2025 IGCSE Additional Mathematics May/June 0606/23 Q7

Find the term independent of \(x\) in the expansion of \(\left(x^2-\dfrac3{x^4}\right)^{15}\).[2]

In the expansion of \((1+ax)^9\) the coefficient of \(x^3\) is \(7\) times the coefficient of \(x^2\).

Given that \(a\) is a positive constant, find the value of \(a\).[3]