For natural numbers $m,n$ ,if ${\left( {1 - y} \right)^m}{\left( {1 + y} \right)^n} = 1 + {a_1}y + {a_2}{y^2} + \ldots \;$ and $a_1= a_2=10,$ then $(m,n)$ =______. 

  • [AIEEE 2006]
  • A

    $(20,45)$

  • B

    $(35,20)$

  • C

    $(45,35)$

  • D

    $(35,45)$

Similar Questions

$(2n + 1) (2n + 3) (2n + 5) ....... (4n - 1)$ is equal to :

$\left( {\begin{array}{*{20}{c}}n\\0\end{array}} \right) + 2\,\left( {\begin{array}{*{20}{c}}n\\1\end{array}} \right) + {2^2}\left( {\begin{array}{*{20}{c}}n\\2\end{array}} \right) + ..... + {2^n}\left( {\begin{array}{*{20}{c}}n\\n\end{array}} \right)$ is equal to

${n^n}{\left( {\frac{{n + 1}}{2}} \right)^{2n}}$ is

Let $\left(2 x ^{2}+3 x +4\right)^{10}=\sum \limits_{ r =0}^{20} a _{ r } x ^{ r } \cdot$ Then $\frac{ a _{7}}{ a _{13}}$ is equal to

  • [JEE MAIN 2020]

The sum of coefficients in the expansion of ${(1 + x + {x^2})^n}$ is