There are two parallel lines `L_1 and I_2` in a plane `I_1` contains mdifferent points nand lcontains n different points `A_1,A_2,.........,A_m and I_2` contains n different points `B_1,B_2,......B_n`. How many triangles are possible with thesevertices?

Two straight lines intersected at a point O.points A_1,A_2….A_n are taken on one lines and points B_1,B_2…B_n on the other if the point O is not to be used the number of triangles that can be drawn using these points as vertices is

The straight lines l_1, ,l_2 & l_3, are parallel & lie in the same plane. A total of m points are taken on the line l_1, n points on l_2, & k points on l_3. How many maximum number of triangles are there whose vertices are at these points ?

Let L_1 and L_2 be two lines intersecting at P If A_1,B_1,C_1 are points on L_1,A_2, B_2,C_2,D_2,E_2 are points on L_2 and if none of these coincides with P, then the number of triangles formed by these 8 points is

The straight lines I_(1),I_(2),I_(3) are parallel and lie in the same plane. A total number of m point are taken on I_(1),n points on I_(2) , k points on I_(3) . The maximum number of triangles formed with vertices at these points are

The straight lines I_(1),I_(2),I_(3) are parallel and lie in the same plane. A total number of m point are taken on I_(1),n points on I_(2) , k points on I_(3) . The maximum number of triangles formed with vertices at these points are

We know that, if a_1, a_2, ..., a_n are in H.P. then 1/a_1,1/a_2,.....,1/a_n are in A.P. and vice versa. If a_1, a_2, ..., a_n are in A.P. with common difference d, then for any b (>0), the numbers b^(a_1),b^(a_2),b^9a_3),........,b^(a_n) are in G.P. with common ratio b^d. If a_1, a_2, ..., a_n are positive and in G.P. with common ration, then for any base b (b> 0), log_b a_1 , log_b a_2,...., log_b a_n are in A.P. with common difference logor.If x, y, z are respectively the pth, qth and the rth terms of an A.P., as well as of a G.P., then x^(z-x),z^(x-y) is equal to