In the closed interval $[0,3]$, the minimum value of the function $f$ given below is $f(x)=2 x^3-9 x^2+12 x$

If $C$ is the unit circle in the complex plane with its center at the origin, then the value of $n$ in the equation given below is _______ (rounded off to 1 decimal place).

$$ \oint_c \frac{z^3}{\left(z^2+4\right)\left(z^2-4\right)} d z=2 \pi i n $$

The directional derivative of the function $f$ given below at the point $(1,0)$ in the direction of $\frac{1}{2}(\hat{i}+\sqrt{3} \hat{j})$ is _______ (Rounded off to 1 decimal place).

$$ f(x, y)=x^2+x y^2 $$

Let $y$ be the solution of the differential equation with the initial conditions given below. If $y(x=2)=A \ln 2$, then the value of $A$ is _________ (rounded off to 2 decimal places).

$$ x^2 \frac{d^2 y}{d x^2}+3 x \frac{d y}{d x}+y=0 \quad y(x=1)=0 \quad 3 x \frac{d y}{d x}(x=1)=1 $$