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7.Binomial Theorem
hard
माना $\sum_{\mathrm{r}=0}^{2023} \mathrm{r}^2{ }^{2023} \mathrm{C}_{\mathrm{r}}=2023 \times \alpha \times 2^{2022}$ है। तो $\alpha$ का मान है___________.
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