Let the coefficient of three consecutive terms \({T}_{r},{T}_{r+1},&{T}_{r+2}\)in the binomial expansion of \({(a+b)}^{1…

Let the coefficient of three consecutive terms \({T}_{r},{T}_{r+1},&{T}_{r+2}\)in the binomial expansion of \({(a+b)}^{12}\) be in a A.P. and let p be the no. of all possible values of r, let q be the sum of all rational term in the binomial expansion \({(\sqrt[4]{3}+\sqrt[3]{4})}^{12}\). then p+q is equal to: