Download PTU BCA 2020 Dec 1st Sem 10045 Mathematics I Question Paper

Download PTU BCA ( Bachelor of Computer Applications) 2020 December 1st Sem 10045 Mathematics I Previous Question Paper

Roll No.
Total No. of Pages : 03
Total No. of Questions : 16
BCA (2014 to 2018) / B.Sc. (IT) (2015 to 2018) (Sem.?1)
MATHEMATICS-I
Subject Code : BSIT/BSBC-103
M.Code : 10045
Time : 3 Hrs. Max. Marks : 60
INST RUCT IONS T O CANDIDAT ES :
1 .
SECT ION-A is COMPULSORY cons is ting of TEN questions carrying TWO marks
each.
2 .
SECT ION-B c ontains SIX q uestions ca rryin g TEN mark s each a nd stu dents hav e
to attempt any FOUR questions .
SECTION-A
Write briefly :
Q1. If A, B, C are any sets, prove that A (B C) ( A B) ( A C) .
Q2. Define partition of sets.
Q3. Let X= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The family {{1,4,8}, {3,5.9},{2, 7}, {6, 10}} is a
partition of X. Determine the equivalence relation corresponding to the above partition.
Q4. Let X = {1, 2, 3, 4} and R = {(x, y): x > y}. Draw the diagraph and matrix of R.
Q5. Using truth table, prove that ~ ( p q) p ~ q.
Q6. Given the proposition over the natural numbers p: n < 4, q : 2n > 17 and r : n is a divisor of
18. What are the truth sets of p q and q r.
n(n 1)
Q7. Prove that the number of edges in a complete graph with n vertices is
.
2
Q8. Draw a simple planar graph with 6 nodes and 11 edges.
Q9. Define recurrence relation with example.
Q10. Solve the recurrence relation S(K) ? S(K ? 1) ? S(K ? 2) = 0.
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SECTION-B
Q11. a) State and prove De Morgan's Laws for sets.
b) The relation R is defined by (a, b) R if and only if 5 divides b ? a. Show that R is an
equivalence relation.
Q12. a) Let R = {(a, b): |a ? b| = 1} and S = {(a, b): a ? b is even} are two relations on
A = {1, 2, 3, 4}. Then
i) Find matrices of R and S.
ii) Draw diagraphs of R and S
iii) Using matrices of R and S, find the relation RS.
b) Test the validity of "If my brother stands first in the class, I will give him a watch.
Either he stood first or I was out of station. I did not give my brother a watch this time.
Therefore I was out of station."
Q13. a) Over the universe of Books, define the proposition B(x): x has a blue cover, M(x): x is
a mathematics book, U(x): x is published in United Estate and R(x, y): The
bibliography of x includes y.
Translate into words :
i) (x)(M (x) B(x)).
ii) (x)(M (x) U (x) B(x))
iii) (x)( B(x))
Express using quantifiers :
i) Every book with blue cover is a mathematics book.
ii) There are mathematics books that are published outside the United States.
iii) Not all books have bibliography.
b) Use Mathematical Induction to show that 1+2 + 4 + ...... + 2n = 2n+ l ? l.
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Q14. Using Dijkstra's Algorithm, find shortest path from A to D.
B
7
C
6
3
5
2
A
5
3
D
2
G
6
3
3
F
4
E
FIG. 1
Q15. a) Find the minimal spanning tree for the following weighted connected graph using
Kruskal's Algorithm.
B
2
D
F
5
4
5
E
3
3
G
4
2
5
4
A
2
C
H
FIG. 2
b) Solve S(K) ? 2 S(K ? 1) + S(K ? 2) = 0, where S(0) = 1, S(l) = 2.
Q16. a) Solve S(K) ? 7 S(K ? 1) + 10S(K ? 2) = 6 + 8K, where S(0) = l, S(l) = 2.
1
1
2
b) Find inverse of the matrix 2
1
3 .
3
1
1
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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