If the co-efficient of x^7 and x^8 in the expansion of 2+x3^n are equal, then the value of n is equal to :

Correct answer: 55. We have, the co-efficient of x^7 and x^8 in the expansion of 2+x3^n are equal. Therefore, C7n2^(n-7)13^7=C8n2^(n-8)13^8 ⇒n-7=48 ⇒n=55.

Q57 / 90 · JEE Main 2021 (25 Jul Shift 2) · Mathematics

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 :

Correct answer: 55

Solution

We have, the co-efficient of

x^{7}

and

x^{8}

in the expansion of

{(2 + \frac{x}{3})}^{n}

are equal.

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

$\Rightarrow n - 7 = 48$

$\Rightarrow n = 55 .$

Hence, the correct answer is 55.

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If the co-efficient of x7 and x8 in the expansion of 2+x3n are equal, then the value of n is equal to :

Solution

Relevant Questions

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 :