Numerically the greatest term in the expansion of 2+3x9 when x=32, is

since(2+3x)9=291+3x29now in the expansion of 1+32x9, we have  Tr+1Tr=9−r+1r32x=10−rr94=90−9r4r ∵x=32∵ Tr+1Tt≥1⇒90−9r4r≥1⇒90≥13r⇒ r≤9013⇒r≤61213.'. Maximum value of r is 6.