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If (1+2x+3x^2)^(10)=a0+a1x+a2x^2++a(20)x...

If `(1+2x+3x^2)^(10)=a_0+a_1x+a_2x^2++a_(20)x^(20),t h e na_1` equals `10` b. `20` c. `210` d. none of these

A

10

B

20

C

210

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`a_(1)=` coefficient of `x` in `(1+2n+3x^(2))^(10)`
`=` coefficient of x in `((1+2x)+3x^(2))^(10)`
`=` coefficient of x in `(.^(10)C_(0)(1+2x)^(10) + .^(10)C_(1)(1+2x)^(9)(3x^(2))+"…..")`
`=` coefficient of x in `.^(10)C_(0)(1+2x)^(10)`
`= .^(10)C_(0)2..^(10)C_(1) = 20`
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