Sunday, July 28, 2019

Matrices and Determinants II

BCA

Practice Questions

Matrices and Determinants

Q1 Find A^-1

^{Q2 IF}

^{a) A+B, Check if A+B=B+A}
^{b) A-B}
c) B-A, Check if A-B=B-A

d) AXB, Check if AXB=BXA

e) (A)'

f ) A²
g) 3A + A²

Q 3 IF
$A=\begin{bmatrix} \frac{3}{2} & 2 &8 &1\\ 2& \frac{-1}{2} &5 &2\\ 1&3 & 11&3 \\ 1&1 & 9 & 1 \end{bmatrix} B=\begin{bmatrix} \frac{3}{5} & 2 &8& 2\\ 2& \frac{-3}{2} &5&1 \\ 1&3 & 9&5 \\ 1&3 & 9 &3 \end{bmatrix}$
a) A-B

b) A X B

Q4 Find the determinant of the following

$a) \begin{vmatrix} 1 &8 \\ 5&3 \end{vmatrix}$

$b) \begin{vmatrix} 1 &8&2 \\ 5&3&1 \\ 4&3&2 \end{vmatrix}$

$c) \begin{vmatrix} 1 &8&2 &1\\ 5&3&1&2 \\ 4&3&2&1\\ 4&3&2&1 \end{vmatrix}$

Solutions

Ans 1

$A^{-1}=\begin{bmatrix} \frac{-39}{2} &6 & 14\\ -13 &\frac{11}{2} &\frac{17}{2} \\ \frac{13}{2}& \frac{-5}{2} & \frac{-19}{2} \end{bmatrix}$

Ans 2

a)
$A+B=\begin{bmatrix} \frac{21}{10} & 4 & 16 \\ 4& -2 & 10\\ 2& 6 & 18 \end{bmatrix}$

$B+A=\begin{bmatrix} \frac{21}{10} & 4 & 16 \\ 4& -2 & 10\\ 2& 6 & 18 \end{bmatrix}$

hence A+B=B+A

b)
$A-B=\begin{bmatrix} \frac{9}{10} & 0 & 0 \\ 0& 1 & 0\\ 0& 0 & 0 \end{bmatrix}$

c)
$A-B=\begin{bmatrix} \frac{9}{10} & 0 & 0 \\ 0& 1 & 0\\ 0& 0 & 0 \end{bmatrix}$

$B-A=\begin{bmatrix} \frac{-9}{10} & 0 & 0 \\ 0& -1 & 0\\ 0& 0 & 0 \end{bmatrix}$

hence A-B is not equal to B-A

d)
$A X B=\begin{bmatrix} \frac{129}{10} & 24 & 94\\ \frac{26}{5}& \frac{79}{4} &\frac{117}{2} \\ \frac{78}{5}& \frac{49}{2} & 104 \end{bmatrix}$

$B X A= \begin{bmatrix} \frac{129}{10} & \frac{121}{5} & \frac{434}{5}\\ 5 & \frac{79}{4} & \frac{107}{2} \\ \frac{33}{2} & \frac{35}{2}& 104 \end{bmatrix}$

Hence AXB is not equal to BXA
e)
$A'=\begin{bmatrix} \frac{3}{2} &2 &1 \\ 2& \frac{-1}{2} &3 \\ 8& 5 &9 \end{bmatrix}$

f)
$A^2=\begin{bmatrix} \frac{57}{4} &26 &94 \\ 7& \frac{77}{4} &\frac{117}{2} \\ \frac{33}{2}& \frac{55}{2} &104 \end{bmatrix}$

g)

$3A+A^2=\begin{bmatrix} \frac{75}{4}& 32 & 118 \\ 13& \frac{71}{4} & \frac{147}{2}\\ \frac{39}{2}&\frac{73}{2} & 131 \end{bmatrix}$

Ans 3

a)
$A-B=\begin{bmatrix} \frac{9}{10} & 0 & 0 & -1\\ 0& 1 &0 &1 \\ 0 &0 &2 &-2 \\ 0& -2 & 0 & -2 \end{bmatrix}$

b)
$A X B=\begin{bmatrix} \frac{139}{10} & 27 & 103 & 48\\ \frac{36}{5}& \frac{103}{4} &\frac{153}{2} &\frac{69}{2} \\ \frac{103}{5}&\frac{79}{2} &149 &69 \\ \frac{63}{5}&\frac{61}{2} & 103 & 51 \end{bmatrix}$

Ans 4

a) -37

b)
$\frac{-13}{4}$

c) 0

Saturday, July 27, 2019

Result

Test Dated 27/07/2019

S#	Candidate Name	Topic	Max Marks 50
1	Ravkirat Gulati	Linear equations and quadrilateral	36
2	Rhea Khanna	Integers,data handling and lines & angles	31
3	Kunal	Rational no, square roots and cube roots	44

Thursday, July 25, 2019

Matrices and Determinants

Q1 If

$A=\begin{bmatrix} 1 &3 & 5\\ -6& 1 & 8\\ -1& 3 & 4 \end{bmatrix} B=\begin{bmatrix} 4 &-1 &3 \\ 2 & 5 &4 \\ -9& 2 & 6 \end{bmatrix}$

Find

a) A+B

b) A-B

c) AxB

d) Adj(A)

e) A^-1

^f) (A')

^{Q2 Find the product of the following matrices}

$a)\begin{bmatrix} 3 \\ -1 \\ 9 \end{bmatrix} \begin{bmatrix} 1 & 8 & 6 \end{bmatrix}$

$b)\begin{bmatrix} 1 & 8 & 6 \end{bmatrix} \begin{bmatrix} 3 \\ -1 \\ 9 \end{bmatrix}$

$c) \begin{bmatrix} 1 & 3 &2 \\ -1& 7 &-1 \\ 2& 3& 6 \end{bmatrix} \begin{bmatrix} 2 & 5& 6\\ 1& 3& -2 \end{bmatrix}$

$d) \begin{bmatrix} 1 & 6 &2 \\ 2 & -4 & 1 \end{bmatrix} \begin{bmatrix} 1 & 2 &6 \\ 4& 3 & 1\\ 8&6 & 9 \end{bmatrix}$

$e) \begin{bmatrix} 1 & 6 &2 \\ \end{bmatrix} \begin{bmatrix} 1 & 2 &6 \\ 4& 3 & 1\\ 1&6 & 9 \end{bmatrix}$

