If $x = a\sin^3 t$ and $y = a\cos^3 t$, then the value of $\dfrac{d^2y}{dx^2}$ at $t = \dfrac{\pi}{3}$ is equal to

An aeroplane at an altitude of 1 km is flying horizontally at 600 km / hr, passes directly over an observer. Then the rate at which it is approaching the observer when it is 1250 meters away from him is........

The line $x + y = 0$ touches the curve $y^2 = ax^3 + b$ at $(1, -1)$ then values of $a$ and $b$ respectively are ...........

The function $f(x) = x(x + 3)e^{-\left(\frac{1}{2}\right)x}$ satisfies all the conditions of Rolle's theorem in $[-3, 0]$, then $c =$