A.P., G.P., H.P. Complete Revision

Let the positive numebrs a,b,c,d be in A.P. Then abc,abd,acd,bcd re (A) not in A.P., G.P., H.P. (B) in A.P. (C) in G.P. (D) in H.P.

In an equilateral triangle, inradius r , circumradius R and ex-radius r_1 are in A.P. (b) G.P. (c) H.P. (d) none of these

If tanbeta=2sinalphasingammacos e c(alpha+gamma), then cotalpha,cotbeta,cotgamma are in (a)A.P. (b) G.P. (c) H.P. (d) none of these

If a,b,c are non zero real numbers such that 3(a^2+b^2+c^2+1)=2(a+b+c+ab+bc+ca) then a,b,c are in (A) A.P. only (B) G.P. only (C) A.P., G.P., and H.P. (D) A.P. and G.P.both

In triangle ABC, if cosA+2cosB+cosC=2,t h e na ,b ,c are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If a_n= int_0^pi(sin(2n-1)x)/sinx dx, then a_1a_2a_3 are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If cos2B=(cos(A+C))/(cos(A-C)), then tan A,tan B,tan C are in (a)A.P.(b) G.P.(c) H.P.(d) none of these