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`

There are m points on the line AB and n points on the line AC, excluding the point A. Triangles are formed joining these points

m points on one straight line are joined to n points on another straight line. The number of points of intersection of the line segments thus formed is (A) ^mC-2.^nC_2 (B) (mn(m-1)(n-1))/4 (C) (^mC_2.^nC_2)/2 (D) ^mC_2+^nC_2

Let N denotes,the greatest number of points in which m straight lines and n circles intersect. Then,

Find the point of intersection of the following pairs of lines: y=m_1x+a/(m_1)\ a n d\ y=m_2x+a/(m_2)dot

If m parallel lines in a plane are intersected by a family of n parallel lines, the number of parallelograms that can be formed is a. 1/4m n(m-1)(n-1) b. 1/4m n(m-1) c. 1/4m^2n^2 d. none of these

Assertion: If each of m points on one straight line be joined to each of n points on the other straight line terminated by the points, then number of points of intersection of these lines excluding the points on the given lines is (mn(m-1)(n-1))/2 Reason: Two points on one line and two points on other line gives one such point of intersection. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Two straight lines having variable slopes m_(1) and m_(2) pass through the fixed points (a, 0) and (-a, 0) respectively. If m_(1)m_(2)=2 , then the eccentricity of the locus of the point of intersection of the lines is

Find the equation of the straight line drawn through the point of intersection of the lines x+y=4\ a n d\ 2x-3y=1 and perpendicular to the line cutting off intercepts 5,6 on the axes.

The direction cosines of the lines bisecting the angle between the line whose direction cosines are l_1, m_1, n_1 and l_2, m_2, n_2 and the angle between these lines is theta , are

Line m in the xy-plane contains the points (2, 4) and (0, 1).Which of the following is an equation of line m ?