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Question

Find the coefficient of x4 in the expansion of (2−x+3x2)6

A
3661
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B
1830
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C
3300
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D
none of the above
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Solution

The correct option is D none of the above
We want the coefficient of x4 in (2x01x+3x2)6 will be in the case (x0)3(x1)1(x2)2 , (x0)2(x1)4(x2)0 and (x0)4(x1)0(x2)2
Coefficient of x4 in:
(x0)3(x1)1(x2)2=6!(2)3(1)1(3)23!1!2!=4320
(x0)2(x1)4(x2)0=6!(2)2(1)4(3)02!4!0!=60
(x0)4(x1)0(x2)2=6!(2)4(1)0(3)24!0!2!=2160
So, total will be 2160+604320=2100
i.e., none of the above.

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