Value Σ limits_{ r =0}^{22}{ }^{22} C _{ r }{ }^{23} C _{ r } is .......

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7.Binomial Theorem

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The value $\sum \limits_{ r =0}^{22}{ }^{22} C _{ r }{ }^{23} C _{ r }$ is $.......$

A

${ }^{45} C _{23}$

B

${ }^{44} C _{23}$

C

${ }^{45} C _{24}$

D

${ }^{44} C _{22}$

(JEE MAIN-2023)

Solution

$\sum \limits_{ r =0}^{22}{ }^{22} C _{ r } \cdot{ }^{23} C _{ r }=\sum \limits_{ r =0}^{22}{ }^{22} C _{ r } \cdot{ }^{23} C _{23- r }$

$={ }^{45} C _{23}$

Standard 11

Mathematics

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(JEE MAIN-2023)