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 ?

If 20 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 ?

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

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)

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 .

Let f(n) be the number of regions in which n coplanar circles can divide the plane. If it is known that each pair of circles intersect in two different points and no three of them have common points of intersection, then (i) f(20) = 382 (ii) f(n) is always an even number (iii) f^(-1)(92) = 10 (iv) f(n) can be odd

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.

Two lines are drawn at right angles, one being a tangent to y^2=4a x and the other x^2=4b ydot Then find the locus of their point of intersection.

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

Two straight lines are drawn through any point X and exterior to a circle to intersect the circle at points A, B and points C, D respectively . Prove that DeltaXACandDeltaXBD are equiangular.

Column I, Column II Number of straight lines joining any two of 10 points of which four points are collinear, p. 30 Maximum number of points of intersection of 10 straight lines in the plane, q. 60 Maximum number of points of intersection of six circles in the plane, r. 40 Maximum number of points of intersection of six parabolas, s. 45