IIT-JEE Exam

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

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IIT-JEE Other Question

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 A value of b for which the equations
x^2 + bx - 1 = 0
x^2 + x + b = 0,
have one root in common is,