IIT-JEE Exam

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

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IIT-JEE Other Question
Four fair dice D1, D2, D3 and D4, each having six faces numbered 1, 2, 3, 4, 5, and 6, are rolled simultaneously. The probability that D4 shows a number appearing on one of D1, D2 and D3 is
option
a) 127/216
b) 125/216
c) 108/216
d) 91/216
 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)