IIT-JEE Exam

Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to
option
a) 42
b) 41
c) 25
d) 34

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IIT-JEE Other Question

A signal which can be green or red with probability 45 and 15 respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 34. If the signal received at station B is green, then the probability that the original signal was green is
option
a) 3/5
b) 20/23
c) 9/20
d) 6/7 Let f be a function defined on R (the set of all real numbers) such that f(x) = 2010 (x - 2009)^1 (x - 2010)^2(x - 2011)^3 (x - 2012)^4, for all x (R). If g is a function defined on R with values in the interval (0,0) such that f (x) = ln (g (x)), for all x R, then the number of points in R at which g has a local maximum is