If (³⁰C₁)² + 2(³⁰C₂)² + 3(³⁰C₃)² +... + 30(³⁰C₃₀)² = (α 60!)/((30!)²) then α is equal to:

Binomial Theorem and Its Simple Applications: JEE Main 2023 Mathematics question

JEE Main 2023 · 24 Jan, Evening shift · Q3006

JEE Main 202324 Jan, Evening shiftMathematicsHardBinomial Theorem and Its Simple Applications131× since 2002

{({}^{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

JEE Main 202324 Jan, Evening shiftMathematicsHardBinomial Theorem and Its Simple Applications131× since 2002

{({}^{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 :