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Question

The coefficient of term independent of x in the expansion of(x33x2)10, is

A
53
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B
45
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C
6
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D
12
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Solution

The correct option is A 53
The (r+1)th term in the expansion of (x33x2)10 is given by
Tr+1=(1)r.10Cr(x3)10r.(3x2)r
Tr+1=(1)r10Crx55r23r5
For term to be independent of x,
55r2=0
r=2
Substituting we get
T3=(1)210C233

=10(9)2(27)
=53

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