Q3 Solve the following equation using cramer's rule

2x +   y + z = 3
  x –   y – z = 0
  x + 2y + z = 0

Q4 Find the determinant of the following

$a) \begin{vmatrix} -1 & 4\\ 2& 3 \end{vmatrix}$

$b) \begin{vmatrix} 1 & 3 & -2\\ 6 & 1 & 2\\ 4 & 3 & 7 \end{vmatrix}$

Solutions

Ans 1

$a) \begin{bmatrix} 5 & 2 & 8\\ -4 & 6 & 12\\ -10 & 5 & 10 \end{bmatrix}$

$b) \begin{bmatrix} -3 & 4 & 2\\ -8 & -4 & 4\\ 8 & 1 & -2 \end{bmatrix}$

$c) \begin{bmatrix} -35 & 24 & 45\\ -94 & 27 & 34\\ -34 & 24 & 33 \end{bmatrix}$

$d) \begin{bmatrix} -20 & 3 & 19\\ 16 & 9 & -38\\ -17 & -6 & 19 \end{bmatrix}$

$e) \frac{1}{57}\begin{bmatrix} -20 & 3 & 19\\ 16 & 9 & -38\\ -17 & -6 & 19 \end{bmatrix}$

$f) \begin{bmatrix} 1 & -6 & -1\\ 3 & 1 & 3\\ 5 & 8 & 4 \end{bmatrix}$

Ans 2

$a) \begin{bmatrix} 3 & 24 & 18\\ -3 & -8 & -6\\ 9 & 72 & 54 \end{bmatrix}$

b) [49]

c) Not defined

$d) \begin{bmatrix} 41 & 32 & 30\\ -6 & -2 & 17\\ \end{bmatrix}$

$e) \begin{bmatrix} 27 & 32 & 30\\ \end{bmatrix}$

Ans 3

x=1, y=-2, z=3

Ans 4

a) -11 b) -129

Tuesday, July 23, 2019

Courses@INFATE Academy

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Wednesday, July 17, 2019

Polygons

INFATE ACADEMY

www.infate.in

blog.infate.in

Grade 8

Polygons, Quadrilaterals and Parallelograms

Practice Questions

Q1 Find the measure of exterior angle of a regular polygon of

a)8 sides b) 5 sides c) 12 sides

Q2 Is it possible to have a regular polygon each of whose exterior angles is 25 degree?

Q3 What is the minimum interior angle possible for a regular polygon?

Q4 Find the measure of each interior angle of a regular polygon.
a)Triangle b) Polygon with 13 sides c) Polygon with 11 sides

Q5 What is the sum of all interior angles of a polygon of following sides?
a) 5 sides b) 9 sides c) k+1 sides

Q6 What is the number of diagonals in the following..?

a)Octagon b) Decagon c) Polygon with 14 sides

Q7 Find the number of sides of a regular polygon whose each exterior angle measures 60 degree.

Q8 Find the measure of exterior and interior angle of octagon.

Q9 The four angles of Quadrilateral are in ratio of 2:3:5:8. Find each angle of Quadrilateral.

Q10 The measure of two angles of Quadrilateral are 110 and 70 degree. Also the other two angles are equal. Find the measure of the equal angles.

Q 11 Prove that the sum of the angles of a quadrilateral is 360 degree.

Q12 Three angles of Quadrilateral are equal and the fourth angle is of 60 degrees. Find the measure of three remaining angles.

Q13 ABCD is a parallelogram in which $\angle A$ = 100 degree. Find the measure of each of the remaining angles( $\angle B \angle C \angle D$ )

Q14 If one adjacent angle is half the other. Find the measure of all the angles of a parallelogram.

Q15 If the two adjacent angles of Parallelogram are equal. What is the measure of each of these angles.

Q16 The sum of two opposite angles of a parallelogram is 120 degrees. Find the measure of each of its angle.

Q17 Two adjacent angles of a Parallelogram are (2x+8) and (4x+4). Find the measure of each angle .

Q18 The length of diagonals of Rhombus are 6cm and 8 cm respectively. Find the length of each side.

Sunday, June 9, 2019

Advance Database Management System-Notes

Quick Notes

DBMS Notes

Functional Dependency: It is an association between two attributes of the same table ( relation)

Let X and Y are attributes of the same table then

X->Y states that if two tuple agree on the values in attribute "X", they must also agree on value in attribute "Y"

Keys in Database

A key is a set of one or more attributes, which is used for unique identification with in a table

Types of keys

1) Super Key: A Super key is a set of one or more attributes that uniquely identifies each record with in a table.

2) Candidate Key: Candidate key is a minimal superkey, which contains no extra attributes. Also it contain maximum possible attributes which uniquely identifies each record or A table may have one or more choices for the primary key. Collectively these are known as candidate keys

3) Primary Key: Primary key is an attribute which uniquely identifies each record with in a table.

4) Foreign Key : A foreign key are attributes in a table whose value match as primary key in another table.

a) Foreign key can contain duplicate value

b) Also can contain NULL value

Prime attribute: It is present in any of the candidate key

Non prime attribute: It is not present in Candidate key.

Secondary / Alternate keys: Once we have selected the one primary key then remaining attributes in a table are called secondary keys or alternate keys. or the candidate keys which are not selected as primary key are also called secondary key or alternate keys.

Composite key or concatenated key: Whenever we choose multiple attribute to create a primary key then that primary key is called composite key.

Normalization is breaking of table and relation in multiple tables so that we reduce the redundancy and we can make it more efficient and error free.

First Normal form: A table is said to be in first normal form if and only if

1) Values of each attribute is atomic

2) No composite values

3) All entries in any column must be of the same kind

4) Each column must have a unique name

5) No two rows are identical

Second Normal Form: A relation is said to be in 2NF if it is in 1NF and All non prime attributes are fully functional dependent on any key of R.

1) Table should be in first form and

2) It should not have any partial dependencies.

Third Normal Form: A relation is said to be in 3NF,

1) If it is in 2 NF

2) And it should not have any transitive dependencies

BCNF: A relation is said to be in BCNF( Boyce codd Normal Form)

1) If it is in 3 NF

2) For any dependency A->B(A should be super key). IF A is non prime then B is prime attribute.

Partial Dependency: A part of primary key A-> Non prime attribute B

Transitive Dependency: Non prime A-> Non prime B

4 NF: A relation is said to be in 4NF If and only if

1) It is in BCNF

2) It should not have MVD(Multi valued dependencies

5 NF: A relation is said to be in 5 NF if and only if

1) It is in 4 NF

2) Join dependency exists decompose the table. Decomposition should not create new data or loss of data during the operation.

Shadow Paging(Database Recovery)

-Requires fewer disk access than do-log methods
-Maintain two page tables during the life cycle of transaction When transaction starts both pages tables are identical.
-Shadow page table is never changed over duration of transaction.
-Current page table may be changed during write operation
-All I/P and o/p operations use the current P.T to locate db pages on disk.
-Store shadow Page table in non-volatile storage.

Directory
1) Current page table
2) Shadow page table
When Transaction commits system writes current page table to non-volatile storage. The current PT then becomes new shadow Page Table
Advantages of shadow paging over log-based techniques
1) Log-record overhead is removed.
2) Faster Recovery(Undo/Redo Transaction)

Drawbacks of shadow paging
1) Commit Overhead
Single transaction
a) actual data blocks
b) Current P.T
c) Disk address of current page table

2) Data Fragmentation
Location property is lost. Shadow paging causes database pages to change location

3) Garbage collection: When transaction commits, database pages containing old unison of data changed by transaction become inaccessible.

