Discrete Mathematics
Q31.
If the ordinary generating function of a sequence \{a_{n}\}_{n=0}^{\infty} \; is \; \frac{1+z}{(1-z)^{3}} then a_{3}-a_{0} is equal to ______.Q32.
Let A be a finite set having x elements and let B be a finite set having y elements. What is the number of distinct functions mapping B into A.Q33.
Let f: B \rightarrow C and g: A \rightarrow B be two functions and let h = f\cdotg. Given that h is an onto function which one of the following is TRUE?Q34.
Suppose X and Y are sets and |X| and |Y| are their respective cardinality. It is given that there are exactly 97 functions from X to Y. From this one can conclude thatQ35.
An articulation point in a connected graph is a vertex such that removing the vertex and its incident edges disconnects the graph into two or more connected components. Let T be a DFS tree obtained by doing DFS in a connected undirected graph G. Which of the following options is/are correct?Q36.
Let : A\rightarrowB be injective (one-to-one) function. Define g:2^{A}\rightarrow 2^{B} as: g(C) = {f (x)| x \inC), for all subsets C of A. Defineg:2^{B}\rightarrow 2^{A} as : h(D) = {x | x \in A, f (x) \in D}, for all subsets D of B. Which of the following statements is always true?Q37.
Consider the set of all functions f:{0,1,...,2014}\rightarrow{0,1...,2014} such that f(f(i))=i, for 0\leqi\leq2014 . Consider the following statements. P. For each such function it must be the case that for every i, f(i) = i, Q. For each such function it must be the case that for some i,f(i) = i, R. Each such function must be onto. Which one of the following is CORRECT?Q39.
Consider the following directed graph: Which of the following is/are correct about the graph?[MSQ]Q40.
In a directed acyclic graph with a source vertex s, the quality-score of a directed path is defined to be the product of the weights of the edges on the path. Further, for a vertex v other than s, the quality-score of v is defined to be the maximum among the quality-scores of all the paths from s to v. The quality-score of s is assumed to be 1. The sum of the quality-scores of all vertices on the graph shown above is ______