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 a,b,c,d,e,x are real and (a^2+b^2+c^2+d^2)x^2-2(ab+bc+cd+de)x+(b^2+c^2+d^2+e^2)le0 then a,b,c,d,e are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If (b+c)/(a+d)= (bc)/(ad)=3 ((b-c)/(a-d)) then a,b,c,d are in (A) H.P. (B) G.P. (C) A.P. (D) none of these

If a,b,c are in A.P ,then 3^(a),3^(b),3^(c) shall be in (A) A.P (B) G.P (C) H.P (D) None of these

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 are such unequal real numbers that (a^(2)+b^(2)+c^(2))p^(2)-2 (ab+bc+cd) p+ (b^(2)+c^(2)+d^(2)) le 0 then a,b,c, d are in -

If a,b,c,d and p are distinct real numbers such that (a^(2)+b^(2)+c^(2))p^(2)-2(ab+bc+cd)p+(b^(2)+c^(2)+d^(2))<=0 then prove that a,b,c,d are in G.P.

If a,b,c,d are distinct positive then a^n/b^ngtc^n/d^n for all epsilon N if a,b,c,d are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

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 a,b, and c are in G.P.then a+b,2b, and b+c are in a.A.P b.G.P.c. H.P.d.none of these