Q.Do we need a banked road for a two-wheeler? Explain.

Not strictly -- a two-wheeler can turn on a flat road purely with friction, by having the RIDER lean at $\theta=\tan^{-1}(v^2/rg)$; but banking still helps by reducing the leaning angle needed and the demand on friction.

Unlike a four-wheeler, a two-wheeler rider taking an unbanked, flat turn does not simply rely on friction alone in a naive point-mass sense -- the rider must also LEAN their body (and the vehicle) towards the centre of the curve, at an angle $\theta=\tan^{-1}\left(\frac{v^2}{rg}\right)$ with the vertical (derived in Long Answer Q3). This leaning is what balances the torque due to the centrifugal (pseudo) force acting effectively at the rider's centre of mass against the torque due to the ground's reaction forces at the narrow contact patch, preventing the rider from toppling outward -- so, strictly speaking, a two-wheeler CAN take a flat, unbanked turn safely, purely through friction plus the rider's own leaning, without needing the road itself to be banked. That said, banking is still genuinely useful for a two-wheeler too: it reduces both the angle the rider needs to lean at any given speed and the demand placed on friction, making the turn safer and less strenuous, particularly at higher speeds or when the road surface is not perfectly reliable. So banking is not strictly NECESSARY for a two-wheeler the way it functionally is for stability at high speed on a four-wheeler, but it remains a genuine safety improvement.

Recognise that a two-wheeler's stability against toppling comes from the rider's own leaning angle (a torque-balance condition), not purely from the road's banking, and compare this to how a four-wheeler instead relies on its wide wheelbase.

Assuming a two-wheeler needs banking in exactly the same way a car does, without accounting for the rider's ability to actively lean and thereby balance the toppling torque even on a flat road.