If the co-efficient of x 7 and x 8 in the expansion of 2 + x 3 n are equal, then the value of n is equal to :

We have, the co-efficient of x 7 and x 8 in the expansion of 2 + x 3 n are equal. Therefore, C 7 n 2 n - 7 1 3 7 = C 8 n 2 n - 8 1 3 8 ⇒ n - 7 = 48 ⇒ n = 55 .

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Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremGeneralEasy2 minPYQ_2021

MathematicsEasynumerical

If the co-efficient of $x^{7}$ and $x^{8}$ in the expansion of ${(2 + \frac{x}{3})}^{n}$ are equal, then the value of $n$ is equal to :

Answer:

55.00

Solution:

We have, the co-efficient of $x^{7}$ and $x^{8}$ in the expansion of ${(2 + \frac{x}{3})}^{n}$ are equal.

Therefore, ${}^{n}C_{7} 2^{n - 7} \frac{1}{3^{7}} = {}^{n}C_{8} 2^{n - 8} \frac{1}{3^{8}}$

$\Rightarrow n - 7 = 48$

$\Rightarrow n = 55 .$

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:General

⏱ 2mℹ️ Source: PYQ_2021

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