The perimeter of a triangle is $10 \text{ cm}$. If one of its sides is $4 \text{ cm}$,then the remaining sides of the triangle,when the area of the triangle is maximum,are

Let the function $f(x)=2 x^3+(2 p-7) x^2+3(2 p-9) x-6$ have a maxima for some value of $x < 0$ and a minima for some value of $x > 0$. Then,the set of all values of $p$ is $......$

Let $V_1$ be the volume of a given right circular cone with $O$ as the centre of the base and $A$ as its apex. Let $V_2$ be the maximum volume of the right circular cone inscribed in the given cone whose apex is $O$ and whose base is parallel to the base of the given cone. Then,the ratio $V_2 / V_1$ is

Find all the points of local maxima and local minima of the function $f$ given by $f(x) = 2x^3 - 6x^2 + 6x + 5$.

$A$ helicopter is flying along the curve given by $y = x^{3/2} + 7, (x \geq 0)$. $A$ soldier positioned at the point $(1/2, 7)$ wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is

Let the sum of the maximum and the minimum values of the function $f(x) = \frac{2x^2 - 3x + 8}{2x^2 + 3x + 8}$ be $\frac{m}{n}$,where $\gcd(m, n) = 1$. Then $m + n$ is equal to :