BCA-02
June Examination 2016
BCA Pt. I Examination
Discrete Mathematics
Paper BCA-02
Time 3 Hours Max. Marks 100
Note The question paper is divided into three sections B and C. Write answer as per the given instructions.
Section A 10 × 2 20
(Very Short Answer Questions)
Note: Answer all questions. As per the nature of the question delimit your answer in one word, one sentence or maximum upto 30 words. Each question carries 2 marks.
Write the names of different types of number system?
Explain sub sets?
What is contradiction?
Explain Domain and Range of Relation with example.
What is Poset?
Define the term Injective function.
Write the elementary properties of groups?
220
BCA-02 200 4 (P.T.O.)
220
BCA-02 200 4 (Contd.)
(viii) What is Rings?
Explain the Duality principle in Booleam algebra.
Explain the XNOR gate?
Section B 4 × 10 40
(Short Answer Questions)
Note: Answer any four questions. Each answer should not exceed
200 words. Each question carries 10 marks.
Explain the subtraction of binary No by compliment method
with example.
Describe the Laws of algebra of sets?
Make the Truth Table for the following:

What is inverse Relation? Explain with example.
Draw Hasse diagram of the poset where
aRb if a/b
Let f RuR and g RuR be two function such that f
g x/2 then find fog and gof?
Let f be a homomorphism from a group G into a group G1 then the
following are true
f e1, where e and e1 are identities of G and G1 respectively.
f for all a in G.
A subgroup N of a group G is normal in G if and only if xN Nx, for
each x∈G
BCA-02 200 4 (P.T.O.)
220
Section C 2 × 20 40
(Long Answer Questions)
Note: Answer any two questions. You have to delimit your each
answer maximum upto 500 words. Each question carries 20
marks.
10) Perform the following conversions.
(475)10
(110111)2
(765)8
(FIC)16
11) Describe following terms, with suitable example.
Domain and Range of Relation
Inverse Relation
Reflexive Relation
Symmetric Relation
Transitive Relation
Anti-symmetric Relation
Equivalence Relation
12) Write the negation of following statements.
If it is humid, then he wears cotton shirt but no cap.
If he makes money, then he will purchase a car or airship.
He plays only if the weather is cold.
If it rains, then he does not wear rain coat.
220
BCA-02 200 4
13) Transform the following Boolean expression into sum of
products.
x1x2 x1x x
1
2
1
1
1
3
1
x1x2 x . x x x
1
3
1
1
1
3 2
1
3
1 1 h h
Transform the following Boolean functions into conjunctive
normal form.
x2, x3) x1 (x1 x2) (x1 x2 x3)
x2, x3) (x1 x2) (x2 x3) (x1 x3)