How many of the following genotypes possibly represent normal wings in Drosophila?
(i) \( Vg^+Vg^+ \)
(ii) \( Vg^+Vg^{ni} \)
(iii) \( Vg^+Vg^{no} \)
(iv) \( Vg^+Vg^{st} \)
(v) \( Vg^+Vg \)
In Drosophila, the normal wing phenotype is determined by the presence of at least one dominant \( Vg^+ \) allele. The recessive alleles \( Vg^{ni}, Vg^{no}, Vg^{st}, Vg \), etc., cause abnormal wing development only when present in homozygous recessive combinations.
Step 1: Evaluate each genotype. \( Vg^+Vg^+ \): Both alleles are wild type, so the wings are normal.
Normal wings. \( Vg^+Vg^{ni} \): One dominant \( Vg^+ \) allele is sufficient for normal wings.
Normal wings. \( Vg^+Vg^{no} \): One dominant \( Vg^+ \) allele is sufficient for normal wings.
Normal wings. \( Vg^+Vg^{st} \): One dominant \( Vg^+ \) allele is sufficient for normal wings.
Normal wings. \( Vg^+Vg \): One dominant \( Vg^+ \) allele is sufficient for normal wings.
Normal wings. Step 2: Count the genotypes. All five genotypes contain at least one dominant \( Vg^+ \) allele and hence represent normal wings. \[ \text{Genotypes representing normal wings} = (i), (ii), (iii), (iv), (v). \] Thus, the correct answer is: \[ \mathbf{(D) \ (i), (ii), (iii), (iv), \text{and} (v)}. \]
Given, the function \( f(x) = \frac{a^x + a^{-x}}{2} \) (\( a > 2 \)), then \( f(x+y) + f(x-y) \) is equal to