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?Q35.
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 thatQ36.
Consider the function y=|x| in the interval [-1, 1]. In this interval, the function isQ37.
Consider the following directed graph: Which of the following is/are correct about the graph?[MSQ]Q38.
Let G be a simple, finite, undirected graph with vertex set \{v_1,...,v_n\}. Let \Delta (G) denote the maximum degree of G and let N=\{1,2,...\} denote the set of all possible colors. Color the vertices of G using the following greedy strategy: for i = 1,...,n color(v_i)\leftarrow min\{ j \in N: \text{ no neighbour of } v_i \text{ is colored } j\} Which of the following statements is/are TRUE?Q39.
Consider a simple undirected unweighted graph with at least three vertices. If A is the adjacency matrix of the graph, then the number of 3-cycles in the graph is given by the trace ofQ40.
The following simple undirected graph is referred to as the Peterson graph.Which of the following statements is/are TRUE?MSQ