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

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 respectively the p^(th),q^(th)andr^(th) terms of a H.P., then Delta=|{:(bc,ca,ab),(p,q,r),(1,1,1):}| equals

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 ,c are the p t h ,q t h ,r t h terms, respectively, of an H P , show that the points (b c ,p),(c a ,q), and (a b ,r) are collinear.

If pth, qth and rth terms of a HP be respectively a,b and c , has prove that (q-r)bc+(r-p)ca+(p-q)ab=0 .

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

If a , b , c are all positive and are pth ,qth and rth terms of a G.P., then show that =|(loga, p,1),(logb, q,1),(logc ,r,1)|=0

If the pth, qth and rth terms of a G.P, are x,y and z repectively, then prove that |{:(logx,p,1),(logy,q,1),(logz,r,1):}|=0