5 persons entered a lift cabin in the cellar of a 7-floor building apart from cellar. If each of the independently and with equal probability can leave the cabin at any floor out of the 7 floors beginning with the first, then the probability of all the 5 persons leaving the cabin at different floors is
If the line x cos α + y sin α = 2√3 is tangent to the ellipse \(\frac{x^2}{16} + \frac{y^2}{8} = 1\) and α is an acute angle then α =
If the angle between the asymptotes of a hyperbola is 30° then its eccentricity is
If sin y = sin 3t and x = sin t, then \(\frac{dy}{dx}\) =