Q1: A lemniscate curve between the tangents will be transitional throughout if the polar deflection angle of its apex, is

ANS:E -

At the apex, where the transition curve joins the circular curve, the deflection/deviation angle (angle between tangent and chord) is half of the intersection angle of the circle ∆.
The polar deflection angle is 1/3 of the deviation angle.
So, 1/2 * 1/3 * ∆ = ∆/6.