If `a_n= int_0^pi (sin(2n-1)x)/(sinx) dx`. Then the number `a_1,a_2,a_3` …….. Are in (A) A.P (B) G.P (C) H.P (D) none of these

If a_iepsilon R-[0},i=1,2,3,4 and xepsilon R and (sum_(i=1)^ a_i^2) x^2-2x(sum_(i=)^3 a_ia_(i+1)+)+sum_(i=2)^4 a_i^2ge0 then a_1,a_2,a_3,a_4 are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If x,a_1,a_2,a_3,…..a_n epsilon R and (x-a_1+a_2)^2+(x-a_2+a_3)^2+…….+(x-a_(n-1)+a_n)^2le0 , then a_1,a_2,a_3………a_n are in (A) AP (B) GP (C) HP (D) none of these

Let a_1,a_2,a_3…………., a_n be positive numbers in G.P. For each n let A_n, G_n, H_n be respectively the arithmetic mean geometric mean and harmonic mean of a_1,a_2,……..,a_n On the basis of above information answer the following question: A_k,G_k,H_k are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

Let a_n=int_0^(pi/2) (1-cos2nxdx)/(1-cos2x) , then a1, a2, a3 is in

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 ax^2+2bx+c=0 and a_1x^2+2b_1x+c_1=0 have a common root and a/a_1,b/b_1,c/c_1 are in AP then a_1,b_1,c_1 are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If a_n int_0^(pi/2) (sin^2nx)/(sin^2x) dx, then |(a_1,a_51, a_101),(a_2, a_52, a_102),(a_3, a_53, a_103)= (A) 1 (B) 0 (C) -1 (D) none of these

If a,b,c,d are distinct positive then a^n/b^ngtc^n/d^n for all epsilon N if a,b,c,d are in (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+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