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Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 1 Number Systems Ex 1.4 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.4

Question 1.
Visualise 3.765 on the number line, using successive magnification.
Answer:

Point P in fig. 4 represents 3.765 on the number line.

Question 2.
Visualise \(4 . \overline{26}\) on the number line, up to 4 decimal places.
Answer:
\(4 . \overline{26}\) = 4.2626 up to 4 decImal places.

Point P in fig 5 represents 4.2626. i.e.. \(4 . \overline{26}\) up to 4 decimal places on the number line.

Punjab State Board PSEB 7th Class Maths Book Solutions Chapter 7 Congruence of Triangles Ex 7.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.1

1. Identify the pairs of congruent figures and write the congruence in symbolic form.

Question (i).

Answer:
In figure
Radius of circle C₁ = 2 cm
Radius of circle C₂ = 1.5 cm
As radius of circle C₁ ≠ Radius of circle C₂
∴ Circle C₁ is not congruent to circle C₂

Question (ii).

Answer:
In figure
Length of line segment AB = 6 cm
Length of line segment MN = 7 cm
As length of line segment AB ≠ Length of line segment MN
∴ AB is not congruent to MN

Question (iii).

Answer:
In ΔXYZ and ΔPQR
XY = PQ, YZ = PR, XZ = QR
So, ΔXYZ and ΔPQR have the same size and shape
∴ ΔXYZ ≅ ΔQPR

Question (iv).

Answer:
In figure ΔABC and ΔDEF do not have the same size and shape
∴ ΔABC and ΔDEF are do not have the same size and shape.
∴ ΔABC and ΔDEF are not-congruent.

Question (v).

Answer:

Question (vi).

Answer:

2. If ΔPQR as ΔOMN under the correspondence PQR ↔ OMN, write all the corresponding congruent parts of the triangle.
Solution:
For better understanding of the correspondence, let us draw a diagram of given correspondence.

The correspondence is PQR → OMN
This means vertices P ↔ O, Q ↔ M, R ↔ N
Sides : PQ ↔ OM, QR ↔ MN, RP ↔ NO
and Angles: ∠PQR ↔ ∠OMN, ∠QRP ↔ ∠MNO, ∠RPQ ↔ ∠NOM

3. Draw any two pairs of congruent triangles.
Solution:
Two pairs of congruent triangles are :
(i) Draw a ΔABC in which AB = 5 cm, BC = 4 cm and CA = 6 cm.
Draw another ΔPQR in which PQ = 6 cm, QR = 5 cm and RP = 4 cm shown in the following figure.


Make a trace copy of ΔABC using a tracig paper and superinpose it on ΔPQR, where C falls on P, A falls on Q and B falls on R. We observe that ΔABC will corr. ΔPQR.
∴ ΔABC ≅ ΔQRP

(ii) Draw a ΔXYZ in which XY = 5 cm, YZ = 6 cm and ZX = 3 cm. Draw another ΔLMN in which LM = 5 cm, MN = 6 cm and NL = 3 cm. Since both ΔXYZ and ΔLMN have the same size and shape.

4. If ΔABC ≅ ΔZYX, write the parts of ΔZYX that correspond to.
(i) ∠B
(ii) CA
(iii) AB
(iv) ∠C
Solution:
First of all we draw a diagram of given correspondence.

The correspondence is ABC ↔ ZYX.
This means A ↔ Z, B ↔ Y, C ↔ X
Therefore
(i) ∠B = ∠Y
(ii) CA = XZ
(iii) AB = ZY
(iv) ∠C = ∠X

5. Multiple Choice Questions :

Question (i).
If ΔABC as ΔXYZ under the correspondence ABC ↔ XYZ. Then
(a) ∠A = ∠Z
(b) ∠X = ∠B
(c) ∠A = ∠X
(d) ∠C = ∠X.
Answer:
(c) ∠A = ∠X

Question (ii).
Two line segments are congruent if,
(a) They are parallel
(b) They intersect each other
(c) They are part of same line
(d) They are of equal length.
Answer:
(d) They are of equal length.

Question (iii).
Two triangles ΔABC and ΔLMN are congruent AB = LM, BC = MN. If AC = 5 cm then LN is :
(a) 3 cm
(b) 15 cm
(c) 5 cm
(d) Can’t find.
Answer:
(c) 5 cm

6. Two right angles are always congruent. (True/False)
Answer:
True

7. Two opposite sides of a rectangle are always congruent. (True/False)
Answer:
True

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 1 Number Systems Ex 1.3 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.3

Question 1.
Write the following in decimal form and say
what kind of decimal expansion each has:

(i) \(\frac{36}{100}\)
Answer:
The decimal expansion of \(\frac{36}{100}\) is terminating.

