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Questions  >>  CBSE XI  >>  Math  >>  Binomial Theorem
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Q)

True or False :If the expression of $(x-\large\frac{1}{x^2})^{2n}$ contains a term independent of $x$,then $n$ is a multiple of $2$

$\begin{array}{1 1}(A)\;\text{True}\\(B)\;\text{False}\end{array} $

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A)
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  • $T_{r+1}=nC_ra^{n-r}b^r$
$(x-\large\frac{1}{x^2})^{2n}$
$\Rightarrow 2nC_r (x)^{2n-r}.(\large\frac{1}{x^2})^r$
$\Rightarrow 2nC_r (x)^{2n-r}.\large\frac{1}{x^{2r}}$
$\Rightarrow 2nC_r (x)^{2n-r-2r}$
$\Rightarrow 2n-3r=0$
$2n=3r$
$n=\large\frac{3r}{2}$
Hence n is multiple of 3.
Hence the given statement is False.
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