^ 10 C_1 + ^ 10 C_3 + ^ 10 C_5 + ^ 10 C_7 + ^ 10 C_9 = - Vidyadip

MCQ

$^{10}{C_1}{ + ^{10}}{C_3}{ + ^{10}}{C_5}{ + ^{10}}{C_7}{ + ^{10}}{C_9} = $

✓
${2^9}$
B
${2^{10}}$
C
${2^{10}} - 1$
D
None of these

✓

Answer

Correct option: A.

${2^9}$

a
(a) We know that

${2^{n - 1}} = {\,^n}{C_0} + {\,^n}{C_2} + {\,^n}{C_4} + .... = {\,^n}{C_1} + {\,^n}{C_3} + {\,^n}{C_5} + .....$

So, $^{10}{C_1} + {\,^{10}}{C_3} + {\,^{10}}{C_5} + ..... + {\,^{10}}{C_9} = {2^{10 - 1}} = {2^9}$

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