Twitter Facebook Delicious Digg Stumbleupon Favorites More

Monday, 13 March 2017

IPU BCA Semester 2 - Mathematics (End Term Paper 2015)

Second Semester [BCA]
Paper Code: BCA-102 

Subject: Mathematics

[2011 onwards] 
IPU BCA Semester 2 - Mathematics (End Term Paper 2015)

Time: 3 Hours Maximum Marks: 75
Note: Attempt any five questions including Q. no.1 which is compulsory. Select one question from each Unit.

Question 1:
(a) Let R be the relation in the natural number N defined by the open sentence "(x-y) is divisible by 5", prove that R is an equivalence relation. (4)

(b) Consider the bounded lattice L (4)

Find the compliments of a & c, if they exist.

(c) If f(x) = x³, then find f⁻ⁱ for all X ∈ R.   (4)
(d) Show that (A ⋃ E)c = Ac ⋂ Bc. (4)
(e) Define homomorphic and isomorphic graph. (4)
(f) Define Tauology and Contradiction.


Question 2:
(a) Let R and S be the following relations on:
B = {a, b. c, d}, R = {(a,a), (a,c), (c, b), (c,d), (d, b)} and
S = {(b, a), (c, c), (c, d), (d, a)}
Find the following composition relations.
(i) ROS
(ii) SOR
(iii) ROR
(iv) SOS

(b) Let U = {a, b, c, d, e}, A = (a,b,d) and B = (b, d, e).
(i) A ⋃ E
(ii) B ⋂ A
(iii) B — A
(iv) Ac ⋂ B
(v) Bc — Ac (6.5)

Question 3:
(a) Let R be the relation in the natural numbers N = {1, 2, 3, .... ..} defined by the open sentence "2x+y=10", that is, let R = {(x,y)| (x∈ N. y∈N, 2x + y = 10}.
(i) the domain of R
(ii) the range of R
(iii) R⁻ⁱ                                                              (6)
(b) Among 50 students in a class, 26 got an A in the first examination and 21 got an A in the second examination. If 17 students did not get an A in the either examination, how many students got A in both the examination? (6.5)


Question 4:
(a) Let B = {2, 3, 4, 5, 6, 8, 9, 10} be ordered by “x is a multiple of y”. (6)
(i) Find all maximal elements of E.
(ii) Find all minimal elements of B.
(iii) Does B have a first or a last element?

(b) State whether or not each of the following subsets of N is totally ordered: (6.5)
(i) {24, 2, 6)
(ii)  {3,15, 5}
(iii) {15,5,30}
(iv) {1,2, 3,... )

Question 5:
(a) Let R be the relation on A. (6)
A = {2, 3, 4, 6, 8, 12, 36, 48}.
R =  {(a, b) | a is divisor of b}. Draw Hasse diagram.

(b) Consider the lattice M is given below figure: (6.5)

(i) Find complements of a and b, if exist.
(ii) Is M distributive? Complemented?


Question 6:
(a) Give an example of Isomorphic graphs. Show that the graph G₁ and  G₂ are not isomorphic. (6)

(b) Define Adjacent matrix. Find the adjacency matrix of the graph G. (6.5)

Question 7:
(a) Define
(i) bipartite graph
(ii) Hamilton Graph
(iii) Cut-Vertical.

(b) Draw the directed graph of following incidence matrix:

       e₁  e₂   e₃   e₄   e₅   e₆
  V₁ │ 1   0    0    0    1    0  │
  V₂ │ 1   1    0    0    0    1  │
  V₃ │ -1  0    0    0    0    1  │
  V₄ │ 0   0    1    1    0    1  │ 

Also find the degree of all vertex.

Unit IV

Question 8:
(a) Construct the truth table of the following: (6)
(i) (~p ⋁ q) ⋁ ~p
(ii) (~q → ~p) → (p → q)
(b) Verify whether following are tautologies or not: (6.5)
(i) (q → p) ↔ (~q ⋁ p)
(ii) (p ⋀ (q — p)) → p

Question 9:
(a) Consider the following: (6)
p: Today is Monday.
q: It is hot.
r: It is not raining.
Write in simple sentence the meaning of the following:
(i) ~r  ⤇(r ⋀ q)
(ii) (p ⋁ r)c ⇔ a

(b) What is the truth value of the quantification (∃ x)Q(x), if the statement Q(x) and inverse of discourse is given as follows:                                  (6.5)
(i) Q(x): x > 32 U = {all real numbers}
(ii) Q(x): x = x + 2 U = {all real numbers}
(iii) Q (x) : x² < 12 U = {positive integer not exceeding 3}.



Post a Comment

NodeJS Tutorial

NodeJS Tutorial

Maths Resources

Maths Resources
Maths Resources

Buy Books

Buy Books
Buy Books

Geography Quiz

Geography Quiz
Geography Quiz

History MCQs

History MCQs
History Quiz For Competitive exams


Popular Posts


Recent Posts

Unordered List

Express Print Zone

Eduvictors Quizzes

Online Quizzes, Study notes for CBSE Class 6 - 12

Text Widget


Study notes for Competitive Exams

Developer Bytes

Developer Bytes
Developer Bytes
Powered by Blogger.

Blogger Tutorials

Blogger Templates

Sample Text

Copyright © IP University Musings BCA, MCA, BBA, MBA, BTech Question Papers and Study Notes | Powered by Blogger
Design by SimpleWpThemes | Blogger Theme by