If the function $f(x)$ defined by $f(x) = \begin{cases} ax + 1 & \text{if } x \leq 3 \\ bx + 3 & \text{if } x > 3 \end{cases}$ is continuous at $x = 3$, then $(a - b) =$ ..........

If $f(x), g(x)$ be twice differentiable functions, satisfying $f''(x) = g''(x), f'(1) = 2g'(1) = 4$ and $f(2) = 3g(2) = 9$ then $f(x) - g(x)$ at $x = 4$ is equal to

If $y = \cos^2\left[\cot^{-1}\left(\sqrt{\dfrac{1 - x}{1 + x}}\right)\right]$ then $\dfrac{dy}{dx} = $ ........

If $\sqrt{\dfrac{x}{y}} + \sqrt{\dfrac{y}{x}} = 6$, then $\dfrac{dy}{dx} =$