Some points on a plane are marked and they are connected pair wise by line segments. If the total number line segments is 10, then number of points are?  

Let the number points in plane be ‘x’. If each point is joined to remaining $(x-1)$points,  total number of line segments formed may be $x(x-1)$.

But each line segment is counted exactly twice at its end point

So, total number of line segments formed is $\frac{x(x-1)}{2}$

So, $\frac{x(x-1)}{2}=10$

$\begin{array}{l}{x}^2-x=20\\ x^2-x-20=0\\ (x-5)(x+4)=0\end{array}$

$x=5$ or  $-4$

Number of points con not be negative so number of points are 5