(a) (i) Given that \(\left(x^2-\dfrac1{px}\right)^8=x^{16}-4x^{13}+qx^{10}+rx^7+\cdots\), find the value of each of the constants \(p\), \(q\) and \(r\).

(ii) Explain why there is no term independent of \(x\) in the binomial expansion of \(\left(x^2-\dfrac1{px}\right)^8\).

(b) In the binomial expansion of \(\left(1-\dfrac{\sqrt{x}}2\right)^n\), where \(n\) is a positive integer, the coefficient of \(x\) is 30. Form an equation in \(n\) and hence find the value of \(n\).