DBMS checkpoints

Checkpoints

The following problem occurs during recovery procedure:
• searching the entire log is time-consuming as we are not aware of the
consistency of the database after restart. Thus, we might unnecessarily redo
transactions, which have already output their updates to the database.
Thus, we can streamline recovery procedure by periodically performing check
pointing. Check pointing involves:
• Output of all the log records currently residing in the non-volatile memory onto
stable storage.
• Output all modified buffer blocks to the disk.
• Write a log record < checkpoint> on a stable storage.
During recovery we need to consider only the most recent transactions that started
before the checkpoint and is not completed till, checkpoint and transactions started
after check point. Scan backwards from end of log to find the most recent
<checkpoint> record. Continue scanning backwards till a record <Ti start> is found.
Need only consider part of the log following above start record. The earlier part of the
log may be ignored during recovery, and can be erased whenever desired. For all
transactions (starting from Ti or later) with no <Ti commit>, execute undo (Ti ).
(Done only in case immediate modification scheme is used). Scanning forward in the
log, for all transactions starting from Ti or later with a <Ti commit>, execute redo(Ti).

Important Concepts

Data warehouse concepts
Extract transform load
Data warehousing and Data mining
K mean clustering
Multimedia Database
Spatial database
Explain Star Schema and Snow Flake Design
Apriori algorithm

System Catalog: The system catalogue is a collection of tables and views that contain important information about a database.In relational DBMSs the catalogue is stored as relations.
The DBMS software is used for querying, updating, and maintaining the catalogue. This allows DBMS routines (as well as users) to access. The information stored in the catalogue can be accessed by the DBMS routines as well as users upon authorisation with the help of the query language such as SQL.
The information stored in a catalogue of an RDBMS includes:
• the relation names,
• attribute names,
• attribute domains (data types),
• descriptions of constraints (primary keys, secondary keys, foreign keys, NULL/ NOT NULL, and other types of constraints),
• views, and
• storage structures and indexes (index name, attributes on which index is defined, type of index etc).
Security and authorisation information is also kept in the catalogue, which describes:
• authorised user names and passwords,
• each user’s privilege to access specific database relations and views,
• the creator and owner of each relation. The privileges are granted using GRANT command. A listing of such commands is given in Figure 1.
The system catalogue can also be used to store some statistical and descriptive information about relations. Some such information can be:
• number of tuples in each relation,
• the different attribute values,
• storage and access methods used in relation.
All such information finds its use in query processing.

Data Dictionary

The data dictionary stores useful metadata, such as field descriptions, in a format that is independent of the underlying database system. Some of the functions served by the Data Dictionary include:
• ensuring efficient data access, especially with regard to the utilisation of indexes,
• partitioning the database into both logical and physical regions,
• specifying validation criteria and referential constraints to be automatically enforced,
• supplying pre-defined record types for Rich Client features, such as security and administration facilities, attached objects, and distributed processing (i.e., grid and cluster supercomputing).

Catalog system vs Data Dictionary

A catalogue is closely coupled with the DBMS software; it provides the information stored in it to users and the DBA, but it is mainly accessed by the various software modules of the DBMS itself, such as DDL and DML compilers, the query optimiser, the transaction processor, report generators, and the constraint enforcer.
On the other hand, a Data Dictionary is a data structure that stores meta-data, i.e., data about data. The software package for a stand-alone data dictionary or data repository may interact with the software modules of the DBMS, but it is mainly used by the designers, users, and administrators of a computer system for information resource management. These systems are used to maintain information on system hardware and software configurations, documentation, applications, and users, as well as other information relevant to system administration.

Passive and Active Data Dictionary

If a data dictionary system is used only by designers, users, and administrators, and not by the DBMS software, it is called a passive data dictionary; otherwise, it is called an active data dictionary or data directory. An active data dictionary is automatically updated as changes occur in the database. A passive data dictionary must be manually updated.
The data dictionary consists of record types (tables) created in the database by system-generated command files, tailored for each supported back-end DBMS. Command files contain SQL statements for CREATE TABLE, CREATE UNIQUE
INDEX, ALTER TABLE (for referential integrity), etc., using the specific SQL statement required by that type of database.

Data Dictionary Features

A comprehensive data dictionary product will include:
• support for standard entity types (elements, records, files, reports, programs, systems, screens, users, terminals, etc.), and their various characteristics (e.g., for elements, the dictionary might maintain Business name, Business definition, name, Data type, Size, Format, Range(s), Validation criteria, etc.)

• support for user-designed entity types (this is often called the “extensibility” feature); this facility is often exploited in support of data modelling, to record and cross-reference entities, relationships, data flows, data stores, processes, etc.

• the ability to distinguish between versions of entities (e.g., test and production)

• enforcement of in-house standards and conventions.

• comprehensive reporting facilities, including both “canned” reports and a reporting language for user-designed reports; typical reports include:

• detail reports of entities

• summary reports of entities

• component reports (e.g., record-element structures)

• cross-reference reports (e.g., element keyword indexes)

• where-used reports (e.g., element-record-program cross-references).

• a query facility, both for administrators and casual users, which includes the ability to perform generic searches on business definitions, user descriptions, synonyms, etc.

• language interfaces, to allow, for example, standard record layouts to be automatically incorporated into programs during the compile process.

• automated input facilities (e.g., to load record descriptions from a copy library).
• security features

• adequate performance tuning abilities

• support for DBMS administration, such as automatic generation of DDL (Data Definition Language).
Data Dictionary Benefits

The benefits of a fully utilised data dictionary are substantial. A data dictionary has the potential to:
• facilitate data sharing by
• enabling database classes to automatically handle multi-user coordination, buffer layouts, data validation, and performance optimisations,
• improving the ease of understanding of data definitions,
• ensuring that there is a single authoritative source of reference for all users
• facilitate application integration by identifying data redundancies,
• reduce development lead times by
• simplifying documentation
• automating programming activities.
• reduce maintenance effort by identifying the impact of change as it affects:
• users,
• data base administrators,
• programmers.
• improve the quality of application software by enforcing standards in the development process
• ensure application system longevity by maintaining documentation beyond project completions
• data dictionary information created under one database system can easily be used to generate the same database layout on any of the other database systems BFC supports (Oracle, MS SQL Server, Access, DB2, Sybase, SQL Anywhere, etc.)
These benefits are maximised by a fully utilised data dictionary. As the next section will show, our environment is such that not all of these benefits are immediately available to us.

