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 a,b,c,d are rational and are in G.P. then the rooots of equation (a-c)^2 x^2+(b-c)^2x+(b-x)^2-(a-d)^2= are necessarily (A) imaginary (B) irrational (C) rational (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 pth,qth and rth terms of an A.P. are a, b, c respectively, then show that (i) a(q-r)+b(r-p)+c(p-q)=0

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 the pth, th, rth terms of a G.P. are x, y, z respectively, prove that x^(q-r).y^(r-p) .z^(p-q) = 1 .

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

The roots of the equation (q-r)x^2+(r-p)x+p-q=0 are (A) (r-p)/(q-r),1 (B) (p-q)/(q-r),1 (C) (q-r)/(p-q),1 (D) (r-p)/(p-q),1

The roots of the equations x ^2−x−3=0 are a. imaginary b. rational. c. irrational d. none of these.

If a,b,c are rational and are in G.P and a-b, c-a, b-c are in H.P. then the equations ax^2+4bx-c=0 and a(b-c)x^2+b(c-a)x+c(a-b)=0 have (A) imaginary roots (B) irrational roots (C) rational roots (D) a common root