Correct option: (a) ap = aq
Explanation:
Tr+1 = ncr an–r br
given (x + 1)p+q
∴ Tr+1 = p+qcr ∙ xp+q–r ∙ (1)r
Tr+1 = (p+q)cr ∙ x(p+q–r) (1)
given: coefficient of xr = ar
First to find coefficient of xp.
we will put q = r
∴ T1 = (p+q)cr ∙ x(p) ------ from (1)
∴ coefficient of xp = p+qcr
∴ ap = p+qcr (2)
similarly coefficient of xq is obtained by putting p = r
∴ from (1)
T2 = q+pcr xq
∴ coefficient of xq = q+pcr
i.e. aq = q+pcr (3)
from (2) & (3)
ap = q+pcr, aq = p+qcr
∴
ap = aq