If {}^{21}{C₁} + 3.{}^{21}{C₃} + 5.{}^{21}{C₅} + ......19{}^{21}{C_{19}} + 21.{}^{21}{C_{21}}

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7.Binomial Theorem

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If ${}^{21}{C_1} + 3.{}^{21}{C_3} + 5.{}^{21}{C_5} + ......19{}^{21}{C_{19}} + 21.{}^{21}{C_{21}} = k$ Then number of prime factors of $k$ is

A

$1$

B

$2$

C

$3$

D

$4$

Solution

$\mathrm{k}=\frac{21\left((1+1)^{20}+(1-1)^{20}\right)}{2}=21 \times 2^{19}=3 \times 7 \times 2^{19}$

Standard 11

Mathematics

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