The minimum value of $2x^2 + x - 1$ is

Let $f(x)=x^2+\frac{1}{x^2}$ and $g(x)=x-\frac{1}{x}$ for $x \in R-\{-1,0,1\}$,then the local minimum of $\frac{f(x)}{g(x)}$ is

$A(1,15), B(3,-12), C(6,12)$ are three consecutive turning points of a continuous curve $y=f(x)$. If $f(x)=0$ only for $x=\alpha$ and $x=\beta$,then $|\beta-\alpha| < $

Two sides of a triangle are given. If the area of the triangle is maximum,then the angle between the given sides is (in $^{\circ}$)

The perimeter of a sector is constant. If its area is to be maximum,the sectorial angle should be

$A$ manufacturer can sell $x$ items at a price of rupees $\left(5 - \frac{x}{100}\right)$ each. The cost price of $x$ items is Rs. $\left(\frac{x}{5} + 500\right)$. The number of items that the manufacturer should sell to earn the maximum profit is