Gate Exam

For each element in a set of size 2n,an unbiased coin is tossed. The 2ncoin tosses are
independent. An element is chosen if the corresponding coin toss were head. The probability
that exactly n elements are chosen is:

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Gate Other Question

A relation R is defined on ordered pairs of integers as follows:
(x,y)R(u,v)if x < u andy> v. Then R is:
(A) Neither a Partial Order nor an Equivalence Relation
(B) A Partial Order but not a Total Order
(C) A Total Order
(D) An Equivalence Relation
Let S = {1,2,3 ,m},m>3. Let X1 X be subsets of S each of size 3. Define a function ffrom Sto the set of natural numbers as, f(i)is the number of sets Xthat