IGNOU MTE13 Solved Assignment 2023  MTE
₹251.00
Please read the following points before ordering this IGNOU Assignment Solution.
Share with your Friends
IGNOU MTE13 Assignment Question Paper 2023
Course Code: MTE13
Assignment Code: MTE13/TMA/2023
Maximum Marks: 100
1. Check whether the following statements are true or not. Justify your answers with a short proof or a counter example.
i) If the contrapositive of a statement is true, then the statement itself is also true.
ii) \(a_{n}+3 a_{n1}+2 a_{n2}=2^{n}\) is a linear homogeneous recurrence relation.
iii) A particular solution of the recurrence relation \(a_{n}2 a_{n1}+a_{n2}=1\) has the form \(C n^{2}\).
iv) The edge chromatic number of the graph \(K_{6}\) is 5 .
v) If a dice is rolled thrice, then the probability of getting a 6 each time is \(\frac{1}{72}\).
vi) Every odd cycle has the same chromatic and edge chromatic numbers.
vii) Every Eulerian graph is Hamiltonian.
viii) \(S_{4}^{3}\) gives the number of ways in which any 3 objects can be placed in any 4 boxes.
ix) There exists a selfcomplementary planar graph on 5 or more vertices.
x) The number of partitions of 6 is 10 .
2. a) Draw the logic circuit for the Boolean expression \(\left(\left(x_{1} \wedge x_{2}\right)^{\prime} \vee x_{3}\right)^{\prime} \wedge x_{2}\).
b) Express the following statements in symbolic form.
i) There is a man in the park with blue eyes.
ii) Every blueeyed man in the park is wearing a red hat.
iii) If a man wears no hat, then he has black eyes.
c) Using generating functions find \(S_{n}=1+2+3+\ldots+n\).
3. a) There are about 77 crore ways to arrange the letters of the word “COMBINATORICS”. Count the exact number of such ways.
b) Solve the recurrence relation:
\[
a_{n}6 a_{n1}+9 a_{n2}=3^{n}
\]
c) List all the onto mappings from the set \(\{a, b, c, d\}\) to \(\{1,2,3,4\}\). How many onto mappings are there form \(\{a, b, c, d\}\) to \(\{1,2,3,4,5\}\) ? d) For any statements \(p, q\) and \(r\), prove that \((p \rightarrow q) \wedge(\sim q \rightarrow r) \wedge r \wedge \sim q \Rightarrow \sim p\).
4. a) Draw three nonisomorphic induced subgraphs of the following graph, each having the same number of vertices. Justify your choice.
b) Is the complement of the Peterson graph planar? Justify your answer.
c) What do you understand by a subdivision of a graph? Is every subdivision of a Hamiltonian graph Hamiltonian? Justify.
5. a) Let \(C_{n}\) denote the number of \(n\)tuples whose entries are 0 or 1 only, and two consecutive entries of which are zero.
i) Find \(C_{1}\) and \(C_{2}\).
ii) Find a recurrence relation for \(C_{n}\).
b) write down and count all the partitions of the number 7 . To verify your answer use the generating function for \(P_{n}\), taking \(n=7\) in Theorem 5 (of Unit 5, Block2).
6. a) Express \(x^{5}\) in terms of falling factorials and hence evaluate \(S_{5}^{m}\) for \(m=0,1,2,3,4,5\).
b) Find a recurrence relation for \(a_{n}\), the number of ways to arrange cars in a row with \(n\) spaces if we can use Maruti 800, Tata Safari or Scorpio. A Tata Safari or Scorpio requires two spaces, whereas a Maruti 800 requires just one space. Assume that you have unlimited number of each type of car and we do not distinguish between 2 cars of the same type.
c) Define the nth Bell number. Using the formula for Bell numbers or otherwise, determine \(B_{5}\)
d) Show that if 7 colours are used to paint 50 bicycles and each bicycle is coloured with a single colour, at least 8 bicycles will have the same colour.
