Discrete Mathematics
Q121.
In the lattice defined by the Hasse diagram given in following figure, how many complements does the element 'e' have?Q122.
Consider the set X={a, b,c,d,e} under the partial ordering R={(a,a),(a,b),(a,c),(a,d),(a,e),(b,b),(b,c),(b,e),(c,c),(c,e),(d,d),(d,e),(e,e)}. The Hasse diagram of the partial order (X, R) is shown below. The minimum number of ordered pairs that need to be added to R to make (X, R) a lattice is _____.Q123.
The following is the Hasse diagram of the poset [{a,b,c,d,e}, \prec ] The poset is:Q124.
Let \delta denote the minimum degree of a vertex in a graph. For all planar graphs on n vertices with \delta \geq 3, which one of the following is TRUE?Q125.
In an undirected connected planar graph G, there are eight vertices and five faces. The number of edges in G is _________.Q126.
Consider a random experiment where two fair coins are tossed. Let A be the event that denotes HEAD on both the throws, B be the event that denotes HEAD on the first throw, and C be the event that denotes HEAD on the second throw. Which of the following statements is/are TRUE?Q127.
In an examination, a student can choose the order in which two questions (QuesA and QuesB) must be attempted. If the first question is answered wrong, the student gets zero marks. If the first question is answered correctly and the second question is not answered correctly, the student gets the marks only for the first question. If both the questions are answered correctly, the student gets the sum of the marks of the two questions. The following table shows the probability of correctly answering a question and the marks of the question respectively. \begin{array}{c|c|c} \text{question} & \text{probabiloty of answering correctly} & \text{marks} \\ \hline \textsf{QuesA} & 0.8 & 10 \\ \textsf{QuesB} & 0.5 & 20 \end{array} Assuming that the student always wants to maximize her expected marks in the examination, in which order should she attempt the questions and what is the expected marks for that order (assume that the questions are independent)?Q128.
K4 and Q3 are graphs with the following structures Which one of the following statements is TRUE in relation to these graphs?Q129.
Two numbers are chosen independently and uniformly at random from the set {1, 2, ..., 13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ___________Q130.
A class of 30 students occupy a classroom containing 5 rows of seats, with 8 seats in each row. If the students seat themselves at random, the probability that sixth seat in the fifth row will be empty is: