The roots of equation `x^2+2(a-3)x+9=0` lie between -6 and 1 and `2, h_1, h_2, …, h_20 [a]` are in H.P., where [a] denotes the integeral part of a and `2,a_1,a_2,..a_20` [a] are in A.P. then `a_3h_18=` (A) 6 (B) 12 (C) 3 (D) none of these

If a,b,c are in A.P ,then 3^(a),3^(b),3^(c) shall be in (A) A.P (B) G.P (C) H.P (D) None of these

Let [x] = greatest integer le x . Suppose roots of the quadratic equation x^(2)+2(b-3)x+9=0 lie between -6 and 1 . Suppose (1)/(2),(1)/(h_(1)),(1)/(h_(2)),…,(1)/(h_(20)),(1)/([b]) are in A.P. and 2,a_(1),a_(2),…,a_(20) ,[b] are also in A.P., then a_(3)h_(18)=

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 a^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 (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_1,a_2, a_3………. are in H.P. and f(k) =sum_(r=1)^n a_r-a_k, the a_1/(f(1)), a_2/(f(2)), a_3/(f(3)), …….., a_n/(f(n)) are in (A) A.P. (B) G.P (C) H.P. (D) none of these

If 2, h_(1), h_(2),………,h_(20)6 are in harmonic progression and 2, a_(1),a_(2),……..,a_(20), 6 are in arithmetic progression, then the value of a_(3)h_(18) is equal to

If the roots of 2x^(3)+kx^(2)-x+1=0 are in H.P then k=