IIT-JEE Exam

Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively. Suppose a = 6, b = 10 and the area of the triangle is 15 3. If angle ACB is obtuse and if r denotes the radius of the incircle of the triangle, then r2 is equal to

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Two parallel chords of a circle of radius 2 are at a distance 3+1 apart. If the chords subtend at the centre, angles of ki and 2 ki, where k > 0, then the value of [k] is [Note : [k] denotes the largest integer less than or equal to k]. Let f(x) = x^2 and g(x) = sinx for all x (R). Then the set of all x satisfying (f o g o g o f) (x) = (g o g o f) (x), where (f o g) (x) = f(g(x)), is