Please submit your Assignment on 2 March 2015, after that assignment will not be acceptable.
BCA-II Year
MATHS – II
ASSIGNMENT -2 ( RELATION AND FUNCTION)
1.
2.
3.
4.
5.
6. Show that (fog)-1 = g-1of-1
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Please submit your Assignment on 2 March 2015, after that assignment will not be acceptable.
BCA-II Year
ASSIGNMENT (UNIT-1 SET THEORY)
Maths-II
1. Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B) = 36,
find n(A ∩ B)
2. If n(A - B) = 18, n(A ∪ B) = 70 and n(A ∩ B) = 25, then find n(B)
3. In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person
likes at least one of the two drinks. How many like both coffee and tea?
4. There are 35 students in art class and 57 students in dance class. Find the number
of students who are either in art class or in dance class.
• When two classes meet at different hours and 12 students are enrolled in both
activities.
• When two classes meet at the same hour.
5 . In a group of 100 persons, 72 people can speak English and 43 can speak French.
How
many can speak English only? How many can speak French only and how many can
speak both English and French?
6.In a competition, a school awarded medals in different categories. 36 medals in dance, 12
medals in dramatics and 18 medals in music. If these medals went to a total of 45 persons
and only 4 persons got medals in all the three categories, how many received medals in
exactly two of these categories?
7.If A = {1, 3, 5}, B = {3, 5, 6} and C = {1, 3, 7}
(i) Verify that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
(ii) Verify A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
8. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4} and B = {2, 4, 6, 8}.
(i) Find A'
(ii) Find B'
9.Let A = {3, 5, 7}, B = {2, 3, 4, 6} and C = {2, 3, 4, 5, 6, 7, 8}
(i) Verify (A ∩ B)' = A' ∪ B'
(ii) Verify (A ∪ B)' = A' ∩ B'
10. Let A = {x : x is a natural number and a factor of 18} and B = {x : x is a natural
number and less than 6}. Find A ∪ B.
11.Let X = {1, 2, 3, 4}, Y = {2, 3, 5} and Z = {4, 5, 6}.
(i) Verify X ∪ Y = Y ∪ X
(ii) Verify (X ∪ Y) ∪ Z = X ∪ (Y ∪ Z)
12. Let A = {x : x is a natural number and a factor of 18}
B = {x : x is a natural number and less than 6}
Find A ∪ B and A ∩ B. Also find P(AUB), P(A ∩ B), P(A), P(B)
13. If P = {multiples of 3 between 1 and 20} and Q = {even natural numbers upto 15}.
Find the intersection of the two given set P and set Q.
14. Let A = {0, 1, 2, 3, 4, 5}, B = {2, 4, 6, 8} and C = {1, 3, 5, 7}
Verify (A ∩ B) ∩ C = A ∩ (B ∩ C)
15.Given three sets P, Q and R such that:
P = {x : x is a natural number between 10 and 16},
Q = {y : y is a even number between 8 and 20} and
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Please submit your Assignment on 2 March 2015, after that assignment will not be acceptable.
R = {7, 9, 11, 14, 18, 20}
(i) Find the difference of two sets P and Q
(ii) Find Q - R
(iii) Find R - P
(iv) Find Q – P
16.Find the cardinal number of a set from each of the following:
(i) P = {x | x ∈ N and x2 < 30}
(ii) Q = {x | x is a factor of 20}
17. For each statement, given below, state whether it is true or false along with the
explanations.
(i) {9, 9, 9, 9, 9, ……..} = {9}
(ii) {p, q, r, s, t} = {t, s, r, q, p}
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18.Fill in the blanks with
Recall that
a)
b)
c)
d)
e)
f)
2
{2}
1.5
-1.5
15
-15
,
,
,
, =, or ≠.
is the set of all integers and φ is the empty set, {}.
