Punjab Technical University 2010 M.C.A -104 Computer Mathematical Foundation - Question Paper
PTU MCA-104 Computer Mathematical Foundation May 2010 ques. Paper
Roll No...........................................t
Total No. of Questions : 091
[Total No. of Pages : 02
COMPUTER MATHEMATICAL FOUNDATION SUBJECT CODE :MCA - 104 (N2)
Paper IP : [BO 104]
| Note: Please fill subject code and paper I Don OMR|
Time : 03 Hours Maximum Marks : 60 Instruction to Candidates:
1) Attempt any one question from each Sections A, B, C & D.
2) Section-E is Compulsory.
3) Use of non-programmable Scientific Calculator is allowed.
Section - A
Ql) Show that set of real numbers in [0, 1] is uncountable set.
Q2) Let R be a relation on A. Prove that
(a) If R is reflexive, so is R'1.
(b) R is symmetric if and only if R = R-1.
(c) R is antisymmetric if and only if R n R_1 c I
Section - B
Q3) If x and y denote any pair of real numbers for which 0 < x < y, prove by mathematical induction 0 < xn < y" for all natural numbers n.
Q4) (a) Obtain disjunctive normal forms for the following
(i) p A (p q).
(ii) p(pq)[v-(-qv~ p)].
(b) Define biconditional statement and tautologies with example.
Section - C
Q5) Find the ranks of A, B and A+B, where
|
1 1 |
-f |
'-1 |
-2 |
-f | ||
|
A = |
2 -3 |
4 |
and B - |
6 |
12 |
6 |
|
3 -2 |
3 |
_ 5 |
10 |
5 |
Q6) Solve the following equations by Gauss-Jordan method. 2x - y + 3z = 9,
x + y + z = 6, x ~y + z = 2.
Section - D
(1 x 10 = 10)
Q7) (a) Show that the degree of a vertex of a simple graph G on n vertices can not exceed n-1.
(b) A simple graph with n5 vertices and k components cannot have more
(n-kink + l) A than -'-i-L edges.
2
Q8) Define breadth first search algorithm (BFS) and back tracking algorithm for shortest path with example.
Section - E
Q9) a) Draw the truth table for - (p v q) v (~ p a ~ q).
b) Define principle of mathematical induction.
c) Prove that A - B = A n B\
*d) Using Venn diagram show that A A (B C) = (A A B) A C.
e) If A and B are two m x n matrices and 0 is the null matrix of the type m x n, show that A + B = 0 implies A = -B and B = -A.
f) If A and B are two equivalent matrices, then show that rank A = rank B.
g) Prove that every invertible matrix posseses a unique inverse.
h) Draw the graphs of the chemical molecules of
i) Methane (CH4).
ii) Propane (C3Hg).
i) Draw the digraph G corresponding to adjacency matrix
0 0 11 0 0 10 110 1 1110
A =
j) Give an example of a graph that has an Eulerian circuit and also Hamiltonian circuit.
J-319 2
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Attachment: |
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