If `a_1,a_2,a_3,.....a_n....` are in G.P. then the determinant 'Delta=|[loga_n , loga_(n+1),loga_(n+2)],[loga_(n+3),loga_(n+4),loga_(n+5)],[loga_(n+6),loga_(n+7),loga_(n+8)]|` is equal to- (A) -2 (B) 1 (C) -1 (D) 0

If a_1, a_2, a_3,....... are in G.P. then the value of determinant |(log(a_n), log(a_(n+1)), log(a_(n+2))), (log(a_(n+3)), log(a_(n+4)), log(a_(n+5))), (log(a_(n+6)), log(a_(n+7)), log(a_(n+8)))| equals (A) 0 (B) 1 (C) 2 (D) 3

If a_1, a_2 a_n ,\ a_(n+1) are in GP and a_1>0AAI ,\ t h e n |loga_nloga_(n+2)loga_(n+4)loga_(n+6)loga_(n+8)loga_(n+10)loga_(n+12)loga_(n+14)loga_(n+16)| is equal to- 0 b. nloga_n c. n(n+1)loga_n d. none of these

If a ,b ,c are in G.P., then prove that loga^n ,logb^n ,logc^n are in A.P.

lim_(x->oo)cot^(-1)(x^(-a)log_a x)/(sec^(-1)(a^xlog_x a)),(a >1) is equal to (a) 2 (b) 1 (c) (log)_a2 (d) 0

If a_1, a_2, a_3,.....a_n are in H.P. and a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1 a_n , then k is equal to

If log_a x, log_b x, log_c x are in A.P then c^2=

If a ,\ b ,\ c are in G.P. prove that loga ,\ logb ,\ logc are in A.P.

Q. If log_x a, a^(x/2) and log_b x are in G.P. then x is equal to (1) log_a(log_b a) (2) log_a(log_e a)+log_a log_b b (3) -log_a(log_a b) (4) none of these

1/(1+log_b a+log_b c)+1/(1+log_c a+log_c b)+1/(1+log_a b+log_a c)

If a_1, a_2, a_3, ,a_(2n+1) are in A.P., then (a_(2n+1)-a_1)/(a_(2n+1)+a_1)+(a_(2n)-a_2)/(a_(2n)+a_2)++(a_(n+2)-a_n)/(a_(n+2)+a_n) is equal to a. (n(n+1))/2xx(a_2-a_1)/(a_(n+1)) b. (n(n+1))/2 c. (n+1)(a_2-a_1) d. none of these