If $(2, a)$ and $(b, 19)$ are two stationary points of the curve $y=2x^3-15x^2+36x+c$,then $a+b+c=$

$A$ wire of length $2$ units is cut into two parts,which are bent respectively to form a square of side $x$ units and a circle of radius $r$ units. If the sum of the areas of the square and the circle so formed is minimum,then:

Two stones are thrown vertically upwards with equations of motion $s_1 = 19.6t - 4.9t^2$ and $s_2 = 9.8t - 4.9t^2$ respectively. The maximum height of the first stone is $h$. When the first stone is at its maximum height,the height of the second stone is:

Let $f(x) = x^3 - 6x^2 + 12x - 3$. Then at $x = 2$,$f(x)$ has:

The local maximum value $l$ and local minimum value $m$ of $f(x) = \frac{x^2+2x+2}{x+1}$ in $R - \{-1\}$ exist at $\alpha, \beta$ respectively, then $\frac{l+m}{\alpha+\beta} =$

Statement-$I$: The sequence $a_n = \frac{n^2}{n^3 + 200}, n \in N$ has its $7^{th}$ term as the largest term.
Statement-$II$: The function $f(x) = \frac{x^2}{x^3 + 200}$ attains a local maximum at $x = 7$.