Disadvantages of Data Dictionary

A DDS is a useful management tool, but it also has several disadvantages.
It needs careful planning. We would need to define the exact requirements designing its contents, testing, implementation and evaluation. The cost of a DDS includes not only the initial price of its installation and any hardware requirements, but also the cost of collecting the information entering it into the DDS, keeping it up-to-date and enforcing standards. The use of a DDS requires management commitment, which is not easy to achieve, particularly where the benefits are intangible and long term.
Catalogue in Distributed Database Systems

The data dictionary stores useful metadata on database relations. In a Distributed database systems information on locations, fragmentations and replications is also added to the catalogues.
The distributed database catalogue entries must specify site(s) at which data is being stored in addition to data in a system catalogue in a centralised DBMS. Because of data partitioning and replication, this extra information is needed. There are a number of approaches to implementing a distributed database catalogue.
• Centralised: Keep one master copy of the catalogue,
• Fully replicated: Keep one copy of the catalogue at each site,
• Partitioned: Partition and replicate the catalogue as usage patterns demand,
• Centralised/partitioned: Combination of the above.

Catalogue in Object Oriented Database Systems

An object oriented database systems brings together the features of object-oriented programming and the advantages of database systems under one persistent DBMS interface. Thus, they are very useful in applications with complex interrelationships, complex classes, inheritance etc. However, as far as data dictionary is concerned, it now additionally needs to describe few more classes, objects and their inter-relationships. Thus, a data dictionary for such a system may be more complex from the viewpoint of implementation; however, from the users point of view it has almost similar concepts. This data dictionary should now also store class definitions including the member variables, member functions, inheritances and relationships of various class objects.

ROLE OF SYSTEM CATALOGUE IN DATABASE ADMINISTRATION

Assertion:
Assertions are constraints that are normally of general nature. For example, the age of the student in a hypothetical University should not be more than 25 years or the minimum age of the teacher of that University should be 30 years. Such general constraints can be implemented with the help of an assertion statement. The syntax for creating assertion is:
Syntax:
CREATE ASSERTION <Name>
CHECK (<Condition>);
Thus, the assertion on age for the University as above can be implemented as:
CREATE ASSERTION age-constraint
CHECK (NOT EXISTS (
SELECT *
FROM STUDENT s
WHERE s.age > 25
OR s.age > (
SELECT MIN (f.age)
FROM FACULTY f
));
View : A view is a virtual table, which does not actually store data.view actually is a query and thus has a SELECT FROM WHERE ….. clause which works on physical table which stores the data. Thus, the view is a collection of relevant information for a specific entity.
Example: A student’s database may have the following tables:
STUDENT (name, enrolment-no, dateofbirth)
MARKS (enrolment-no, subjectcode, smarks)
For the database above a view can be created for a Teacher who is allowed to view only the performance of the student in his/her subject, let us say MCS-043.
CREATE VIEW SUBJECT-PERFORMANCE AS
(SELECT s.enrolment-no, name, subjectcode, smarks
FROM STUDENT s, MARKS m
WHERE s.enrolment-no = m.enrolment-no AND
subjectcode ‘MCS-043’ ORDER BY s.enrolment-no;
A view can be dropped using a DROP statement as:
DROP VIEW SUBJECT-PERFORMANCE;

Stored Procedures

Stored procedures are collections of small programs that are stored in compiled form and have a specific purpose. For example, a company may have rules such as:
• A code (like enrolment number) with one of the digits as the check digit, which checks the validity of the code.
• Any date of change of value is to be recorded.
The use of procedure has the following advantages from the viewpoint of database application development.
• They help in removing SQL statements from the application program thus making it more readable and maintainable.
• They run faster than SQL statements since they are already compiled in the database.
Stored procedures can be created using CREATE PROCEDURE in some commercial DBMS.
Syntax:
CREATE [or replace] PROCEDURE [user]PROCEDURE_NAME
[(argument datatype
[, argument datatype]….)]
Triggers
These events may be database update operations like INSERT, UPDATE, DELETE etc. A trigger consists of these essential components:
• An event that causes its automatic activation.
• The condition that determines whether the event has called an exception such that the desired action is executed.
• The action that is to be performed.

Database Security

Basically database security can be broken down into the following levels:
• Server Security
• Database Connections
• Table Access Control
• Restricting Database Access

Statistical Database Security...

Wednesday, June 5, 2019

Maths Question Bank

Maths Practice Question

Grade 7th and 8th

Q1 In an examination,96% of the candidates passed and 50 failed. What is the number of candidates who appeared for the examination.
Ans Given

Passed candidates =96%

Total appeared =100%

Faild=100-96=4%

According to question failed =50

So
4%=50

1%=50/4

1%=12.5

Total=100x12.5=1250

Total candidates appeared in examination =1250

Q2 If the ratio of circumferences of two circles is 4:9, what is the ratios of their areas?(Ans 2:3)

Q3 If the perimeter of a square increases by 25%, what is the increase in its
area?
Let the side of square be x.

Perimeter of square = 4x

Increase in perimeter = 25% of 4x

$= \frac{25}{100} \times 4x \\ \\ = \frac{100x}{100} \\ \\ = x$
New perimeter = 4x +x = 5x

Let the new side be y.

4y = 5x

$y = \frac{5}{4} x \\$
$old \: area = {x}^{2} \\ \\ new \: area \: = {y}^{2} \\ \\ = {( \frac{5}{4}x) }^{2} \\ \\ = \frac{25}{16} {x}^{2}$
$old \: area = {x}^{2} \\ \\ new \: area \: = {y}^{2} \\ \\ = {( \frac{5}{4}x) }^{2} \\ \\ = \frac{25}{16} {x}^{2}$

ans $= \frac{25}{16} {x}^{2} - {x}^{2} \\ \\ = {x}^{2} ( \frac{25}{16} - 1) \\ \\ = {x}^{2} ( \frac{25 - 16}{16} ) \\ \\ = {x}^{2} ( \frac{9}{4} ) \\ \\ = \frac{9}{4} times \: of \: old \: area$

Q4 To John put his hand watch on the table in such a way that at 6 pm hour hands point to East. In which direction the minute hand will point at 9:15 PM?

Ans At 6pm the hour hand is at 6. It is given that the direction is north wrt to John. That means John is sitting on 12 side facing the watch.

Now considering centre of the watch as the point of reference , 6 is in north, 3 (15 min) is in west. At 9.15 min hand will be in WEST.

Q5 Andy walked 35m towards south. The he turned to his left and walked 25 m. He turned to his left and walked 12m. What distance he from the starting point and in which direction?(Ans square root 1154 and north west)

Q6 Two-fifth of one-fourth of three-seventh of a number is 15. What is the half of that number?
Ans 2/5×1/4×3/7 x = 15
6/140 x = 15
x = (15 × 140)/6
x = 350
Half of 350 = 175

Q7 Two numbers are such that the ratio between them is 4:7. If each is increased by 4, the ratio becomes 3:5. Find the larger number.(Ans 56)

Q8 The first angle of a triangle is three times as great as the second angle. The third angle measures 12 degrees less than twice the second angle.
Ans Since angle 2 is being compare to both angle 1 and angle 2, let

∠2 = x

∠1 = 3x

∠3 = 2x - 12

Since there are 3 angles, we can assume we will have a triangle. The sum of the angles of any triangle is equal 180 degrees.

x + 3x + (2x - 12) = 180

x + 3x + 2x - 12 = 180

6x - 12 = 180

6x = 192

x = 32

Substitute this x value into the three angles.

