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in Mathematics by (71.2k points)

Co-efficient of xr is denoted by ar in expansion of (x+1)p+q then

(a) ap = aq 

(b) ap = -aq 

(c) ap aq = +1 

(d) None

1 Answer

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Best answer

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.eaq = q+pcr           (3)

from (2) & (3)

ap = q+pcraq = p+qcr 

∴ 

ap = aq

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