Suppose Σ limits_{ r =0}^{2023} r ^{20023} C _{ r }=2023 × α × 2^{2022} . Then value of α is ..

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7.Binomial Theorem

hard

Suppose $\sum \limits_{ r =0}^{2023} r ^{20023} C _{ r }=2023 \times \alpha \times 2^{2022}$. Then the value of $\alpha$ is $............$

A

$1011$

B

$1013$

C

$1012$

D

$1014$

(JEE MAIN-2023)

Solution

using result

$\sum \limits_{r=0}^n r^{2 n} C_r=n(n+1) \cdot 2^{n-2}$

$=2023 \times \alpha \times 2^{2022} \text { So, }$

$\Rightarrow \alpha=1012$

Standard 11

Mathematics

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