Let A, B, C Be In A.P., And (b – C) X2 + (c – A) X +(a – B) = 0 And 2(a + C) X2 +(b + C) X = 0 Have A Common Root, Then

If a, b, c are three distinct numbers such that a, b, c are in A.P. and a, c – b,  b – a are in G.P. then the ratio a : b : c equals

Let n ∈ N, n > 25. Let A, G, H denote the arithmetic mean, geometric mean and harmonic mean of 25 and n. The least value of n for which A, G, H ∈ {25, 26, …, n}, is

Let a, b, c be distinct real numbers which are in G.P. If ∈ R is such that a + x, b + x, c + x, are in H.P., then x equals  

Suppose a, b, c are in A.P. Let A, G bet the arithmetic mean and geometric mean between a and b, A’ , G’ bet the arithmetic mean and geometric mean between b and c, then