If `a, b, c` are the `pth, qth, rth` terms respectively of an `H.P.`, then the lines `bcx + py+1=0, cax + qy+1=0 and abx+ry+1=0` (A) are concurrent (B) form a triangle (C) are parallel (D) none of these

If a, b, c be the pth, qth and rth terms respectively of a HP, show that the points (bc, p), (ca, q) and (ab, r) are collinear.

If a,b,c be the pth, qth and rth terms respectively of a H.P., the |(bc,p,1),(ca,q,1),(ab,r,1)|= (A) 0 (B) 1 (C) -1 (D) none of these

If a,b,c are positive and are the pth, qth rth terms respectively of a GP then |(loga,p,1),(logb,q,1),(logc, r,1)|=

The lines px +qy+r=0, qx + ry + p =0,rx + py+q=0, are concurrant then

The lines px +qy+r=0, qx + ry + p =0,rx + py+q=0, are concurrant then

If rational numbers a,b,c be th pth, qth, rth terms respectively of an A.P. then roots of the equation a(q-r)x^2+b(r-p)x+c(p-q)=0 are necessarily (A) imaginary (B) rational (C) irrational (D) real and equal

If the lines a x+12 y+1=0,\ b x+13 y+1=0 and c x+14 y+1=0 are concurrent, then a , b , c are in a. H.P. b. G.P. c. A.P. d. none of these

If the lines a x+2y+1=0,b x+3y+1=0a n dc x+4y+1=0 are concurrent, then a ,b ,c are in (a). A.P. (b). G.P. (c). H.P. (d). none of these

If a,b,c, be the pth, qth and rth terms respectivley of a G.P., then the equation a^q b^r c^p x^2 +pqrx+a^r b^-p c^q=0 has (A) both roots zero (B) at least one root zero (C) no root zero (D) both roots unilty

If a , b and c b respectively the pth , qth and rth terms of an A.P. prove that a(q-r) +b(r-p) +c (p-q) =0