The correct option is A [−6421,−2] ∪ [2,6421]
∵T4 is the numerically greatest term in the expansion of (2+ 38x)10
∴∣∣∣T4T3∣∣∣≥1 and ∣∣∣T5T4∣∣∣≤1
∣∣
∣
∣
∣
∣∣10C327(38x)310C228(38x)2∣∣
∣
∣
∣
∣∣≥1
and ∣∣
∣
∣
∣
∣∣10C426(38x)410C327(38x)3∣∣
∣
∣
∣
∣∣≤1
∣∣∣11−33⋅3x16∣∣∣≥1 and ∣∣∣11−44⋅3x16∣∣∣≤1
⇒|x|≥2 and |x|≤6421
⇒2≤|x|≤(6421)
⇒2≤x≤6421 or−6421≤x≤−2