In the expansion of (1 + ax)ⁿ, the first three terms are respectively 1, 12x and 64x². What is n equal to?

In the expansion of (1 + x)^p (1 + x)^q, if the coefficient of x³ is 35, then what is the value of (p + q)? 

What is the remainder when 7ⁿ - 6n is divided by 36 for n = 100?

Direction : Consider the following for the items that follow :  

Let (8 + 3√7) ²⁰  = U + V and (8 - 3√7) ²⁰  = W, where U is an integer and 0 < V < 1.