If the transversal `y=m_r` ​ `x; r=1, 2, 3` cut off equal intercepts on the transversal `x+y=1` then `1+m_1` ​ , `1+m_2` ​ , `1+m_3` ​ are in
(a) A.P.
(a) G.P.
(a) H.P.
(a) None of these

Prove that the lines y=m, x, r=1, 2, 3 . Cut off equal intercepts on the transversal x+y=1 if 1+m_1, 1+m_2 , 1+m_3 are in H.P.

If the numbers p,q,r are in A.P. then m^(7p), m^(7q), m^(7r)(mgt0) are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If the lines a x+2y+1=0,b x+3y+1=0a n dc x+4y+1=0 are concurrent, then a ,b ,c are in (a). A.P. (b). G.P. (c). H.P. (d). none of these

If normals at two points A(x_1, y_1) and B(x_2, y_2) of the parabola y^2 = 4ax , intersect on the parabola, then y_1, 2sqrt(2)a, y_2 are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If 2 (y - a) is the H.M. between y - x and y - z then x-a, y-a, z-a are in (i) A.P (ii) G.P (iii) H.P (iv) none of these

If a,b,c are proper fractiion are in H.P. and x sum_(n=1)^oo a^n, y=sum_(n=1)^oo b^n, z= sum_(n=1)^oo c^n then x,y,z are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If the lines a x+2y+1=0,b x+3y+1=0a n dc x+4y+1=0 are concurrent, then a ,b ,c are a. A.P. b. G.P. c. H.P. d. none of these

If a ,b ,c are in A.P., the a/(b c),1/c ,1/b will be in a. A.P b. G.P. c. H.P. d. none of these

If the lines a x+12 y+1=0,\ b x+13 y+1=0 and c x+14 y+1=0 are concurrent, then a , b , c are in a. H.P. b. G.P. c. A.P. d. none of these

Let an A.P. a G.P. and a H.P. of positive terms have the same first term a, the same last term b and the same numberof terms (2n+1). Let x,y,z be the (n+1)th terms respectively of the A.P., G.P. and H.P. respectively. On the basis of above information anwer the following question: x,y,z are in (A) A.P. (B) G.P. (C) H.P. (D) none of these