Let `T_n` denotes the `n^(th)` term of a `G.P.` with common ratio `2 and (log_2(log_3(log_512 T_100))) = 1`. If three sides of a triangle ABC are the values of `(T_1+ T_2), T_2 and T_3`, then area of the triangle is `sqrt 2160/N`, where N isa positive integer. Find the remainder when Nis divided by `2^10`.

Let T_(n) denotes the n ^(th) term of a G.P. with common ratio 2 and (log _(2) (log _(3) ( log _(512) T _(100))))=1. If three sides of a triangle ABC are the values of (T _(1) + T _(2)), T_(2) and T_(3) then area of the triangle is (sqrt 2160)/(N), where N is a positive integer. Find the remainder when N is divided by 2 ^(10).

If t_(n)" is the " n^(th) term of an A.P., then t_(2n) - t_(n) is …..

If t_(n) denotes the n th term of the series 2+3+6+1+18+ …….then t_(50) is

If the angles of a triangle are 30^0a n d45^0 and the included side is (sqrt(3)+1) cm, then area of the triangle is 1/2(sqrt(3)+1)s qdotu n i t s area of the triangle is 1/2(sqrt(3)-1)s qdotu n i t s

If t_(n)" is the " n^(th) term of an A.P. then the value of t_(n+1) -t_(n-1) is ……

If t_r denotes the r^(th) term of an G.P. and t_1 t_5 t_10 t_16 t_21 t_25 = 512 , then the value of its 13^(th) term is :

If t_r denotes the r^(th) term of an G.P. and t_1 t_5 t_10 t_16 t_21 t_25 = 512 , then the value of its 13^(th) term is :

Let T_(r) denote the rth term of a G.P.for r=1,2,3,... If for some positive integers m and n, we have T_(m)=1/n^(2) and T_(n)=1/m^(2) ,then find the value of T_(m+n/2)

Let T_r denote the rth term of a G.P. for r=1,2,3, If for some positive integers ma n d n , we have T_m=1//n^2 and T_n=1//m^2 , then find the value of T_(m+n//2.)