Download PTU MCA 2020 Dec 2nd Sem 72876 Mathematical Foundations Of Computer Science Question Paper

Download PTU I. K. Gujral Punjab Technical University (IKGPTU) MCA (Master of Computer Applications) 2020 December 2nd Sem 72876 Mathematical Foundations Of Computer Science Previous Question Paper

Roll No.
Total No. of Pages : 02
Total No. of Questions : 18
MCA (2015 to 2018) (Sem.?2)
MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
Subject Code : MCA-201
M.Code : 72876
Time : 3 Hrs. Max. Marks : 60
INST RUCT IONS T O CAND IDAT ES :
1 .
SECT IONS-A, B, C & D c ontains TWO questions eac h carrying TEN marks each
and students has to a ttempt any ONE ques tion from eac h SECT ION.
2 .
SECT ION-E is C OMPULSORY consisting of T EN ques tions ca rryin g TWENTY
marks in all.
3 .
Use of n on-programm able sc ientific ca lc ula tor is a llowed.
SECTION-A
1.
Define Simple and Multi-graph. Prove that an undirected graph possesses an Eulerian path
if it is connected and has either zero or two vertices of odd degree.
2.
a) State and prove Five color theorem.
b) Explain the shortest path problem and also explain the algorithms used to find shortest
path.
SECTION-B
3.
a) Show that A (B C) = (A B) C.
b) Define intersection and union of sets. Prove that A B = A B if A = B.
4.
a) Define Minsets. Let B1, B2, B3 are the subsets of a universal set U. Find all minsets
generated by B1, B2 and B3.
b) Define Partitions of sets. Give all the partitions of {a, b, c, d, e}.
SECTION-C
5.
a) Test the validity of: If he works hard then he will be successful. If he is successful then
he will be happy. Therefore, hard work leads to happiness.
b) Prove that disjunction distributes over conjunction.
6.
a) Use Mathematical induction to show that 1 + 2 + ... ... ... + 2n = 2n ?1 ?1.
b) Define Quantifiers. Explain different types of quantifiers along with examples.
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SECTION-D
7.
Solve by Gauss Elimination method : x ? 2y ? 6z =12, 2x +4y +12z = ?17, x ? 4y ?12z = 22.
8.
Solve by matrix inversion method : x ? y + 3z = 2, 2x + y + 2z = 2, ?2x ? 2y + z = 3.
SECTION-E
Answer briefly :
9.
Define Complete Bipartite graph and give one example.
10. Define Euler and Hamilton graphs.
11. Define Complement of set and give example.
12. Can we say that Cartesian product is commutative? Justify.
13. Define Uncountable set.
14. Define tautologies and contradictions.
15. Prove that p q q p.
16. Define Symmetric and Skew-Symmetric.
1
2
1
3
17. If A
and B
,
Find AB.
3
0
3
1
1
1
18. Define inverse of a Square matrix and find the inverse of
.
3
4
NOTE: Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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