If the points `(p ,\ q),\ (m ,\ n)` and `(p-m ,\ q-n)` are collinear, show that `p n=q m` .

If A xx B = {(p, q), (p, r), (m, q), (m, r)} , Find A and B

In triangle P Q R , if P Q=R Q\ a n d\ L ,\ M\ a n d\ N are the mid-points of the sides P Q ,\ Q R\ a n d\ R P respectively. Prove that L N=M N .

If the p^(t h)a n d q^(t h) terms of a G.P. are q a n d p respectively, show that (p+q)^(t h) term is ((q^p)/(p^q))^(1/(p-q)) .

In A P Q R , if P Q=QR\ a n d\ L ,\ M\ a n d\ N are the mid-points of the sides P Q ,\ P R\ a n d\ R P respectively. Prove that L N=M N

in a G.P (p+q)th term = m and (p-q) th term = n , then find its p th term

If the sum of n terms of an A.P. is (p n+q n^2) , where p and q are constants, find the common difference.

If the sum of n terms of an A.P. is (p n+q n^2) , where p and q are constants, find the common difference.

Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; S={(m/n , p/q)"m , n , p and q are integers such that n ,q"!="0 and q m = p n"} . Then (1) neither R nor S is an equivalence relation (2) S is an equivalence relation but R is not an equivalence relation (3) R and S both are equivalence relations (4) R is an equivalence relation but S is not an equivalence relation

If P = {a , b , c} and A xxB = {(p , q), (p , r), (m , q), (m , r)} Q = {r} , form the sets P xxQ a n d Q xxP .Are these two products equal?

If (p+q)th term of G.P is m, (p-q) th term is n, show that pth term is sqrt(mn) and qth term is m(n/m)^(p/(2q)) .