If (^30C_1)^2 + 2(^30C_2)^2 + 3(^30C_3)^2 + ... + 30 (^30C_30)^2 = (α 60!)/((30!)^2) then α is equal to :

If (^30C_1)^2 + 2(^30C_2)^2 + 3(^30C_3)^2 + ... + 30… — JEE Main 2023 Mathematics PYQ

JEE Main 2023 · 24 Jan · Shift 2

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

then

\alpha

is equal to :

Show answer

Correct option: B

[JEE Main 2023 · 24 Jan · Shift 2]

Practise Binomial Theorem the way it is asked

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