A child with blood group A has father with blood group B and the mother with blood group AB. Choose the option that gives the correct genotypes of father, mother, and the child:

Blood group inheritance follows Mendelian genetics. The genotypes are determined by the alleles inherited from the parents:
IA i (A allele and O allele).IB i (B allele and O allele).IA IB (both A and B alleles are expressed).Now, let's analyze the parental blood groups and their possible offspring:
IB i.IA IB.IA allele. Therefore, the child’s genotype is IA i, receiving IA from the mother and i from the father.Thus, the genotypes of the father, mother, and child are:
IB iIA IBIA iTherefore, the correct answer is Option (A).
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).