If … then … is equal to :

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Binomial Theorem

JEE Main 2023 · 24 Jan, Evening shift · Q3006

MathematicsHard64×since 2002Q3006

{({}^{30}{C_1})^2} + 2{({}^{30}{C_2})^2} + 3{({}^{30}{C_3})^2}\, + \,...\, + \,30{({}^{30}{C_{30}})^2} = {{\alpha 60!} \over {{{(30!)}^2}}}

then

\alpha

is equal to :

JEE Main 2023 · 24 Jan, Evening shift · Q3006

MathematicsHard64×since 2002Q3006

{({}^{30}{C_1})^2} + 2{({}^{30}{C_2})^2} + 3{({}^{30}{C_3})^2}\, + \,...\, + \,30{({}^{30}{C_{30}})^2} = {{\alpha 60!} \over {{{(30!)}^2}}}

then

\alpha

is equal to :