JEE Main 2015 · 10 Apr · Shift 1, Mathematics question 71

$\dfrac{dx}{dt}=2t\cos t$ and $\dfrac{dy}{dt}=2t\sin t$, so the tangent slope is $\tan t$ and the normal is $x\cos t+y\sin t=p$. At the point,
$$x\cos t+y\sin t=2\cos^2t+2t\sin t\cos t+2\sin^2t-2t\sin t\cos t=2.$$
The distance is 2.