If n lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent, then find number of different points at which these lines will cut.

If n lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent, such that these lines divide the planein 67 parts, then find number of different points at which these lines will cut.

If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent. In how many points will they intersect each other ?

Six straight lines are in a plane such that no two are parallel & no three are concurrent. The number of parts in which these lines divide the plane will be

If n straight lines in a plane are such that no two of them are parallel and no three of them are concurrent, prove that they intersect each other in (n(n-1))/2 points.

There are n straight lines in a plane in which no two are parallel and no three pass through the same point. Their points of intersection are joined. Show that the number of fresh lines thus introduced is 1/8n(n-1)(n-2)(n-3)

There are n straight lines in a plane such that n_(1) of them are parallel in onne direction, n_(2) are parallel in different direction and so on, n_(k) are parallel in another direction such that n_(1)+n_(2)+ . .+n_(k)=n . Also, no three of the given lines meet at a point. prove that the total number of points of intersection is (1)/(2){n^(2)-sum_(r=1)^(k)n_(r)^(2)} .

There are 10 points in a plane of which no three points are collinear and four points are concyclic. The number of different circles that can be drawn through at least three points of these points is

The locus of points such that two of the three normals drawn from them to the parabola y^ 2 =4ax coincide is

In a plane there are 37 straight lines, of which 13 passes through the point A and 11 passes through point B. Besides, no three lines passes through one point no line passes through both points A and B and no two are parallel, then find the number of points of intersection of the straight line.