Roots of the equation `a(b-c)x^2+b(c-a)x+c(a-b)=0` are real and equal, then (A) `a+b+c!=0` (B) `a,b,c` are in H.P. (C) `a,b,c` are in A.P. (D) `a,b,c` are in G.P.

If l n(a+c),l n(a-c) and l n(a-2b+c) are in A.P., then (a) a ,b ,c are in A.P. (b) a^2,b^2, c^2, are in A.P. (c) a ,b ,c are in G.P. (d) a ,b ,c are in H.P.

If the roots of equation a(b-c)x^2+b(c-a)x+c(a-b)=0 be equal prove that a,b,c are in H.P.

In a /_\ABC, tan\ A/2 = 5/6 and tan\ C/2 = 2/5 then (A) a,c,b are in A.P. (B) a,b,c are in A.P. (C) b,a,c are in A.P. (D) a,b,c are in G.P.

If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d -c are in G.P.

If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d -c are in G.P.

If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d -c are in G.P.

If a, b, c are in A.P. and b-a, c-b, a are in G.P. then a:b:c=?

Column I, Column II If a ,b ,c ,a n dd are four zero real numbers such that (d+a-b)^2+(d+b-c)^2=0 and he root of the equation a(b-c)x^2+b(c-a)x=c(a-b)=0 are real and equal, then, p. a+b+c=0 If the roots the equation (a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0 are real and equal, then, q. a ,b ,ca r einAdotPdot If the equation a x^2+b x+c=0a n dx^3-3x^2+3x-0 have a common real root, then, r. a ,b ,ca r einGdotPdot Let a ,b ,c be positive real number such that the expression b x^2+(sqrt((a+b)^2+b^2))x+(a+c) is non-negative AAx in R , then, s. a ,b ,ca r einHdotPdot

If a,b,c, are in A.P., b,c,d are in G.P. and c,d,e, are in H.P., then a,c,e are in

If 1/(b-a)+1/(b-c)=1/a+1/c , then (A). a ,b ,a n dc are in H.P. (B). a ,b ,a n dc are in A.P. (C). b=a+c (D). 3a=b+c