABBCC is trihybrid homozygous organism. This organism at the time of fertilization produces only one type of gametes. They are ABC.

So, the correct option is ‘one’.

It is given that the f$ _1$ generation is having genotype AABbCC. The gametes of these parents will contain ABC and AbC alleles. On selfing of this plant, the phenotypic ratio of F$ _2$ generation will be 3:1. Similarly, the genotypic ratio of the F$ _2$ generation will be 1:2:1 where one part will be AABBCC. 2 parts will be AABbCC and 1 part will be AAbbCC.

Since one parent is homozygous AABBCC  the genotype formed will be only 1 type i.e. ABC. The other parent is heterozygous for all genes. About 1/8th or 12.5% of total offspring will be heterozygous at all three-locus.

The cross is made between AAbb to aaBB. The progeny formed shows the genotype AaBb. This progeny is crossed with aabb. The genotypes of the progeny are 4 AaBb, 4Aabb, 4aaBb, 4aabb. The genotypic ratio is 1:1:1:1.

So, the correct option is ‘1:1:1:1’.

Since pointed eyebrow (B) is dominant over smooth eyebrows (b). So, Seema can have smooth eyebrows only if her father is heterozygous for the dominant character. If her father has the genotype Bb and her mother is bb (smooth eyebrows) then her genotype will be either Bb (pointed) or bb(smooth eyebrows). If however, her father is homozygous for the trait the gamete being transferred from him will have the allele B and hence the progeny will only show the genotype Bb for pointed eyebrows. So, the correct option is 'Bb'.

The possible gametes from the given genotype AABbCC are ABC and AbC.

In a trihybrid cross, there are 32 possible combinations of alleles in the Punnett square out of which only one of the 32 combinations is recessive

A trihybrid cross is between two individuals that are heterozygous for three different traits. For example, RrYyCc x RrYyCc is a trihybrid cross where, 

A total number of types of gamete produced by an organism is 2$^n$, where n is the number of heterozygous genes present. As we know that trihybrid plant is heterozygous for three genes, these total possible gametes by it = 2$^3$ = 8. During fertilization, any of the 8 types of sperms can fuse with any of the 8 types of egg to produce 64 possible combinations of zygotes. This makes option A correct but C and D wrong. Four different types of gametes are produced by an organism who is heterozygous for two genes; 2$^2$ = 4 and resultant four gametes produce total 4 x 4 = 16 zygotic combinations. Thus, option B is wrong.

AaBbCC will produce 4 types of gametes which are as follows- ABC, AbC, aBC, abC. The number of gametes formed is decided by the number of heterozygous alleles present in the given genotype. 2^n is the formula used to find it out, where n=number of heterozygous alleles present in the genotype. Say for example, in the above genotype Aa & Bb are the 2 heterozygous alleles, so here n=2. Putting the values in the formula , we get 2^2=4. Hence 4 types of gametes are formed.

For quantitative inheritance by four genes, we have a total of 8 alleles that will determine the phenotypes of the individual. Those offspring with all 8 dominant alleles ( Let's assume it as AABBCCDD ) will show the highest additive effect. Gradually as we keep decreasing the number of dominant alleles, additive effect will become less prominent. Hence, offspring with 7,6,5,4,3,2 and 1 dominant alleles will show different phenotypes. Finally, those individuals with no dominant alleles i.e. all recessive ( aabbccdd ) will show the least additive effect of characters. If we count all of them we have a total of 09 types of phenotypes possible. 

The tetrahybrid cross of AaBbCcDd can be easily calculated by assuming their independent assortment.