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 H.P. (D) `a,b,c` are in G.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.

If l n(a+c),l n(a-c)a n dl 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. (d) a ,b ,c are in H.P.

If lambda!=0,a,b,c,lambda are real such that a^(2)+b^(2)+c^(2)-2 lambda a-4b lambda-8 lambda c+21 lambda^(2)<=0 then (A) a,b,c are in A.P (B) a,b,c are in G.P (C) a,b,c are in H.P (D) a,b,c are in A.G.P

If a,b,c,in R^(+) , and a,b,c, d are in H.P. then

If a/b , b/c , c/a are in H.P., then (a)a^2b,c^2a,b^2c are in A.P. (b)a^2b, b^2c,C62a are in H.P. (c)a^2b,b^2c,c^2a are in G.P. (d) none

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 a, b,c be the sides foi a triangle ABC and if roots of equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal then sin^2 A/2, sin^2, B/2, sin^2 C/2 are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If a,b,c,d, x are real and the roots of equation (a^2+b^2+c^2)x^2-2(ab+bc+cd)x+(b^2+c^2+d^2)=0 are real and equal then a,b,c,d are in (A) A.P (B) G.P. (C) H.P. (D) none of these

If log_(a)x , log_(b)x and log_(c)x are in HP which one of the following is true? (1) (a)/(b+c),(b)/(c+a),(c)/(a+b) are in A.P. (2) b+c, c+a, a+b are in H.P. (3) a ,b ,c are in G.P. (4) a^(2),b^(2),c^(2) are in A.P.