If the coefficients of x^4, x^5 and x^6 in th | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$ 	ext { Coeff. of } x^4={ }^n C_4 $

$ 	ext { Coeff. of } x^5={ }^n C_5 $

$ 	ext { Coeff. of } x^6={ }^n C_6 $

$ { }^n C_4,{ }^n C_5,{ }^n

Vedclass · Accepted Answer

$14$

Vedclass · Answer

$ 	ext { Coeff. of } x^4={ }^n C_4 $

$ 	ext { Coeff. of } x^5={ }^n C_5 $

$ 	ext { Coeff. of } x^6={ }^n C_6 $

$ { }^n C_4,{ }^n C_5,{ }^n C_6 \ldots . A P $

$ 2 . C_5={ }^n C_4+{ }^n C_6 $

$ 2=\frac{{ }^n C_4}{{ }^n C_5}+\frac{{ }^n C_6}{{ }^n C_5} \quad\left\{\frac{{ }^n C_r}{{ }^n C_r}=\frac{n-r+1}{r}ight\} $

$ 2=\frac{5}{n-4}+\frac{n-5}{6} $

$ 12(n-4)=30+n^2-9 n+20 $

$ n^2-21 n+98=0 $

$ (n-14)(n-7)=0 $

$ n_{\max }=14 \quad n_{\min }=7$

If the coefficients of $x^4, x^5$ and $x^6$ in the expansion of $(1+x)^n$ are in the arithmetic progression, then the maximum value of $n$ is :

Similar Questions

The coefficient of $x^4$ in ${\left[ {\frac{x}{2}\,\, - \,\,\frac{3}{{{x^2}}}} \right]^{10}}$ is :

If the ${(r + 1)^{th}}$ term in the expansion of ${\left( {\sqrt[3]{{\frac{a}{{\sqrt b }}}} + \sqrt {\frac{b}{{\sqrt[3]{a}}}} } \right)^{21}}$ has the same power of $a$ and $b$, then the value of $r$ is

If $7^{th}$ term from beginning in the binomial expansion ${\left( {\frac{3}{{{{\left( {84} \right)}^{\frac{1}{3}}}}} + \sqrt 3 \ln \,x} \right)^9},\,x > 0$ is equal to $729$ , then possible value of $x$ is

The greatest coefficient in the expansion of ${(1 + x)^{2n + 2}}$ is

Number of rational terms in the expansion of ${\left( {{3^{\frac{1}{8}}} + {5^{\frac{1}{3}}}} \right)^{400}}$ is