∠1 = 96 degrees

∠2 = 32 degrees

∠3 = 52 degrees

Q9 Peter is three time as old as Anna. The sum of their ages five years from now will be twice Peters present age. The age of Peter is?( Peter Age is 15, Anna is 5 Years old)

Q10 The ratio of two smaller sides of a triangle is 4:3. A rectangle is formed on the largest side of the triangle in such a way that largest side will be the length of the rectangle. The breadth of rectangle is four fifth of its length. Find the length of shortest side of triangle if the perimeter is 1.8 m.
Ans : Ans let the base of triangle be 4x , height be 3x and the length of rectangle or hypotenuse of triangle be h and breadth of rectangle be 4/5h

h = \sqrt{{(3 \cdot a)}^{2} + {(4 \cdot a)}^{2}}

h = 5 \cdot a

so, breath will be

\frac{4}{5} \cdot 5 \cdot a = 4 \cdot a

perimeter = 180 cm

2 \cdot (l + b) = 180

5 \cdot a + 4 \cdot a = 90

9x=180
x=10
so shortest side be the perpendicular 3x=3 x 10 = 30 cm

Q11 A group of boys went to a restaurant for lunch,where 40% of the boys ordered pizza and the remaining six boys ordered burger. How many boys went to the restaurant.

Q12 When a number is reduced by 4, it becomes 80% of itself. find the number.
(Ans 20)

Q13 One of the angles of a certain triangle is three times the second angle and third is 16 smaller than the first. Find the three angles.

Q 14 A frog is at the bottom of a 20 foot well. Each day it jumps up 4 feet but each night it slips back 3 feet. How many days are required for the frog to reach the top of the well?

Ans 4-3=1 ft. gain each day.
15 days=15 ft. gained.
The 16th. day 15+4=19-3=16 ft.
The 17th. day 16+4=20 ft. & out for the frog on the 17th. day.

Q 15 Ankur works in a ten story office building. He gets on at the fourth floor and rides to the floor. He then goes down seven floors, rides up four floors. If the display of the lift indicating position is malfunctioning. Where is Ankur now and how many floors should he move in order to reach the first basement?

Q16 The melting point of Hg(mercury) is -39 degree Celsius. The freezing point of alchohol is -90 degree Celsius. How much more is the melting point of Hg as compared to freezing point of alcohol?

Q 17 A T.V. was sold at 19/24 of its original price. If the original price was INR 12,000 . Calculate the selling price of the T.V. Also calculate discount given.

Q 18 In a bracelet only 0.88 part of 22.5g overall bracelet is made of gold. If the bracelet is cut into five equal pieces. How much gold is there in each piece?

Q 19 There are 120 seats in the balcony of a theatre. If this is 1/5th of the total seat, what is total number of seats in the theatre?
Q 20 Give 3 integers whose sum is -12, of these there should be 2 negative integers and 1 positive integer.
Q 21 The temperature of a place at 12 noon was 14 degree Celsius. If it decreased by 3 degree Celsius each hour, what was the temperature at 8 pm?

Q 22 A boy has INR 35 in his bank account, He deposits INR 50 everyday for the month of July. What will be the amount in his account at the end of 10 days?

Q 23 A man travelled 50 km to east of Meerut and then 90 km to west of it. How far from Meerut was he finally?
Q24 A carton contains 16 boxes of nails and each box weighs $4\frac{3}{4}$ kg. How much would a carton of nails weigh?
Q25 Sapna earns INR 88000 per month. She spends $\frac{7}{8}$ of her income and deposits rest of money in a bank. How much money does she deposits in the bank each month.

Q 26 If the cost of $5\frac{2}{5}$ liters of water is INR $20\frac{1}{4}$ , Find its cost per litre?

Q27 Solve

(-22)-[(-23)-(-17)-(-61)]
=(-22)-[(-23)+17+61]
=(-22)-[55]
=-22-55
=-77

Saturday, June 1, 2019

Parallel Computing- Question Bank

Parallel Computing

June-2018

Q1 What are the problems faced in Superscalar architecture ? Explain how these problems were addressed and resolved in VLIW architecture.

Q2 Define permutation network using an example. Also discuss Perfect Shuffle permutation and Butterfly permutation.

Q3 What is a Parallel Virtual Machine ? Discuss its features and advantages.

Q4 Differentiate between Threads and Processes. Explain the concept of Thread with basic methods in concurrent programming languages for creation and termination of threads.

Q5 Discuss the PRAM model. Which PRAM model can be used to execute any other PRAM algorithm and how can it be used ?

Q6 Explain at least two techniques used for optimization of a parallel code.

Q7 Why are Array processors called as SIMD array computers ? Explain the architecture of SIMD array processer using a block diagram.

Q8 What is meant by Cluster Computing ? Explain the memory organisation in cluster computing.

Q9 What are the different models of distributed systems ? Also discuss various advantages of distributed systems.

Q10 Illustrate Flynn's classification of parallel computer systems. Also list the features of all categories of parallel systems.

Q11 Write short notes on the following

(a) Grid Computing
(b) Handler's Classification
(c) Hyperthreading Technology
(d) Bitonic Sorting Algorithm

Artificial intelligence - Question Bank

Artificial intelligence and knowledge management

June 2018

Q1 Evaluate the following LISP expressions

(i) (greaterp 18 151 76)
(ii) (reverse ((p q) r (s t))
(iii) (list 'a '(b c))
(iv) (cadadr '(x (y z) 1))
(v) (append 'a '(b c d)

Q2 Translate the following statements into WFF :

(i) Every person has a mother

(ii) There is a man and he is father of Joe

Q3 ) Discuss "Chinese Room Test". How did the outcomes of the Chinese Room Test contribute in the development of machine intelligence?

Q4 Differentiate between single agent and multi-agent environment.

Q5 Discuss the components of conceptual graph. Transform the following conceptual graph into FOPL statement :

[PERSON : Anita] E- (AGENT) 4-- [DRINK]
—> (OBJECT) —> [FOOD : MILK] -->
(Instrument Glass)

Q6 (b) Write short notes on any four of the following :

(i) Prenex normal form
(ii) Skolemization
(iii) Clausal form
(iv) Resolution
(v) Unification

Q7 What is an Expert System ? Explain the architecture of an Expert System. Create an expert system to infer, whether a student has secured poor, good, average or excellent marks in the examinations.

Q8 Write A* algorithm. Briefly discuss any application area of A* algorithm.

Q9 Briefly describe the components of "Truth Maintenance System (TMS)".