7. a) Let \(\mathrm{T}\) be a graph such that between every two vertices of it there is exactly one path. Show that \(\mathrm{T}\) is a tree.
b) Define vertex connectivity and cut vertex set of any graph \(G\). Find the vertex connectivity and cut vertex set for the following graph:
c) How many numbers from 0 to 759 are not divisible by either 3 or 7 ?
8. a) Solve the recurrence relation:
\(a_{n}=2 a_{n1}+1\) if \(\mathrm{n} \geq 1\) and \(a_{0}=0\)
using generating function technique. Also find \(a_{5}\) using your answer.
b) Is there a 4regular graph on 7 vertices? Justify your answer.
c) Find the Boolean expression in the DNF form for the function defined in tabular form below:
x  y  z  f(x,y,z) 
1  0  1  1 
0  1  0  0 
0  0  1  1 
1  1  1  1 
1  0  0  0 
0  1  1  1 
1  1  0  1 
0  0  0  0 
MTE13 Sample Solution 2023
Frequently Asked Questions (FAQs)
You can access the Complete Solution through our app, which can be downloaded using this link:
Simply click “Install” to download and install the app, and then follow the instructions to purchase the required assignment solution. Currently, the app is only available for Android devices. We are working on making the app available for iOS in the future, but it is not currently available for iOS devices.
Yes, It is Complete Solution, a comprehensive solution to the assignments for IGNOU. Valid from January 1, 2023 to December 31, 2023.
Yes, the Complete Solution is aligned with the IGNOU requirements and has been solved accordingly.
Yes, the Complete Solution is guaranteed to be errorfree.The solutions are thoroughly researched and verified by subject matter experts to ensure their accuracy.
As of now, you have access to the Complete Solution for a period of 6 months after the date of purchase, which is sufficient to complete the assignment. However, we can extend the access period upon request. You can access the solution anytime through our app.
The app provides complete solutions for all assignment questions. If you still need help, you can contact the support team for assistance at Whatsapp +919958288900
No, access to the educational materials is limited to one device only, where you have first logged in. Logging in on multiple devices is not allowed and may result in the revocation of access to the educational materials.
Payments can be made through various secure online payment methods available in the app.Your payment information is protected with industrystandard security measures to ensure its confidentiality and safety. You will receive a receipt for your payment through email or within the app, depending on your preference.
The instructions for formatting your assignments are detailed in the Assignment Booklet, which includes details on paper size, margins, precision, and submission requirements. It is important to strictly follow these instructions to facilitate evaluation and avoid delays.
Terms and Conditions
 The educational materials provided in the app are the sole property of the app owner and are protected by copyright laws.
 Reproduction, distribution, or sale of the educational materials without prior written consent from the app owner is strictly prohibited and may result in legal consequences.
 Any attempt to modify, alter, or use the educational materials for commercial purposes is strictly prohibited.
 The app owner reserves the right to revoke access to the educational materials at any time without notice for any violation of these terms and conditions.
 The app owner is not responsible for any damages or losses resulting from the use of the educational materials.
 The app owner reserves the right to modify these terms and conditions at any time without notice.
 By accessing and using the app, you agree to abide by these terms and conditions.
 Access to the educational materials is limited to one device only. Logging in to the app on multiple devices is not allowed and may result in the revocation of access to the educational materials.
Our educational materials are solely available on our website and application only. Users and students can report the dealing or selling of the copied version of our educational materials by any third party at our email address (abstract4math@gmail.com) or mobile no. (+919958288900).
In return, such users/students can expect free our educational materials/assignments and other benefits as a bonafide gesture which will be completely dependent upon our discretion.
Related products

IGNOU Assignment Solution
IGNOU MEG14 Solved Assignment 20222023  MEG  Contemporary Indian Literature in English Translation
₹101.00 Go to the App 
IGNOU Assignment Solution
IGNOU MEG04 Solved Assignment 20222023  MEG  ASPECTS OF LANGUAGE
₹101.00 Go to the App