If $f(x)$ and $g(x)$ are twice differentiable functions satisfying $f''(x) = g''(x)$, $f'(1) = 2g'(1) = 4$ and $f(2) = 3g(2) = 9$, then the value of $f(x) - g(x)$ at $x = 4$ is:

If the function $y = \sin^{-1} x$,then $\left(1-x^2\right) \frac{d^2 y}{d x^2}$ is equal to

If $a x^2+2 h x y+b y^2=0$, then $\frac{d^2 y}{d x^2}=$

$A$ function $y = f(x)$ has a second-order derivative $f''(x) = 6(x - 1)$. If its graph passes through the point $(2, 1)$ and at that point the tangent to the graph is $y = 3x - 5$,then the function is

$y=e^{a \sin ^{-1} x} \Rightarrow (1-x^2) y_{n+2}-(2 n+1) x y_{n+1}$ is equal to

If $y = \frac{\alpha x + \beta}{\gamma x + \delta}$,then $2 y_1 y_3 =$