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If m, n, r, in N then .^(m)C(0).^(n)C(r)...

If `m, n, r, in N` then `.^(m)C_(0).^(n)C_(r) + .^(m)C_(1).^(n)C_(r-1)+"…….."+.^(m)C_(r).^(n)C_(0)`
`=` coefficient of `x^(r)` in `(1+x)^(m)(1+x)^(n)`
`=` coefficient of `x^(f)` in `(1+x)^(m+n)`
The value of `r(0 le r le 30)` for which S = `.^(20)C_(r).^(10)C_(0) + .^(20)C_(r-1).^(10)C_(1) + ........ + .^(20)C_(0).^(10)C_(r)` is minimum can not be

A

`0`

B

`1`

C

`30`

D

`15`

Text Solution

Verified by Experts

The correct Answer is:
B, D
`S = .^(30)C_(r)`, is least at `r = 0` and `r = 30`
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