Download PTU BCA 2020 March 1st Sem BSBC 103 Mathematics I Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) BCA 2020 March (Bachelor of Computer Application) 1st Sem BSBC 103 Mathematics I Previous Question Paper

1 | M-10045 (S3)-1068
Roll No. Total No. of Pages : 02
Total No. of Questions : 07
BCA (2014 to 2018)/B.Tech. (CSE) (Sem.?1)
B.Sc.(IT) (2015 to 2018)
MATHEMATICS ? I
Subject Code : BSIT/BSBC-103
M.Code : 10045
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains SIX questions carrying TEN marks each and students have
to attempt any FOUR questions.

SECTION-A
1. Write briefly:
a) If A = {1, 2, a, b}, determine the following sets (i) A ? ? (ii) A ? {1, 2}.
b) Given an example of a relation which is reflexive and symmetric but not transitive.
c) Find relation R if matrix representation of R is
1 0 0
0 1 1
1 1 0
? ?
? ?
? ?
? ?
? ?
.
d) Prove that p ? (q ? r) = (p ?q) ? (p ?r)
e) Use quantifiers to show that 3 is not a rational number.
f) Define Planer and Complete Graph.
g) List two difference between Tree and Graph.
h) Find order of the recurrence Relation T (K) = 2T(k ? 1) ? kT(K ? 3).
i) Define recurrence relation with examples.
j) Prove that the maximum number of edges of simple graph is
( 1)
2
n n ?
.
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1 | M-10045 (S3)-1068
Roll No. Total No. of Pages : 02
Total No. of Questions : 07
BCA (2014 to 2018)/B.Tech. (CSE) (Sem.?1)
B.Sc.(IT) (2015 to 2018)
MATHEMATICS ? I
Subject Code : BSIT/BSBC-103
M.Code : 10045
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains SIX questions carrying TEN marks each and students have
to attempt any FOUR questions.

SECTION-A
1. Write briefly:
a) If A = {1, 2, a, b}, determine the following sets (i) A ? ? (ii) A ? {1, 2}.
b) Given an example of a relation which is reflexive and symmetric but not transitive.
c) Find relation R if matrix representation of R is
1 0 0
0 1 1
1 1 0
? ?
? ?
? ?
? ?
? ?
.
d) Prove that p ? (q ? r) = (p ?q) ? (p ?r)
e) Use quantifiers to show that 3 is not a rational number.
f) Define Planer and Complete Graph.
g) List two difference between Tree and Graph.
h) Find order of the recurrence Relation T (K) = 2T(k ? 1) ? kT(K ? 3).
i) Define recurrence relation with examples.
j) Prove that the maximum number of edges of simple graph is
( 1)
2
n n ?
.
2 | M-10045 (S3)-1068
SECTION-B
2. a) State and prove De Morgan?s law for sets.
b) Let m be a given fixed positive integer. Let R = {(a, b) : a, b ? Z and a ? b is
divisible by m}, show that R is an equivalence relation on Z.
3. a) Prove validity of argument :
If man is bachelor, he is happy.
Therefore Bachelor dies young.
b) By the principle of mathematical induction, prove the following for each n ? N : 1.3
+ 3.5 + 5.7 + ?. + (2n ? 1) (2n + 1) =
2
(4 6 1)
3
n n n ? ?

4. a) Find minimal spanning tree of weighted graph

b) State and prove five colour theorem.
5. Solve recurrence relation S (K + 2) ? 4S (K) = K
2
+ K ? 1.
6. a) Prove that simple graph with k-components and n vertices can have at the most of

( )( 1)
2
n k n k ? ? ?
edges.
b) Obtain recurrence relation of S (K) = 2.4
k
? 5. (?3)
k
of second order.
7. If R = {(a, b) : | a ? b | = 1} and S = {(a, b) : a ? b is even} are two relation on A = {1, 2,
3, 4}. Then draw digraph of R and S. And show that R
2
= S
2
.

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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