AP ICET 2017 Shift 1 Paper

Question : 131 of 200

Marks: +1, -0

If the coefficients of

x^7

and

x^8

are equal in the binomial expansion of

(3+x/2)^n

then

n=

Solution:

(3+x/2)^n=3^n(1+x/6)^n

According to question,

^{n}{C}_{7}{1}/{6^{7}}=^{n}{C}_{8}{1}/{6^{8}}⇒{n!}/{(n-7)!7!}={1}/{6}{n!}/{(n-8)!8!}

⇒{(n-7)!}/{(n-8)!}={8!×6}/{7!}⇒n-7=8×6

∴ n = 55

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