`x=(a^(m+n))/(b^(p+q))` and `y=(c^(x+y))/(d^(g-h))` are two rational numbers, where `a^(2)=b^(3)=64, c^(4)=d^(2)=16,x+y=m+n=5,p+q=g-h=3` then the rational number between `x and y` is

If A.M. and G.M. of x and y are in the ration p : q, then x:y is :

Consider the following relations : R={(x,y)|x,y are real numbers and x= wy for some rational number w} : S={((m)/(n),(p)/(q))} , m, n, p and q are integers such that n, q ne 0 " and "qm = pn }. Then :

If x is a rational number and y is an irrational number, then (a) both x + y a n d x y are necessarily rational (b) both x + y a n d x y are necessarily irrational (c) x y is necessarily irrational, but x + y can be either rational or irrational (d) x + y is necessarily irrational, but x y can be either rational or irrational

a, b, c are in A . P, x is G . M between a and b, y is the G.M between b and c, then b^(2) is

If a^(x) = b^(y) = c^(z) and a, b, c, are in G.P., prove that x, y, z are in H.P.

If (p)/(x) +(q)/(y) =m and (q)/(x) +(p)/(y) =n , then what is (x)/(y) equal to ?

If x,y,z be three numbers in G.P. such that 4 is the A.M. between x and y and 9 is the H.M. between y and z , then y is