If $x = 4t^3 + 3, y = 3t^4 + 4$ and $\dfrac{\frac{d^2x}{dy^2}}{\left(\frac{dx}{dy}\right)^n}$ is constant then the value of $n$ is

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 ...........