List of top Mathematics Questions on Directional derivatives asked in AP PGECET

A unit vector which is perpendicular to the surface of the paraboloid of revolution $z = x^2 + y^2$ at the point (1,2,5) is
The directional derivative of \( f(x,y) = x^3 + y^3 \) at \( (1, 1) \) in the direction of a unit vector which makes an angle of \( \frac{\pi}{3} \) with the x-axis is ___ .