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

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_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_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

Let f(x)=cos(a_1+x)+1/2cos(a_2+x)+1/(2^2)cos(a_1+x)++1/(2^(n-1))cos(a_n+x) where a)1,a_2 a_n in Rdot If f(x_1)=f(x_2)=0,t h e n|x_2-x_1| may be equal to pi (b) 2pi (c) 3pi (d) pi/2

If (a_2a_3)/(a_1a_4) = (a_2+a_3)/(a_1+a_4)=3 ((a_2 -a_3)/(a_1-a_4)) then a_1,a_2, a_3 , a_4 are in :

Let f(x)=cos(a_1+x)+1/2cos(a_2+x)+1/(2^2)cos(a_3+x)+ ........+ 1/(2^(n-1))cos(a_n+x) where a)1,a_2 a_n in Rdot If f(x_1)=f(x_2)=0,t h e n|x_2-x_1| may be equal to (a) pi (b) 2pi (c) 3pi (d) pi/2

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

If a_r is the coefficient of x^r in the expansion of (1+x)^n then a_1/a_0 + 2.a_2/a_1 + 3.a_3/a_2 + …..+n.(a_n)/(a_(n-1)) =

a_1,a_2,a_3 ,…., a_n from an A.P. Then the sum sum_(i=1)^10 (a_i a_(i+1)a_(i+2))/(a_i + a_(i+2)) where a_1=1 and a_2=2 is :

rithmetic mean a, geometric mean G and Harmonic mean H to n positive numbers a_1,a_2,a_3,…..,a_n are given by A=(a_1+a_2+……………+a_n)/n, G=(a_1 a_2 a_n)^(1/2) and G= n/(1/H_1+1/H_2+………+1/H_n) There is a relation in A, G and H given by AgeGgeH equality holds if and only if a_1=a_2=..............=a_n On the basis of above information answer the following question If a,b,c are positive numers such that a+b+c=0 then greatest value a^3b^2c^5 is (A) 3^3.2^2.5^5 (B) 3^10 (C) 2^10 (D) 5^10