Principles of Inheritance and Variation Set-3

Q1. In a large randomly mating population under Hardy–Weinberg equilibrium the frequency of the recessive phenotype ($aa$) is $0.04$. Using $p+q=1$ and $p^2+2pq+q^2=1$, what is the expected frequency of heterozygotes ($Aa$) in the population?

Q2. In a plant species flower colour is determined by two genes $A$ and $B$. Genotype $aa$ produces white flowers irrespective of the $B$ allele (recessive epistasis). For plants with at least one dominant $A$ allele, $A\_B\_$ produce purple and $A\_bb$ produce pink. If two plants of genotype $AaBb$ are selfed, what fraction of the F2 progeny will be pink?

Q3. Three genes are on the same chromosome with recombination frequencies $A\text{--}B=12\%$, $B\text{--}C=8\%$ and $A\text{--}C=20\%$. Which gene lies in the middle and what is the expected frequency of double crossovers involving both intervals in gametes from a heterozygote? (Assume no interference.)

Q4. Assertion (A): Positive interference leads to fewer observed double crossovers than expected by multiplying individual recombination frequencies. Reason (R): Interference reduces the probability of a crossover occurring near an existing crossover; the coefficient of coincidence is defined as $c=\dfrac{\text{observed double crossovers}}{\text{expected double crossovers}}$, and positive interference implies $c<1$ (interference $=1-c$).

Q5. A heterozygous plant with genotype $ABC/abc$ was testcrossed to $abc/abc$ and the progeny counts obtained were: $ABC=320,\ abc=300,\ Abc=40,\ aBC=35,\ AbC=50,\ aBc=45,\ ABc=10,\ abC=8$ (total $808$). Determine the gene order and map distances between adjacent genes (in cM, rounded to one decimal place).

Q6. In a large randomly mating population the frequency of individuals showing a recessive trait is $0.16$. Using Hardy–Weinberg equilibrium ($p+q=1,\; q^2=0.16$), what is the frequency of the dominant allele $p$?

Q7. Recombination frequencies between three linked genes were measured as $r_{AB}=0.10$, $r_{BC}=0.15$ and $r_{AC}=0.25$. Which linear gene order on the chromosome is most consistent with these values?

Q8. A woman with normal vision is known to be the daughter of a color‑blind man and marries a color‑normal man. (Thus the woman is a carrier of an X‑linked recessive allele.) If the couple has two sons and two daughters, what is the probability that exactly one son will be color‑blind and exactly one daughter will be a carrier?

Q9. Assertion (A): In a three‑point test cross the observed number of double crossovers is often lower than the expected number calculated from single crossover frequencies.
Reason (R): Interference reduces nearby crossover events; quantitatively $I = 1 - C$, where $C = \dfrac{\text{observed double crossovers}}{\text{expected double crossovers}}$ and the expected double crossovers ≈ $r_{AB}\times r_{BC}$.
Which of the following is correct?

Q10. In a three‑point test cross the observed recombination frequencies are $r_{AB}=12\%$ and $r_{BC}=9\%$, and the observed double crossover frequency is $0.8\%$. Calculate the coefficient of coincidence $C$ and the interference $I$ (round to two decimal places), where $C=\dfrac{\text{observed double crossovers}}{\text{expected double crossovers}}$ and expected double crossovers $=r_{AB}\times r_{BC}$.