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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