Which of the following statement(s) is/are correct?

Statement $\mathrm{I}:$ If the curve crosses itself (or crosses its own path) then that curve is termed a non-simple curve.

Statement $\mathrm{II}:$ If the curve doesn't cross its own path, then it is termed a simple curve.

Statement $\mathrm{III}:$ If a curve has the same starting point and the endpoint then that graph is termed a closed curve.

 

Find the area under the curve.

$F\left(x\right)=2x-3x^2$ the limit is given as $x=1 to x=2$

Which of the following is a convex polygon?

Equation of curve is given as $y=f\left(x\right)$ which passes through the point $(4,5)$  Given that

$f\left(x\right)=4x^2+2x-5$

Then the equation of the curve is:

What is the ratio of the points in the interior of the following curve to the sum of the points on the curve and the points exterior of the curve?

A circular floor has a red coloured sector OAB of angle ${60}^{\mathrm{o}}$ as shown below. What will be the amount of space occupied by the red coloured sector if the radius of the floor is $42 \mathrm{m}?$