If sum of the coefficient of the first, secon | vedclass

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Question

It is given $^m{C_0} + {\,^m}{C_1} + {\,^m}{C_2} = 46$

$\Rightarrow 2 m+m(m-1)=90$

$\Rightarrow m^{2}+m-90=0$

$\Rightarrow m=9$ as $m>0$

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$84$

Vedclass · Answer

It is given $^m{C_0} + {\,^m}{C_1} + {\,^m}{C_2} = 46$

$\Rightarrow 2 m+m(m-1)=90$

$\Rightarrow m^{2}+m-90=0$

$\Rightarrow m=9$ as $m>0$

Now $(\mathrm{r}+1)^{	ext {th }}$ term of $\left(\mathrm{x}^{2}+\frac{1}{\mathrm{x}}ight)^{\mathrm{m}}$ is

$ = {\,^m}{C_r}{\left( {{x^2}} ight)^{m - r}}{\left( {\frac{1}{x}} ight)^r}$

For this to be independent of $x$

$2 m-3 r=0 \Rightarrow r=6$

If sum of the coefficient of the first, second and third terms of the expansion of ${\left( {{x^2} + \frac{1}{x}} \right)^m}$ is $46$, then the coefficient of the term that doesnot contain $x$ is :-

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