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  

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

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

In a sequence of 21 terms the first 11 terms are in A.P. with common difference 2 and the last 11 terms are in G.P. with common ratio 2. If the middle terms of the A.P. is equal to the middle term of the G.P., then the middle term of the entire sequence is

If the pth term of an A.P. is 1/q and qth term is 1/p and sum of pq terms is 25pq, then p and q are connected by

If t_r denotes the rth term of an A.P., and t_p = 1/q, t_q = 1/p, then which of the following is a root of the equation