If $f(x)=3 \sqrt[3]{x^2}-x^2$,then

Find the minimum value of $2x + 3y$ when $xy = 6$.

Let $f(x) = \frac{\sin \pi x}{x^2}, x > 0$. Let $x_1 < x_2 < x_3 < \ldots < x_n < \ldots$ be all the points of local maximum of $f(x)$ and $y_1 < y_2 < y_3 < \ldots < y_n < \ldots$ be all the points of local minimum of $f(x)$. Which of the following statements are true?
$(1)$ $|x_n - y_n| > 1$ for every $n$
$(2)$ $x_1 < y_1$
$(3)$ $x_n \in (2n, 2n + \frac{1}{2})$ for every $n$
$(4)$ $x_{n+1} - x_n > 2$ for every $n$

$A$ triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having a fence are of the same length $x$. The maximum area (in sq. units) enclosed by the park is

If $f(x)=x^5-5 x^4+5 x^3-10$ has its local maxima and minima at $x=a$ and $x=b$ respectively,then $2 a+b$ is equal to

The minimum value of $e^{(2x^2 - 2x - 1)\sin^2 x}$ is .......