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

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

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 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 the pth, qth, and rth terms of a HP, then the vectors vecu= hati/a + hatj/b + hatk/c and vecv = ( q -r) hati + ( r-p) hatj + ( p-q) hatk