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The coefficient of x^r[0lt=rlt=(n-1)] in...

The coefficient of `x^r[0lt=rlt=(n-1)]` in lthe expansion of `(x+3)^(n-1)+(x+3)^(n-2)(x+2)+(x+3)^(n-3)(x+2)^2++(x+2)^(n-1)` is `^n C_r(3^r-2^n)` b. `^n C_r(3^(n-r)-2^(n-r))` c. `^n C_r(3^r+2^(n-r))` d. none of these

A

`3^(n-r)-2^(n-r)`

B

`""^(n)C_(r)(3^(r)-2^(r))`

C

`""^(n)C_(r)(2^(n-r)-2^(n-r))`

D

none of these

Text Solution

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The correct Answer is:
C
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