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Question

If the coefficient of (2r+4)th term and (r2)th term in the expansion of (1+x)18 are equal then r

A
9
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B
4
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C
6
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D
3
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Solution

The correct option is C 6
In the expansion of (1+x)18
Tr+1=18Cr118rxr
T2r+4=18C2r+31182r3x2r+3
and Tr2=18Cr3118r+3xr3
T2r+4=Tr2
i.e.18C2r+3=18Cr3
18!(182r3)!(2r+3)!=18!(18r+3)!(r3)!
(182r3)!(2r+3)!=(18r+3)!(r3)!
(152r)!(2r+3)!=(21r)!(r3)!
Now, Posibilities are 152r=21rr=6
But we know r is a an integer such that r ϵ [0,18]
Now, 152r=r33r=18r=6
Checking with 2r+3=21r3r=18r=6

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