If three successive terms of as G.P. with commonratio `rgt1` form the sides of a triangle and [r] denotes the integral part of x the `[r]+[-r]=` (A) 0 (B) 1 (C) -1 (D) none of these

Three successive terms of a G.P. will form the sides of a triangle if the common ratio r satisfies the inequality

int_0^1 [x^2-x+1]dx , where [x] denotes the integral part of x , is (A) 1 (B) 0 (C) 2 (D) none of these

int_0^2 x^3[1+cos((pix)/2)]dx , where [x] denotes the integral part of x , is equal to (A) 1/2 (B) 1/4 (C) 0 (D) none of these

If a_1, a_2, a_3(a_1>0) are three successive terms of a G.P. with common ratio r , for which a_3>4a_2-3a_1 holds true is given by a. 1ltrlt-3 b. -3ltrlt-1 c. r gt3 or rlt1 d. none of these

If r ge1 , then the sum of infinite G.P. tends to (i) 0 (ii) oo (iii) 1 (iv) none of these

If a,b,c be the pth, qth and rth terms respectively of a H.P., the |(bc,p,1),(ca,q,1),(ab,r,1)|= (A) 0 (B) 1 (C) -1 (D) none of these

If the sides a , b , c of a triangle A B C form successive terms of G.P. with common ratio r(>1) then which of the following is correct? (a) A >pi/3 ' (b) B≥π/3 '(c) C<π/3 '(d) A < B < π/3

If the sides of triangle ABC are in G.P with common ratio r (r<1) , show that r<1/2(sqrt5+1)

In any triangle, the minimum value of r_1r_2r_3//r^3 is equal to (a) 1 (b) 9 (c) 27 (d) none of these

If sum_(r=1)^n t_r= (n(n+1)(n+2))/3 then sum _(r=1)^oo 1/t_r= (A) -1 (B) 1 (C) 0 (D) none of these