a
\(\begin{array}{l}
For\,vertical\,equilibrium\,on\,the\,road,\\
N\cos \theta  = mg + f\sin \theta \\
mg = N\cos \theta  - f\sin \theta \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)\\
Centripetal\,force\,for\,safe\,turning\,,\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,N\sin \theta  + f\cos \theta  = \frac{{m{v^2}}}{R}\,\,\,\,\,\,...\left( {ii} \right)\\
From\,eqns.\,\left( i \right)\,and\,\left( {ii} \right),\,we\,get\\
\,\,\,\,\,\,\,\,\,\,\,\frac{{{v^2}}}{{Rg}} = \frac{{N\sin \theta  + f\cos \theta }}{{N\cos \theta  - f\sin \theta }}
\end{array}\)

\(\begin{array}{l}
 \Rightarrow \,\frac{{{v^2}_{\max }}}{{Rg}} = \frac{{N\sin \theta  + {\mu _s}N\cos \theta }}{{N\cos \theta  - {\mu _s}N\sin \theta }}\\
\,\,\,\,\,\,{v_{\max }} = \sqrt {Rg\left( {\frac{{{\mu _s} + \tan \theta }}{{1 - {\mu _s}\tan \theta }}} \right)} 
\end{array}\)