IIT-JEE Exam

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.
The probability that X = 3 equals

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IIT-JEE Other Question

In a triangle ABC with fixed base BC, the vertex A moves such that cosB + cosC = 4 sin^2(A/2)..If a, b and c
denote the lengths of the sides of the triangle opposite to the angles A, B and C, respectively, then
(A) b + c = 4a (B) b + c = 2a
(C) locus of point A is an ellipse (D) locus of point A is a pair of straight lines
Two small particles of equal masses start moving in opposite directions from a point
A in a horizontal circular orbit. Their tangential velocities are v and 2v respectively,
as shown in the figure. Between collisions, the particles move with constant speeds.
After making how many elastic collisions, other than that at A, these two particles
will again reach the point A?
(A) 4 (B) 3
(C) 2 (D) 1