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Iff(x) =.^(40)C(1).x(1-x)^(39) + 2..^(40...

If`f(x) =.^(40)C_(1).x(1-x)^(39) + 2..^(40)C_(2)x^(2)(1-x)^(38)+3..^(40)C_(3)x^(3)(1-x)^(37)+"….."+40..^(40)C_(40)x^(40)`, then the value of `f(3)` is

A

120

B

150

C

200

D

240

Text Solution

Verified by Experts

The correct Answer is:
A
`f(x)=.^(40)C_(1).x(1-x)^(39)+2..^(40)C_(2)xxx^(2)(1-x)^(38)+3..^(40)C_(3)xx x^(3)(1-x)^(37)+"...."+40..^(40)C_(40)xxx^(40)`
`T_(r)=r..^(40)C_(r).x^(r)(1-x)^(40-r)`
`= 40x..^(39)C_(r-1).x^(r-1)(1-x)^(40-r)`
`:. f(x)=40x(x+1-x)^(39)`
`= 40x`
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