If the (r+1)th term in the expansion of a1/3b1/6+b1/2a1/621has equal exponents of both a and b, then value of r is

We haveTr+1=21Cra1/3b1/621−rb1/2a1/6r         =21Cra7−r/3b7/2−r/6⋅br/2ar/6=21Cra7−r/2b2/3−7/2Since exponents of a and b in the (r+1)th term are equal.    7−r2=2r3−72⇒212=76r⇒r=9.