There are n is 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 (1/8)n(n-1)(n-2)(n-3)

If n straight lines be drawn in a plane , no two of them being parallel and no three of them being concurrent , how many points of intersection will be there ?

There are n points in a plane of which m points are collinear. How many lines can be formed from these points ?

There are 10 points on a plane of which no three points are collinear. If lines are formed joining these points, find the maximum points of intersection of these lines.

There are n points in a plane , of which no three are collinear expept m which are collinear. Find the number of triangles formed by joining the points.

There are 15 points in a plane of which 4 points lie in one stright line and another 5 points lie in another straight line . The two lines are parallel and no three of the remaining 6 points are collinear . Find (a) the number of straight lines and (b) the number of trangles that can be formed by joining the 15 points .

n lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent. The number of different points at which these lines will cut is a. sum_(k=1)^(n-1)k b. n(n-1) c. n^2 d. none of these

Find the equation of the line passing through the points (1,2,3)a n d(-1,0,4)dot

Two straight lines pass through the fixed points (+-a, 0) and have slopes whose products is pgt0 Show that the locus of the points of intersection of the lines is a hyperbola.

Two parallel straight lines are drawn through the points of intersection of two circles upto their circumference. Then prove that two straight lines are equal.

Straight lines are drawn by joining m points on a straight line of n points on another line. Then excluding the given points, the number of point of intersections of the lines drawn is (no tow lines drawn are parallel and no these lines are concurrent). a. 4m n(m-1)(n-1) b. 1/2m n(m-1)(n-1) c. 1/2m^2n^2 d. 1/4m^2n^2