If the coefficient of x7 and x8 in 2-x-3n are equal- then n is-

The correct option is B 55 Coefficient of x^7 = Coefficient of x^8 ⇒^n C _7 .2^n 7 (1/3)^7 = ^n C _8.2^n 8.( 1/3)^8 ⇒ n!/7!(n 7)! . 2 = n!/8!(n 8)!. 1/3 ⇒ ...

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Byju's Answer

Standard XI

Mathematics

Coefficients of Terms Equidistant from Beginning and End

If the coeffi...

Question

If the coefficient of $x^{7}$ and $x^{8}$ in ${(2 + \frac{x}{3})}^{n}$ are equal, then n is:

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Solution

The correct option is B
55

Coefficient of $x^{7}$ = Coefficient of $x^{8}$

⇒ $^{n} C_{7}$ . $2^{n - 7}$ ${(\frac{1}{3})}^{7}$ = $^{n} C_{8} {.2}^{n - 8} . (\frac{1}{3})^{8}$

⇒ $\frac{n!}{7! (n - 7)!}$ . 2 = $\frac{n!}{8! (n - 8)!}$ . $\frac{1}{3}$

⇒ $\frac{2}{n - 7}$ = $\frac{1}{8.3}$ ⇒ n = 55.

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If the coefficient of x7 and x8 in (2+x3)n are equal, then n is:

The correct option is B 55 Coefficient of x7 = Coefficient of x8 ⇒nC7 .2n−7 (13)7 = nC8.2n−8.(13)8 ⇒ n!7!(n−7)! . 2 = n!8!(n−8)!. 13 ⇒ 2n−7 = 18.3 ⇒ n = 55.

If the coefficient of $x^{7}$ and $x^{8}$ in ${(2 + \frac{x}{3})}^{n}$ are equal, then n is: