1. Find the equation of the normal to the curve
y = (1+x)y + sin-1(sin2) at x = 0.
2. Find the coordinates of the point at which the circles x²+y²-4x-2y = -4 and x²+y²-12x-8y = -36 touch each other.
3. In a triangle ABC, D and E are points on BC and AC respectively, such that BD = 2DC ad AE = 3EC. Let P be the point of intersection of AD and BE. Find BP/PE. (The original problem said using vector methods).
4. Determine te smallest positive value of x (in degrees) for which
tan (x+100°) = tan (x+50°) tan(x)tan(x-50°).
5. Numbers are selected at random, one at a time, from the two-digit numbers 00,01,02...,99 with replacement. An event E occurs if and only if the product of the two digits of a selected number is 18. If four numbers are selected, find the probability that the event E occurs at least 3 times.
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