1.

Let T_(n) denotes the n ^(th) term of a G.P. with common ratio 2 and (log _(2) ( 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).

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