Discrete Mathematics
Q121.
Consider the following Hasse diagrams.i.ii.iii.iv.Which all of the above represent a lattice?Q122.
In the lattice defined by the Hasse diagram given in following figure, how many complements does the element 'e' have?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.
Choose the correct alternatives ( more than one may be correct) and write the corresponding letters only:A non-planar graph with minimum number of vertices hasQ128.
The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is _________Q129.
Consider Guwahati (G) and Delhi (D) whose temperatures can be classified as high (G), medium (M) and low (L). Let P(H_{G}) denote the probability that Guwahati has high temperature. Similarly, P(M_{G}) and P(L_{G} ) denotes the probability of Guwahati having medium and low temperatures respectively. Similarly, we use P(H_{D}),P(M_{D}) and P(L_{D}) for Delhi. The following table gives the conditional probabilities for Delhi's temperature given Guwahati's temperature. Consider the first row in the table above. The first entry denotes that if Guwahati has high temperature (H_{G}) then the probability of Delhi also having a high temperature (H_{D}) is 0.40; i.e., (H_{D}|H_{G}) = 0.40. Similarly, the next two entries are P(M_{D}| H_{G})= 0.48 and P(L_{D}|H_{G}) = 0.12. Similarly for the other rows. If it is known that P(H_{G})= 0.2, P(M_{G})= 0.5, andP(L_{G})= 0.3, then the probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is _______Q130.
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)?