Q10 Differentiate between the following

a) Monotonic reasoning and Non-Monotonic reasoning

b) Predicate logic and Propositional logic
c) Supervised learning and Unsupervised learning

Give suitable examples, expressions and diagrams, while differentiating.

Q11 Write short notes on any two of the following :
(i) Turing Test
(ii) Semantic Nets
(iii) Frames

Q12 Write a short not on the following :
(i) Lambda Function
(ii) Mapcar Function
(iii)Cond Function

Q13 Write a program in Prolog to identify the following relations :
(i) Grandfather (X, Y)
(ii) Sister (X, Y)
Develop appropriate knowledge base and write the rule applicable to the knowledge base.

Q14 Write a program in LISP to find the factorial of a number, entered by the user. Give comments in the program to explain your logic.

Q15 What do you understand by the term "Fuzzyfication" ? Define Fuzzyfunction
"Tall-man".

Advance Internet Technologies- Question Bank

Advanced Internet Technologies

June 2018

Q1 Write a servlet pseudocode that tracks the assignments of a student at University. The fields of the entities are

Student

Roll Number

Name

Assignment

Subject code

Assignment code

Date of receipt

Date of submission

Last date of submission

Maximum marks

Subject

Subject code

Subject name

Result

Student roll no

Subject code

Assignment code

Marks obtained

Generate a report that gives

Student name

Roll no

Subject

Assignments submitted on time

Marks obtained out of Total

All the data in tables is in an RDBMS. Late submission result in 0. You need to mention the different actions that a servlet takes for that assignment real executable code is not expected.

Q2 Explain briefly, the different types of system vulnerabilities.

Q3 Write the XML DTD for the entities in Question 1 above. Make and state any needed assumptions.

Q4 Explain two mechanisms that would allow inclusions of external pieces into a JSP document.

Q5 What is SSL? Describe briefly, the two-way SSL authentication mechanism.

Q6 What is JNDI authentication? Explain with the help of an example.

Q7 Draw the layered architecture of EJB and explain its components briefly.

Q8 Explain the different types of JDBC drivers. Also list their advantages and disadvantages.

Q9 Briefly explain the different types of restrictions on EJB.

Q10 What is session tracking? Explain any one mechanism of session tracking briefly.

Q11 Explain the five basic scripting elements used in JSP.

Q12 Explain how an applet is included in a JSP program with the help of a small code.

Q13 What is Message-Driven Bean? List any four uses of message-driven bean.

Q 14 Describe the following in XML with relevant examples

i) External Entity

ii) Internal Entity

iii) Parameter Entity

Q15 What is Java Bean? Briefly explain the four categories of bean property.

Data Communication and Computer Networks- Question Bank

Data Communication and Computer Networks

June 2018

Q1 Explain the DES algorithm with the help of a suitable example.

Q2 What is the need of hierarchical routing? Explain it with an example.

Q3 Explain Leaky Bucket and Token Bucket traffic shaping mechanisms and compare them.

Q4 A high quality audio signal is limited to 10 kHz. It is to be transmitted using a 7 -bit code. Calculate the required bit rate which needs to be supported by the channel.

Q5 Enlist any two core protocols of Internet layer in TCP/IP reference model. Describe the functionality of these two protocols.

Q6 Explain the concepts of Local Procedure Call(LPC) and Remote Procedure Call (RPC) using suitable examples and diagrams. Why is RPC useful in programming?

Q7 State the need of broadcast routing. Discuss various broadcast routing procedures. Give an example of multicast routing.

Q8 A system uses Slotted ALOHA protocol. In a observation interval, the channel is busy 90% of the time. Calculate the system throughput.

Q9 Explain connection establishment and connection termination process in TCP using three-way handshaking mechanism.

Q10 Why is Stop-and -Wait protocol inefficient for satellite links? How is this inefficiency overcome in Sliding Window protocol? Explain.

Q11 Explain the collision occurrences in Ethernet. How is back-off algorithm implemented in Ethernet?

Q12 Illustrate Count-to-Infinity problem. How can it be resolved?

Q13 Explain the functionalities of SSL. Discuss the merits of SSL.

Advanced Database Management Systems- Question Bank

Advanced Database Management Systems

June 2018

Q1 What are Cursors,Stored Procedures and Triggers? Explain each with the help of an example code.

Q2 Differentiate between Logical and Physical Database design.

Q3 What is a View? Explain any two strategies for implementing the Views.

Q4 What is Hash join? How is Hash join between two relations computed? Explain the algorithm and cost calculation for simple hash join.

Q5 Differentiate between a database management system and a data warehouse.What is need for a data warehouse?

Q6 What is granularity of data ? How does granularity of data items affect the performance of concurrency control?

Q7 Differentiate between Centralized DBMS and Distributed DBMS.

Q8 What is Timestamp Ordering? Explain timestamp based protocol for serializable schedule.

Q9 What is Data Mining? How does Data Mining differ from OLTP? Discuss Classification as a technique for data Mining.

Q10 What are Data Marts? Briefly discuss the significance of data marts.

Q11 What is XML? How does XML differ from HTML? What are the advantages of XML? Create an XML schema for a list of students and their marks.

Q12 Differentiate between Two-phase commit protocol and Three-phase commit protocol in distributed databases. "The three-phase commit protocol increases the system's availability and does not allow transactions to remain blocked until a failure is repaired" Justify the statement.

Q13 What are Semantic Databases? List the features of semantic databases. Explain the process of searching the knowledge in semantic databases.

Q14 What is a Data Dictionary? List some features of a data dictionary. What are various approaches to implement a Distributed Database Catalogue?

Q15 What is Shadow Paging? Illustrate with an example. Give the advantages and disadvantages of shadow paging.

Q16 Define Multi-valued Dependency. What is Trivial Multi-valued Dependency? State the Fourth normal form.

Q17 Explain any one clustering technique for data mining.

Q18 What is Query Optimization? Briefly discuss the techniques of Query Optimization with suitable examples.

Q19 Explain the following

i) Temporal Databases

ii) Dynamic SQL

iii) OLAP

iv) Spatial Databases

Q20 Explain the process of Query optimization with suitable example.

Q21 What is the difference between Document Type Definition (DTD) and XML Schema ? Explain using an example.

Q22 Explain Data mining in the context of knowledge discovery in databases.

Q23 What is Join dependency ? Explain it with the help of an example. What is trivial join dependency?

Q24 Consider a small institute in which students register for programmes run by the
institute. A programme can be a full or part time programme or both. Every student
necessarily registers in at least one programme and at most three programmes,
Assuming suitable attributes, design an EER Diagram for the same.

Q25 Explain the reference architecture for distributed database management systems.

Q26 What are triggers ? Explain the utility of triggers in DBMS. Give suitable SQL code for triggers.

Q27 What is a System catalogue ? What is the information stored in catalogue of RDBMS ?

Q28 Compare and contrast the following :

(i) JDBC and ODBC
(ii) B-Tree Indexes and R-Tree Indexes used in PostgreSQL.

