અભિવ્યક્તિ $(5+x)^{500}+x(5+x)^{499}+x^{2}(5+x)^{498}+\ldots . x^{500}$ $x>0$ માં  $x ^{101}$ નો સહુગુણક ......... છે.

  • [JEE MAIN 2022]
  • A

    ${ }^{501} C _{101}(5)^{399}$

  • B

    ${ }^{501} C _{101}(5)^{400}$

  • C

    ${ }^{501} C _{100}(5)^{400}$

  • D

    ${ }^{500} C _{101}(5)^{399}$

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  • [JEE MAIN 2019]

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$\left( \begin{array}{l}30\\0\end{array} \right)\,\left( \begin{array}{l}30\\10\end{array} \right) - \left( \begin{array}{l}30\\1\end{array} \right)\,\left( \begin{array}{l}30\\11\end{array} \right)$ + $\left( \begin{array}{l}30\\2\end{array} \right)\,\left( \begin{array}{l}30\\12\end{array} \right) + ....... + \left( \begin{array}{l}30\\20\end{array} \right)\,\left( \begin{array}{l}30\\30\end{array} \right) = .$ . ..

  • [IIT 2005]

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  • [JEE MAIN 2021]

$(x-1) (x- 2) (x-3)...............(x-10)$ ના વિસ્તરણમાં $x^8$ નો સહગુણક મેળવો