IIT-JEE Exam

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

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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 Let (x, y) be any point on the parabola y^2 = 4x. Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio 1 : 3. Then the locus of P is