Curve

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.

Which of the following statement(s) is/are incorrect regarding the non-simple curve?

Statement $\mathrm{I}:$ If the curve crosses itself (or crosses its own path) but the curve has a different starting point and different endpoint then it is termed a simple closed curve.

Statement $\mathrm{II}:$ If the curve crosses itself (or crosses its own path) and has the same starting point and the endpoint then that curve is termed a non-simple closed curve.

Statement $\mathrm{III}:$ If the curve crosses itself (or crosses its own path) but the curve has a different starting point and different endpoint then it is termed a non-simple open curve.

Which of the following statement(s) is/are incorrect regarding the non-simple curve?

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

Statement $\mathrm{II}:$ If the curve crosses itself (or crosses its own path) but curve has a different starting point and different endpoint then it is termed a non-simple open curve.

Statement $\mathrm{III}:$ If the curve crosses itself (or crosses its own path) but curve has a different starting point and different endpoint then it is termed a simple open curve.

Which of the following statements is correct regarding types of curves?

Which one of the following graphs is for a non-simple closed curve?

Match list $\mathrm{I}$ with list $\mathrm{II}$ and select the correct answer with code:

Which one of the following statements is correct regarding the cardioid graph shown below?

Graph $\mathrm{I}$:

Which one of the following statement is correct regarding the graph shown below?

Graph $\mathrm{I}$:

Match list $\mathrm{I}$ with list $\mathrm{II}$ and select the correct answer with code:

A curve crosses its own traced path is known as _____ curve.

Which one of the following statements is correct regarding the graphs shown below?

Graph $\mathrm{I}$:

Graph $\mathrm{II}$:

Find the equation of the curve which passes through the point $(1,2)$ and has the slope $\frac{dy}{dx}=2x-3$

Find the equation of the curve by eliminating '$t$'

$x=3-2t, y=4+5t-t^2$

If the equation of tangent to the curve $y^2=4x^2-3x$ is $2x-3ay+5=0$ at point $(1,2)$ what should be the value of '$a$':

Find the value of 'a' if area bounded by the curve is $6$ sq units and equation of curve is $F\left(x\right)=2x^2-5a$ from $x=2 to 4$

Find the area under the curve.

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

Find the equation of the curve for which $\frac{dy}{dx}=x^2+2x-2$ passes through the point $(2,3)$

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 will be 'a' in the curve $4x^2=a{y}^2+3y$ if the equation of tangent at point $(1,2)$ is $2x-3y+5=0$:

What will be the equation of normal to the curve $2y^2=3x$ at point P$(2,4)$