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Question

Find the term independent of x in (2+3x4x2)(x+1x)10

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Solution

Given, (x+1x)10

We know that general term is tr+1=nCrXnr.ar

Where n= 10 , X=x, a=1x

Hence,

tr+1=10Crx10r.(1x)r

tr+1=10Crx10r.1xr

=10Crx10rr

=10Crx102r

For independent term of x

x102r=x0

By compare of power of x we get

10-2r=0

r=5

Hence,

t5+1=10C5x102×r

t6=10C5x0

t6=10C5

6th term is independent of x , which is 10C6


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