For positive real numbers `a ,bc` such that `a+b+c=p ,` which one holds? (a) `(p-a)(p-b)(p-c)lt=8/(27)p^3` (b)`(p-a)(p-b)(p-c)geq8a b c` (c)`(b c)/a+(c a)/b+(a b)/clt=p` (d) none of these

If a,b,c are distinct real numbers such that a, b,c are in A.P.and a^(2),b^(2),c^(2) are in H.P, then

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 (1)/(a),(1)/(b),(1)/(c) are in A.P.prove that: (b+c)/(a),(c+a)/(b),(a+b)/(c) are in A.P.

If three unequal positive real numbers a,b,c are in G.P.and b-c,c-a,a-b are in H.P.then the value of a+b+c depends on

If the four consecutive coefficients in any binomial expansion be a,b,c and d then (A) (a+b)/a,(b+c)/b,(c+d)/c are in H.P. (B) (bc+ad)(b-c)=2(ac^2-b^2d) (C) b/a,c/b,d/c are in A.P. (D) none of these

If a,b,c are in A.P.the (a)/(bc),(1)/(c),(2)/(b) will be in a. A.P b.G.P.c.H.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

Simplify (p^(a)/p^(b))^(c)xx(p^(b)/p^(c))xx(p^(c)/p^(a))

If a^(2)+b^(2),ab+bc, and b^(2)+c^(2) are in G.P. then a,b,c are in a.A.P.b.G.P.c.H.P.d.none of these