Relational Database Management System

Relational Database Management System is the most widely used type of DBMS. This note provides an information about Relational Database Management System.

Summary

Relational Database Management System is the most widely used type of DBMS. This note provides an information about Relational Database Management System.

Things to Remember

  • Field properties are the sets of characteristics that are associated with each field.
  • A primary key is the field that uniquely identifies in a table.
  • A compound key is a key that consists of multiple columns because one column is not sufficient unique.
  • A record row in a database is called tuple.
  • A foreign key is the linking pin between two tables.

MCQs

No MCQs found.

Subjective Questions

Q1:

Find the area of the triangles whose vertices are as follows:

(3, -4), (-2, 3) and (4, 5)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Given vertices are of triangle are:</p> <p>(x<sub>1</sub>, y<sub>1</sub>) = (3, -4)</p> <p>(x<sub>2</sub>,y<sub>2</sub>) = (-2, 3)</p> <p>(x<sub>3</sub>, y<sub>3</sub>) = (4, 5)</p> <p>We have,</p> <p>\begin{align*} \text {Area of triangle} &amp;= \frac 12 |[(x_1y_2 - x_2y_1) + (x_2y_3 - x_3y_2) + (x_3y_1 - x_1y_3)]|\\ &amp;= \frac 12 |[{3 &times; 3 - (-2) &times; (-4)} + {(-2) &times; 5 - 4 &times; 3} + {4 &times; (-4) - 3 &times; 5}]|\\ &amp;= \frac 12 |[(9 - 8) + (-10 - 12) + (-16 - 15)]|\\ &amp;= \frac 12 |[1 - 22 - 3]|\\ &amp;= \frac 12 |1 - 53|\\ &amp;= \frac 12 &times;|-52|\\ &amp;= \frac 12 &times; 52\\ &amp;= 26 \;\text{square units}_{Ans}\\ \end{align*}</p>

Q2:

Find the area of the triangles whose vertices are as follows:

 

(-3,2), (5, -2) and (1, 3)


Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Given vertices are of triangle are:</p> <p>(x<sub>1</sub>, y<sub>1</sub>) = (-3, 2)</p> <p>(x<sub>2</sub>,y<sub>2</sub>) = (5, -2)</p> <p>and (x<sub>3</sub>, y<sub>3</sub>) = (1, 3)</p> <p>We have area of triangle,</p> <p>\(\frac{1}{2}\)|[x<sub>1</sub> y<sub>2</sub>-x<sub>2</sub> y<sub>1</sub>)+(x<sub>2</sub> y<sub>3</sub>- x<sub>3</sub> y<sub>2</sub>)+(x<sub>3</sub> y<sub>1</sub>-x<sub>1</sub> y<sub>3</sub>)]|</p> <p>&there4; Area of triangle =\(\frac{1}{2}\)|[{(-3)&times;(-2)-5&times;2}+{(5&times;3-1&times;(-2)}+{1&times;2-(-3)&times;3}]|</p> <p>=\(\frac{1}{2}\)|[(6-10)+(15+2)+(2+9)]|</p> <p>=\(\frac{1}{2}\)|[-4+17+11]|</p> <p>=\(\frac{1}{2}\)|24|=\(\frac{1}{2}\)&times;24</p> <p>= 12 square units.Ans.</p>

Q3:

Prove that the following points are collinear.

(1,4),(3,-2) and (-3,16)

 

 


Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Here,(1,4),(3,-2) and (-3,16)</p> <p></p> <p>Given vertices are, (x<sub>1</sub> y<sub>1</sub>)=(1,4), (x<sub>2</sub>, y<sub>2</sub>)=(3,-2) and (x<sub>3</sub>, y<sub>3</sub>)=(-3,16)</p> <p>Using formula,</p> <p>Area of triangle= \(\frac{1}{2}\)|[{1&times;(-2)-3&times;4}+{3&times;16-(-3)&times;(-2)}+{(-3)&times;4-1&times;16}]|</p> <p> = \(\frac{1}{2}\)|[-2-12+48-6-12-16]|</p> <p> = \(\frac{1}{2}|[-48+48]|= \frac {1}{2}\)&times;0=0 square units.</p> <p>&there4; The three points (1,4),(3,-2) and (-3,16) are collinear.Proved</p> <p></p>

Q4:

Prove that the following points are collinear.

