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Home  >>  CBSE XI  >>  Math  >>  Binomial Theorem
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$49^n+16n-1$ is divisible by

$\begin{array}{1 1}(A)\;3\\(B)\;19\\(C)\;64\\(D)\;29\end{array} $

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1 Answer

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Toolbox:
  • $(a+b)^n=nC_0a^nb^1+nC_1a^{n-1}b^2.........nC_n a^0b^n$
$(49)^n+16n-1$
$\Rightarrow (1+48)^n+16n-1$
$\Rightarrow 1+48n+.....48^n+16n-1$
$\Rightarrow 64n+nC_2(48)^2+nC_3(48)^3+......+(48)^n$
$\Rightarrow 64(n+nC_2(6)^2+nC_3(6)^348+......+(6)^n8^{n-2}$
$\therefore 49^n+16n-1$ is divisible by 64
Hence (C) is the correct answer.
answered Jun 26, 2014 by sreemathi.v
 

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