IIT-JEE Exam

Consider the statements:
P : There exists some x such that f(x) + 2x = 2(1 + x2)
Q : There exists some x  such that 2f(x) + 1 = 2x(1 + x)

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IIT-JEE Other Question

A tangent PT is drawn to the circle x2 + y2 = 4 at the point P(sqrt(3),1) . A straight line L, perpendicular to PT is a tangent to the circle (x -3)2 + y2 =1. The equation of l are Let an denote the number of all n digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let bn = the number of such n digit integers ending with digit 1 and cn = the number of such n digit integers ending with digit 0.
The value of b^6 is??