(-1,0),(2,2) and (\(\frac{1}{2}\),1)

 


Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Given points are :</p> <p>(x<sub>1</sub>,y<sub>1</sub>)=(-1,0),(x<sub>2</sub>,y<sub>2</sub>)=(2,2), and (x<sub>3</sub>, y<sub>3</sub>)= (\(\frac{1}{2}\),1)</p> <p>Using the formula for area of traingle,we get,</p> <p>Area of \(\triangle\)=\(\frac{1}{2}\)|[{(-1)&times;2-2&times;0}+{2&times;1-\(\frac{1}{2}\)&times;2}+{ (\(\frac{1}{2}\)&times;0-(-1)&times;1}]|</p> <p> =\(\frac{1}{2}\)|[-2-0+2-1+0+1]|</p> <p> =\(\frac{1}{2}\) |0|=\(\frac{1}{2}\)&times; 0= 0 square units</p> <p>&there4;The three points (-1,0),(2,2) and (\(\frac{1}{2}\),1)are collinear.Proved.</p>

Q5:

Prove that the following points are collinear.

 (a,b+c),(b,c+a) and (c,a+b)


Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Here, given points are,</p> <p>(x<sub>1</sub>,y<sub>1</sub>)=(a,b+c),(x<sub>2</sub>,y<sub>2</sub>)=(b,c+a) and (x<sub>3</sub>,y<sub>3</sub>)=(c,a+b)</p> <p>Using the formula for the area of traingle, we get,</p> <p>Area of \(\triangle\)=\(\frac{1}{2}\)|[{a(c+a)-b(b+c)} + {b(a+b)-c(c+a)}+ {c(b+c)-a(a+b)}]|</p> <p>= \(\frac{}{}\)|[ac+a<sup>2</sup>-b<sup>2</sup>-bc+ab+b<sup>2</sup>-c<sup>2</sup>-ca+cb+c<sup>2</sup>-a<sup>2</sup>-ab]|</p> <p>= \(\frac{1}{2}\)|0|=\(\frac{1}{2}\)&times;0=0 square units</p> <p>&there4; The three points (a,b+c),(b,c+a) and (c,a+b) are collinear. Proved.</p>

Q6:

P(a,0) and Q (0,b) lie on a line.If third points R(x,y) also lies on the given line.Prove that \(\frac{x}{a}\)+ \(\frac{y}{b}\)=1


Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Here given points,</p> <p>P(a,0),Q(0,b) and R(x,y) are collinear.</p> <p>So, area of \(\triangle\)PQR=0</p> <p>or,|[ab-xb-ay]|=0</p> <p>or, ab-xb-ay=0</p> <p>or, ab=xb+ay</p> <p>Dividing both sides by ab, we get,</p> <p>\(\frac{ab}{ab}\)=\(\frac{xb}{ab}\)+\(\frac{ay}{ab}\)</p> <p>or, 1=\(\frac{x}{a}\)+\(\frac{y}{b}\)</p> <p>&there4; \(\frac{x}{a}\)+\(\frac{y}{b}\)=1 Proved.</p>

Q7:

If points (2,7),(3,6) and (k,5) are collinear find the value of k.


Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Here given points are:</p> <p>(2,7), (3,6) and (k,5)</p> <p>Since the given points are collinear, so,</p> <p> Area of traingle =0</p> <p>or, \(\frac{1}{2}\)[x<sub>1</sub> y<sub>2</sub>-x<sub>2</sub>y<sub>1</sub>+x<sub>2</sub>y<sub>3</sub>-x<sub>3</sub> y<sub>2</sub>+x<sub>3</sub>y<sub>1</sub>-x<sub>1</sub> y<sub>3</sub>]=0</p> <p>or, (2.6-3.7+3.5-k.6+k.7-2.5)=0</p> <p>or, 12-21+15-6k+7k-10=0</p> <p>or, k-31+27=0</p> <p>or, k-4=0</p> <p>&there4;k=4.Ans.</p>

Q8:

If (3,a),(4,5) and (1,6) are vertices of a triangle and area of the triangle is 5 square units.Find value of a.


Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Here given,</p> <p>Vertices of traiangle (3,a),(4,5) and (1,6)</p> <p>Area of triangle =5 square units</p> <p>So, \(\frac{1}{2}\)[x<sub>1</sub>y<sub>2</sub>-x<sub>2</sub>y<sub><span style="font-size: xx-small;">1</span></sub><span style="font-size: xx-small;">+</span>x<sub>2</sub>y<sub>3</sub>-x<sub>3</sub>y<sub>2</sub>+x<sub>3</sub>y<sub>1</sub>-x<sub>1</sub>y<sub>3</sub>]=5</p> <p>or, [3.5-4.a+4.6 -1.5 +1.a -3.6]=10</p> <p>or, -3a+39-23=10</p> <p>or, -3a=10-16</p> <p>or, -3a=-6</p> <p>&there4; a=2.Ans.</p> <p></p>

Q9:

If points (a,b), (a1,b1) and (a-a1,b-b1) lies on the same line then prove ab1=a1b.


Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Here given collinear points are,</p> <p>(a,b),(a',b') and (a-a',b-b')</p> <p>So, area of triangle =0</p> <p>or, \(\frac{1}{2}\)[x<sub>1</sub>y<sub>2</sub>-x<sub>2</sub>y<sub>1</sub>+x<sub>2</sub>y<sub>3</sub>-x<sub>3</sub>y<sub>2</sub>+x<sub>3</sub>y<sub>1</sub>-x<sub>1</sub>y<sub>3</sub>]=0</p> <p>or, a.b'-a'.b+a'.(c-b')-(a-a').b'+(a-a').b-a.(b-b')=0</p> <p>or, ab'-a'b+a'b-a'b'-ab'+a'b'+ab-a'b-ab+ab'=0</p> <p>or, -a'b+ab'=0</p> <p>&there4;ab'=a'b.Proved.</p>

Q10:

Co-oridinates of point P,Q and R are (-1,5),(3,1) and (5,7) respectively.If L,M and N are mid-points of QR,RP andPQ respectively then prove that \(\triangle\) PQR=4(\(\triangle\)LMN).


Type: Long Difficulty: Easy

Show/Hide Answer
Answer: <p>Here given, Co-ordinates of vertices of \(\triangle\)PQR are P(-1,5), Q(3,1) and R(5,7)</p>
<p>Now, area of\(\triangle\)PQR=\(\frac{1}{2}\)|[{(-1)&times;1-3&times;5}+{3&times;7-5&times;1)}+{5&times;5-(-1)&times;7}]|</p>
<p>=\(\frac{1}{2}\)|[-1-15+21-5+25+7]|</p>
<p>= \(\frac{1}{2}\)|[-21+53]|=\(\frac{1}{2}\)|32|=\(\frac{1}{2}\)&times;32=16 square units</p>
<p>If L,M and N are the mid points of QR,RP, and PQ respectively, then,</p>
<p>Co-ordinates of L=(\(\frac{3+5}{2}\),\(\frac{1+7}{2}\))=(\(\frac{8}{2}\),\(\frac{8}{2}\))=(4,4)</p>
<p>Co-ordinates of M=(\(\frac{5-1}{2}\),\(\frac{7+5}{2}\))=(\(\frac{4}{2}\),\(\frac{12}{2}\))=(2,6)</p>
<p>Co-ordinates of N=(\(\frac{-1+3}{2}\),\(\frac{5+1}{2}\))=(\(\frac{2}{2}\),\(\frac{6}{2}\))=(1,3)</p>
<p>Now, area of \(\triangle\)LMN=\(\frac{1}{2}\)|[(4&times;6-2&times;4)+(2&times;3-1&times;6)+(1&times;4-4&times;3)]|</p>
<p>=\(\frac{1}{2}\)|[24-8+6-6+4-12]|</p>
<p>=\(\frac{1}{2}\)|[34-26]|=\(\frac{1}{2}\)|8|=\(\frac{1}{2}\)&times;8=4 square units</p>
<p>Here,\(\triangle\)PQR=4\(\triangle\)LMN)</p>
<p>or, 16=4(4)</p>
<p>&there4;16=16 Proved.</p>

Videos

Area of triangles and quadrilaterals
Triangle area proofs | Perimeter, area, and volume | Geometry | Khan Academy
Area of Triangles & Quadrilaterals
Relational Database Management System

Relational Database Management System

Relational Database Management System

It is the most widely used type of DBMS. In addition to store and timely retrieval of data, it also preserves the relation between different sets of data.

Relationship: It is a link or association between several entries.

List of different types of relationship

  • One to one e.g: Driver and car
  • One to many e.g: Teacher and students
  • Many to many e.g: Books and readers
  • Many to one e.g: Students and school

Field property

Field properties are the sets of characteristics that are associated with each field.

Field properties of MS Access

http://www.takveen.com/images/ms_access_2007/field-properties.JPG

Difference between database and DBMS

Database DBMS
1. It is a collection of data or related information. 1. It is a software package to manage database
2. It consists of data. 2. It manages data in the database.
3. It is a part of DBMS 3. It is a software system which contains database.
Example: phone diary, data of SLC exam, etc. Example: FoxPro, Access, etc.

Primary key

A primary key is the field that uniquely identifies in a table. Each record in the table must be unique. Every table has only one primary key.

Types of primary key

  • Compound (Composite key):A compound key is a key that consists of multiple columns because one column is not sufficient.
  • Foreign key:A foreign key is the linking pin between two tables.

Tuple

A record row in a database is called tuple.


Wizard

A wizard is a small program that interviews us, asking questions about what we want to accomplish, then it takes over answers and creates the table, query or whatever according to our specification.

Difference between Design view and Wizard

Design view Wizard
It takes more time. It saves our time

We can make our design. We can choose formats from premade ones.
We can create any field according to our requirement. We can copy fields from any of the simple table.

Lesson

Database Management System - MS Access

Subject

Computer Science

Grade

Grade 10

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