In the diagram, \(OP=2\mathbf a\), \(SR=5\mathbf a\), \(OS=3\mathbf b\) and \(QR=\mathbf b\).

The point \(X\) lies on \(PS\) and on \(OQ\). It is given that \(PX=\lambda PS\) and \(OX=\mu OQ\).

(a) Express \(\overrightarrow{OX}\) in terms of \(\lambda\), \(\mathbf a\) and \(\mathbf b\).

(b) Express \(\overrightarrow{OQ}\) in terms of \(\mathbf a\) and \(\mathbf b\).

(c) Find the values of \(\lambda\) and \(\mu\).

(d) Find \(OX:OQ\).

(e) Find \(PX:XS\).