If the 4th term in the expansion of 2+38x10 has the maximum numerical value, then the range of values of x is

Since T4   is the numerically greatest term in the expansion of  2101+3x1610 ∴T4T3≥1andT4T5≥1 or,T4T3≥1andT5T4≤1 Now,Tr+1Tr=n−r+1r⋅xTaking r = 3 and r = 4 and replacing x by 3x/16 x and n by 10, in the above two, we get11−33⋅3x16≥1and 11−44⋅3x16≤1or, |x|≥2 and |x|≤6421If x is positive, then | x | = x ∴x≥2 and x≤6421 ∴2≤x≤6421----1If x is negative, then | x | = – x∴−x≥2and−x≤6421or,  x≤−2 and x≥−6421∴−6421≤x≤−2