______
______
______
______
______
______
{2, 4, 6}
{2, 4, 6}
g)
h)
i)
j)
k)
l)
φ
______
54 ______
{6, 12, 18, …}
54 ______
{6, 12, 18}
{1, 3, 3, 5} ______
{1, 3, 5}
{-3, 1, 5}
______
{1, 3, 5}
{3, 1, 5}
______
{1, 3, 5}
19.Let A = {x, y} and B = {x, y, z}. write true and false
a) Is A a subset of B?
f) B ∩ A = {x, y} = A
b) Is B a subset of A?
g) A x B = {(x, x), (x, y), (x, z), (y, x),
(y, y), (y, z)}
h) B x A = {(x, x), (x, y), (y, x), (y, y),
(z, x), (z, y)}
i) P(A) = {φ, {x}, {x, y}}
c) A U B = {x, y, z} = B
d) B U A = {x, y, z} = B
e) A ∩ B = {x, y} = A
j) P(B) = {φ, {x}, {y}, {z}, {x, y},
{x, z}, {y,z}, {x, y, z}}
Assignment # 1
BCA-402
Operating Systems
Q1.
What is an operating System ? Why is the Operating system viewed as a “Resource Manager “?
Q2.
Describe Layered Approach based design for an O.S. What are its advantages?
Q3.
Describe functions of an Operating System.
Q4.
Define the essential properties of the following types of operating system:
a) Batch
b) Interactive
c) Time sharing
d) Real time
Q5.
Distinguish between Multi-programming and Multi-tasking.
Q6.
Explain the following memory allocation algorithm.
1) First – Fit
2) Best – Fit
3) Worst- Fit
Q7. Write short note on Page Fault. Write the steps to handle a page fault.
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Assignment # 2
BCA-402
Operating Systems
Q1.
Explain the concept of Process & its states.
Q2.
What is a Process Control Block? Explain all it’s components in brief.
Q3.
Discuss the purpose of short-term , medium term and long term schedulers.
Q4.
Define the following terms:
a) Average Waiting time
b) Time slice or quantum
c) Response time.
d) Turn - around time
e) CPU utilization
Q5.
Q6.
Explain Semaphore. How can a semaphore be used to enforce mutual exclusion? Elaborate the
Dinning Philosophers Problem.
Define critical section? What are the requirements to solve critical section problem?
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ASSIGNMENT – 2
BCA-IV Semester
OT
Instructions:



Last date of submission is 21st April 2015 and no assignments will be accepted after due
date.
Students have to submit assignments in a separate new register. Sheets in a folder will not
be accepted.
Incomplete assignments will not be accepted.
Q1: What is sequencing problem? Give the assumptions underlying the sequencing problem.
Q2: How will you solve the sequencing of n jobs on three machines and sequencing of n jobs on
two machines? Explain with steps and an example.
Q3: Find the optimum sequence for the following problem to minimize time and also obtain
elapsed time and idle time of all the machines:
J1
J2
J3
J4
J5
J6
A
13
8
12
7
10
6
B
8
9
10
7
6
11
C
13
12
11
14
15
14
Q4: A book binder has one printing press, one binding machine, and the manuscripts of a
number of different books. The time required to perform the printing & binding
operations for each book is shown below. Determine the order in which books should be
processed, in order to minimize the total time required to turn out all the books and idle
time on both the machines:
J1
J2
J3
J4
J5
J6
Printing time (hrs)
30
120
50
20
90
100
Binding time (hrs)
80
100
90
60
30
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Q5: Write short notes on:
(a) Idle time on a machine.
(b) Total elapsed time T.
Q6: What is an Assignment problem? Discuss the Hungarian method of solution. Give
various areas of its application.
Q7: Explain the similarities and differences between assignment and transportation
problem.
Computer Graphics & Multimedia Applications
Assignment # 1
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BCA-IV
Q1.
Define Computer Graphics. What are the different application areas of CG?
Q2.
Explain the process of Scan Conversion.
Q3.
Explain the role of CG in the field of:
a.
Entertainment
b.
Engineering
Q4.
Explain Framework for Interactive Graphics.
Computer Graphics & Multimedia Applications
Assignment # 2
BCA-IV
Q1. Explain any two Color generation techniques with diagram.
Q2. Find all the points to draw a circle of radius 10.
Q3. Write down the algorithm for DDA line drawing.
Q4. Explain CRT and its all components with the help of suitable
diagrams.
Q5. Differentiate Raster & Random Scan Graphics in detail.
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