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

If A and B are coefficients of $x^r$ and $x^{n-r}$ respectively in the expansion of $(1+x)^n$ then

$\begin{array}{1 1}(A)\;A=B\\(B)\;A\neq B\\(C)\;A=\lambda B\text{ for some }\lambda\\(D)\;\text{None of these}\end{array} $

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A)
Toolbox:
  • Coefficient of $x^k$ in $(1+x)^n=nC_k$
$A$=Coefficient of $x^r=nC_r$
$B$=Coefficient of $x^{n-r}=nC_{n-r}=nC_r$
$\therefore A=B$
Hence (A) is the correct answer.
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