If `x ,y ,a n dz` are in G.P. and `x+3+,y+3,a n dz+3` are in H.P., then `y=2` b. `y=3` c. `y=1` d. `y=0`

If y-z,2(y-a),y-x are in H.P. prove that x-a,y-a,z-a are in G.P.

If x, y, z are in A.P. and t a n^(-1)x ,""t a n^(-1)y""a n d""t a n^(-1)z are also in A.P., then (1) 2x""=""3y""=""6z (2) 6x""=""3y""=""2z (3) 6x""=""4y""=""3z (4) x""=""y""=""z

If a,x,b are in H.P. And a,y,z,b are in G.P.,then the value of (yz)/(x(y^3+z^3)) is

If 5x-y,2x+y,x+2y are in "A.P" and (x-1)^(2),xy+1,(y+1)^(2) are in G.P (x!=0) then x+y=

If x ,y ,a n dz are pth, qth, and rth terms, respectively, of an A.P. nd also of a G.P., then x^(y-z)y^(z-x)z^(x-y) is equal to a.x y z b. 0 c. 1 d. none of these

If the positive numbers 3,x,5,y are in a G.P., then : (x,y)=

The complex numbrs x and y such that x,x+2y,2x+y are n A.P. and (y+1)^2, xy+5, (x+1)^2 are in G.P. are (A) x=3, y=1 (B) x=-1+2sqrt(2)i, y=1/3 (-1+2sqrt(2)i) (C) x=sqrt(2)+i, y=3sqrt(5)-sqrt(2)i (D) x=-1(1+2sqrt(2)i), y= - 1/3 (1+2sqrt(2)i)

Given that x+y+z =15 when a,x,y,z,b are in A.P and 1/x+1/y+1/z=5/3 when a,x,y,z,b are in H.P .Then

Three distinct points A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3)) lie on the parabola y=3x^(2). If x_(1),x_(2),x_(3) are in A.P.and y_(1),y_(2) and y_(3) are in G.P.then the common ratio of the GP is