Question

${}^{10}{C}_1$ + ${}^{10}{C}_3$ + ${}^{10}{C}_5$ + ${}^{10}{C}_7$ + ${}^{10}{C}_9$ =

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is 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, ${}^{10}{C}_1$ + ${}^{10}{C}_3$ + ${}^{10}{C}_5$ + .........+ ${}^{10}{C}_9$ = $2^{10-1}$ = $2^9$