Q29 What is multiversion two-phase locking ? Explain with an example.

Q30 What are the different type of security features, needed for a multilevel security system ? Explain the encryption technique for a multilevel security system.

Q31 Describe the following with suitable example or a diagram :
(i) Data Grid
(ii) Data Mart
(iii) Deadlock
(iv) Checkpoint
(v) Referential Integrity Constraint

Q32 What are views ? What is their significance in DBMS ? How are views created in SQL ? Explain it with the help of an SQL statement.

Q33 Differentiate between the following

(i) Centralized and Distributed Databases
(ii) Clustering and Classification approaches in Data Mining
(iii) Star Schema and Snowflake Schema

Q34 What are deadlocks ? How are deadlocks detected ? Explain with the help of an example.

Q35 What is semi-structured data ? Explain with the help of an example. What is the difference between a well formed XML document and a valid XML document ?

Q36 What is data warehousing ? Discuss various characteristics of data warehousing ?

Q37 What are multimedia databases ? Discuss the challenges of designing multimedia databases.

Q38 What is multi-valued dependency ? State the fourth normal form.

Friday, May 31, 2019

Computer Graphics-2

Computer Graphics(Practice questions)

Q1 Write a transformation matrix for a 3-D rotation, in homogenous coordinate system with respect to x,y and z axes respectively.

Q2 What is the limitation of DDA line generation algorithm? How does Bresenham line generation algorithm overcome this limitation?

Q3 Define an "Oblique projection". Derive a general transformation matrix for an oblique projection.

Q4 How can frame buffer be used to put colour and intensity on the screen?

Q5 Explain the term " sweep representation". How can a cylinder be produced by using the concept of sweep representation?

Q6 What is the need of the concept of "shading" in computer graphics? List merits and demerits of Phong shading.

Q7 Explain the terms "Cel animation" and "Sprite animation". Which of the two techniques is better for creating animation? Justify your answer.

Q8 Define the use of following formats:

1) GIF

2)JPEG

3) WPG

4)TIFF

5)MPEG

Q9 Write pseudo code for Bresenham circle generation algorithm. Use this algorithm to produce a circle of radius r=4 units, in the first quadrant from x=0 to x=y.

Q10 Write pseudocode for DDA line drawing algorithm for a line segment with negative slope.

Q11 Differentiate between the following.

a) Drawing and painting

b) CAD and CAM

c) Plotter and Printer

Q11 Determine the final co-ordinates of the perspective projection of an object, when the object is first rotated w.r.t. the Y axis by -30 degree and X-axis by 45 degree and finally it is projected onto Z=0 plane with center of projection at (0,0,-5).

Q12 Find the general transformation matrix for the reflection about the line y=-x.

Q13 " Simultaneous shearing is not the same as shearing in one direction, followed by shearing in another direction. What is the maximum number of objects that can be handled by Z-buffer algorithm? Give two advantages and two disadvantages of Z-buffer algorithm.

Q14 What is the difference between ray tracing and ray casting? Explain how a ray tracing method can be used to achieve realism in computer graphics.

Q15 What is the problem of aliasing? How does the technique of anti aliasing work to get rid of the problem of aliasing?

Q16 Explain the following

1) Panning

2) Compression in digital video

3) Morphing

4) Scholastic Animation

5) Icon based authoring tools

Q17 Discuss the role of image editing tools in creating and editing multimedia elements. Briefly describe the criteria behind the selection of an image editing tool.

Q18 Define the term intensity interpolation. Explain Gouraud shading.

Q19 Write Z-Buffer algorithm for hidden surface detection. Explain how this algorithm is applied to determine the hidden surfaces.

Q 20 What is image filtering? Why is it required?

Q21 Compute the intermediate points on the line drawn from (0,0) to (5,10) using Bresenham's algorithm.

Q22 What is the difference between parallel and perspective projection? Categorize the various types of parallel projections.

Q23 Explain the concept of window to view port transformation with the help of suitable diagram.

Q24 What is the advantage of using homogenous co-ordinate system? Write the transformation matrix in homogenous co-ordinate system for "xy-shear" about origin.

Q25 Why do we use an authoring tool in the context of multimedia? Explain the features of any two types of authoring tools.

Q26 Explain the following terms with the help of an example/diagram, if needed.

a) Tweening

b) Volume rendering

c) Fractual models

d) Morphing

Q27 Derive a general 2D transformation matrix for rotation about the origin. Perform a 45 degree rotation of a square having vertices A(0,0), B(0,2), C(2,2), D(2,0) about the origin.

Q28 Explain Cyrus Beck parametric line clipping algorithm.

Q29 Derive the 2-D transformation matrix for reflection about the line y=mx, where m is constant. Use the transformation matrix to reflect the triangle A(0,0), B(1,1), C(2,0) about the line y=2x

Q30 Explain pseudocode for Sutherland Hodgeman polygon clipping algorithm. Using this algorithm clip the following polygon against the rectangular window ABCD.

Q31 What are refreshing display devices? Describe the working principle of CRT displays with the help of suitable diagram. Differentiate between Random and Raster Scan display devices.

Q32 Write the three main properties of Bezier curve. Explain the condition for smoothly joining two bezier curve segments.

Q33 Explain the following terms with the help of suitable diagram/ example if needed.

1) Oblique Projection

2) Bezier Surfaces

3) Object space approach in Visible-surface detection

4) Specular Reflection

5) GIF File compression

6) Hypermedia

7) Representational Animation

8) Ray tracing

Q34 What are the differences between Gouraud and Phong shading?

Q35 Explain Cohen-Sutherland line clipping algorithm.

Q36 Explain the working principle of plasma panel displays. Give the advantages and disadvantages.

Q37 Compute 2D transformation matrix for rotating a point (12,6) about the point (3,2) by an angle 30 degree in clockwise direction.

Q38 Compute co-ordinate points of circle drawn with centre at (0,0) and radius 5, using mid point circle algorithm.

Q39 Show that the simultaneous shearing Shxy(a,b) is not same as the shearing in x direction, Shx(a) followed by a shearing in y-direction, Shy(b).

Q40 Prove the following properties of Bezier curve.

i) P(u=1)=Pn

ii) P'(0)=n(P1-P0)

Q41 Explain the formation of an image in vector graphics with the help of an example. Explain any two file formats that use vector graphics.

Q42 Write a short note on sound editing tools.

Q43 Explain the scan line polygon filling algorithm with the help of suitable diagram.

Q44 Define the term ray casting. Explain any one method of ray casting.

Q45 Derive a transformation matrix for a perspective projection of point P(x, y, z) onto a x =4 plane as viewed from E(6,0,0).

Q46 Why Bresenham line drawing algorithm is better than DDA algorithm? Draw a line segment joining (4,8) and (8,10) using Bresenham line drawing algorithm.

Q47 Given four control point P0(2,2),P1(3,4), P2(5,4) and P3(4,2) as vertices of Bezier curve. Determine four points on Bezier Curve.

