If the fourth term in the binomial expansion of x 1 1 + l o g 10 x + x 1 12 6 is equal to 200 , and x >…

If the fourth term in the binomial expansion of x11+log10x+x1126 is equal to 200, and x>1, then the value of x is
  1. 100
  2. 104
  3. 103
  4. 10

Solution

General term for the given binomial is
Tr+1= 6Crx11+log10x6-rx112r
Given T4=200, putting r=3
⇒T4= 6C3x11+log10x3x1123=200
⇒x11+log10x32⋅x14=10
⇒x321+log10x+14=10
⇒321+log10x+14log10x=1
⇒x=10,10-4
⇒x=10 ( as x>1)

Asked in: JEE Main 2019 (08 Apr Shift 2)

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