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Question

The term independent ofx in the expansion of (1+x+2x3)(3x22−13x)9 is

A
1354
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B
1554
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C
1754
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D
1954
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Solution

The correct option is C 1754
Given, (1+x+2x3)(3x2213)9
=[(3x2213x)9]+x(3x2213x)9+[2x3(3x2213x)9]
Therefore for (3x2213)9
Tr+1=(1)r9Cr392r2r9x183r
Therefore only terms indicated by the square bracket have independent term because the term not having a square bracket has an independent term for r=193 which is not possible.
Therefore, the independent terms are T7 in first term and T8 in last term.
Therefore sum of the coefficients of the independent terms is
=9C6332329C73522
=8427(8)2(36)243(4)
=1754

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