Q48 Explain the differences between the following

i) Multimedia and interactive multimedia

ii) Hypertext and hypermedia

iii)Procedural animation and representational animation

Q49 Explain ambient and diffused reflection. Give general mathematical expression for combined effect of ambient and diffused reflection.

Q50 What is frame buffer? How can you use frame buffer for putting color and controlling intensity on display device?

Q51 What is the advantage of using homogenous co-ordinate system? Consider a square (0,0),(0,2),(2,0),(2,2). Perform composite transformation of the square by using the following steps. (Give the co-ordinates of the square at each intermediate steps)

i) Scale by using Sx=2 and Sy=3

ii)Rotation of 45 degree in the anticlockwise direction.

iii) Translate by using Tx=3 and Ty=5

Q52 Why are hidden surface algorithm needed? Explain scan line method for visible surface determination.

Q53 Derive a 3D-transformation matrix for rotation relation matrices for about Z-axis, X-axis and Y-axis, respectively.

Q54 What are the number of memory bits required for 8-bit plane frame buffer for a 512 x 512 raster? Also calculate the refresh rate for the same raster(512 x 512), if pixels are accessed at the rate of 250 nano seconds.

Q55 Differentiate between Random and Raster Scan display devices.

Q56 Use DDA line generation algorithm to draw a line from (2,2) to (8,6).

Q57 Derive a general transformational matrix for 3-D rotation about x-axis.

Q58 Perform a 45 degree rotation of triangle A(1,1), B(5,1), C(3,5) about an aribitary point (3,3).

Q59 Explain any one method of polygon Representation with the help of an example.

Q60 How many key frames does a 45 seconds animation film sequence with no duplication require if there are four in between frames for each pair of key frames? What will happen if duplication is allowed?

Q61 Why file compression techniques are beneficial in computer graphics?

Q62 Write a procedure to implement the Bresenham line generation algorithm. What are the advantages of this algorithm over the DDA line generation algorithm.

Q63 What are the merits and demerits of Gouraud Shading, constant shading and phong shading?

Q64 Explain all the four cases of Sutherland-Hodgman polygon clipping algorithm.

Q65 Derive the 2-D transformation matrix for reflection about the line y=mx+c, where m and c are constants. Use this transformation matrix to reflect the triangle A(0,0), B(4,0) and C(4,4) about the line y=2x+5.

Q66 Explain the terms window and viewport in the context of clipping. Derive a general transformation matrix for window to viewport mapping.

Q67 Write a short note on diffuse reflection.

Q68 Obtain a transformation matrix for perspective projection for a given object projected onto x=5 plane as viewed from [8,0,0].

Q69 Differentiate between the following.
i) Morphing and panning
ii) Motion specific animation and motion generalized animation.

Q70 Given p0(1,2), P1(2,3),P2(4,3), P3(3,2) as the vertices of Bezier curve. Determine 5 points on Bezier curve.

Q71 What are the limitations of refreshing display devices? What is refresh rate in 1024 x 1024 raster if pixels are accessed at the rate of 250 nanoseconds?

Q72 Illustrate the Bresenham line generation algorithm by digitizing the line with the end points(20,5) and (25,10).

Q73 Explain the Cyrus Beck line algorithm to clip a line segment for a non-convex clipping window.

Q74 Define the term projection. Categorise various types of perspective and parallel projections.

Q75 Explain the term anti-aliasing with the help of diagram. How does the technique of anti-aliasing work to get rid of the problem of aliasing?

Q76 Explain the process of simulating positive non-zero acceleration.

Q77 Define the following

a) Virtual reality
b) Icon based authoring tools
c) Frame buffer
d) Bitmap images
e) File Compression
f) 3-D modelling and animation tools

Q78 A square ABCD is given with vertices A(0,0), B(2,2) and D(0,2). Illustrate the effect of

i)x-shear
ii)y-shear
iii)xy-shear

On the given square when a=3 and b=4, where a is shearing in x-direction and b is shearing in y-direction.

Q79 Write pseudocode for midpoint circle generation algorithm.

Q80 What is difference between Hypertext and Hypermedia? Briefly describes various links used in Hypermedia.

Q81 Reflect the triangle where vertices are A(-1,0), B(0,2) and C(1,0) about
i) The horizontal line y=2

ii) The vertical line x=1
iii) The line y=x+3

Q82 What are the various types of audio and video formats?

Q83 What is foreshortening factor in the context of parallel projection? How it is related to Isometric, Diametric and Trimetric projection?

Q84 Explain the basic Ray tracing algorithm with the help of suitable diagram.

Q85 Find the transformation matrix for the reflection about the line y=4x.

Q86 Determine the expression of frame spacing which can be used to simulate positive acceleration in any animation.

Q85 Write a short note on loss less audio formats.

Q86 How Raster scan display devices are different from Random scan display devices? Can we use frame buffers to control picture color and intensity, justify your answer with suitable arguments.

Q87 Explain the terms " Parametric Continuity" and "Geometric Continuity" in Bezier curves.

Q88 Discuss Area Subdivision Method. What are the conditions to be satisfied, in Area Subdivision Method, so that it is finalized that no further surface division is required?

Q89 How many key frames does a 30 seconds animation film sequence with no duplicates require? How the results are affected if five in between frames are inserted between each pair of key frames?

Q90 Differentiate between Bitmap and Vector graphics.

Q91 Find the final coordinates of the triangle ABC, A(-3,0), B(-1,1), C(-1,-1) when it is subjected to clockwise rotation of 45 degree about an axis passing through an arbitrary point P(-1,1). Draw a suitable figure to demonstrate your solution.

Q92 Derive a general perspective transformation matrix with respect to an arbitrary centre of projection C(a,b,c). Obtain the perspective transformation matrix onto Z=-5 plane where the centre of projection is at (0,0,18).

Q93 Prove that two successive rotations are additive
$\therefore R(\theta_{1}). R(\theta_{2})=R(\theta_{1}+\theta_{2})$
Draw a suitable diagram to demonstrate your solution.

Q94 Perform 45 degree rotation of triangle ABC A(0,2), B(-1,-1), C(1,-1) about the origin.

Q95 What is the utility of tabular representation of polygon surface? Can you implement a polygon surface with just a vertex table and an edge table? Justify your answers.

Q96 What are the maximum number of objects that can be handled by Z-buffer algorithm? What will happen if the Z- buffer algorithm is used and it is found that two polygons have the same z-value?

Q97 Write a short note on Stochastic animation and its area of application.

Q98 Differentiate between calligraphic display device and raster scan display devices.

Q99 Determine the number of memory bits required for a 4 bit plane buffer for a 512 x 512 raster.

Q100 Determine the final coordinates of a polygon ABCD A(1,4), B(-4,1), C(-1,-1), D(2,-2) when it is scaled upto twice its size with respect to an arbitary point P(1,1).