(ii) \(\frac{1}{11}\)
Answer:

Thus, \(\frac{1}{11}\) = 0.0909…. = \(0.\overline{09}\)
The decimal expansion of \(\frac{1}{11}\) is non- terminating.

(iii) 4\(\frac{1}{8}\)
Answer:
4\(\frac{1}{8}\) = \(\frac{33}{8}\)

Thus, 4\(\frac{1}{8}\) = 4.125
The decimal expansion of 4\(\frac{1}{8}\) is terminating.

(iv) \(\frac{3}{13}\)
Answer:

Thus, \(\frac{3}{13}\) = 0.230769230769…. = \(0.\overline{230769}\)
The decimal expansion of 4\(\frac{2}{11}\) is non-terminating recurring.

(v) \(\frac{2}{11}\)
Answer:

Thus, \(\frac{2}{11}\) = 0.1818….. = \(0 . \overline{18}\)
The decimal expansion of \(\frac{2}{11}\) is non-terminating recurring.

(vi) \(\frac{329}{400}\)
Answer:

Thus, \(\frac{329}{400}\) = 0.8225
The decimal expansion of \(\frac{329}{400}\) is terminating recurring.

Question 2.
You know that \(\frac{1}{7}\) = \(0 . \overline{142857}\). Can you predict what the decimal expansions of \(\frac{2}{7}\), \(\frac{3}{7}, \frac{4}{7}, \frac{5}{7}, \frac{6}{7}\) are, without actually doing the long division? if so, how? [Hint: Study the remainders while finding the value of \(\frac{1}{7}\) carefully.]
Answer:
While finding the decimal expansion of \(\frac{1}{7}\) by long division, we observe that the remainder 3, 2, 6, 4, 5 and 1 repeat in that order and the digits 1, 4, 2, 8, 5 and 7 repeat in that order in the quotient. So, in the decimal expansion of \(\frac{2}{7}\), the same digits recur beginning with 2. Thus,

Question 3.
Express the following in the form \(\frac{p}{q}\), where p and q are integers and q ≠ 0:
(i) 0.\(\overline{6}\)
Answer:
Let x = 0.\(\overline{6}\)
∴ x = 0.6666…
∴ 10x = 6.6666…
∴ 10x = 6 + x
∴ 10x – x = 6
∴ 9x = 6
∴ x = \(\frac{6}{9}\)
∴ x = \(\)
Thus. 0.\(\overline{6}\) = \(\frac{2}{3}\)

(ii) 0.4\(\overline{7}\)
Answer:
Let x = 0.4\(\overline{7}\)
∴ x = 0.4777…..
∴ 10x = 4.7777…..
∴ 10x = 4.3 + 0.4777…..
∴ 10x = 4.3 + x
∴ 9x = 4.3
∴ 9x = \(\frac{43}{10}\)
∴ x = \(\frac{43}{90}\)
Thus, 0.4\(\overline{7}\) = \(\frac{43}{90}\)

(iii) 0.\(\overline{001}\)
Answer:
Let x = 0.\(0 . \overline{001}\)
∴ x = 0.001001001 ……
∴ 1000 x = 1.001001001 ……
∴ 1000 x = 1 + 0.001001001 ……
∴ 1000 x = 1 + x
∴ 999 x = 1
∴ x = \(\frac{1}{999}\)
Thus, \(0 . \overline{001}\) = \(\frac{1}{999}\)

Question 4.
Express 0.99999 ….. in the form \(\frac{p}{q}\). Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.
Answer:
Let x = 0.99999 …..
∴ 10x = 9.99999 ……
∴ 10x = 9 + 0.99999 ……
∴ 10x = 9+x
∴9x = 9
∴ x = 1
Thus, 0.99999 ….. = 1
in other words, 0.\(\overline{9}\) = 1.
This also follows the rule mentioned in ‘Remember’ section that 0.\(\overline{m}\) = \(\frac{m}{9}\). As per rule, 0.\(\overline{9}\) = \(\frac{9}{9}\) = 1.

The answer seems to be tricky. Actually, there is no situation that gives the decimal expansion of a rational number \(\left[\frac{p}{q}\right]\) as 0.\(\overline{9}\).
This is an imaginary illustration of recurring decimal number.
You may say that 0.\(\overline{3}\) + 0.\(\overline{6}\) = 0.\(\overline{9}\) But in simple fraction form 0.\(\overline{3}\) and 0.\(\overline{6}\) add up to give 1. Thus, 0.\(\overline{9}\) = 1.

Question 5.
What can the maximum number of digits be in the repeating block of digits in the decimal expansion of \(\frac{1}{17}\)? Perform the division to check your answer.
Answer:
The maximum number of digits in the repeating block of digits in the decimal expansion of \(\frac{1}{17}\) can be 16(17 – 1).

Thus, \(\frac{1}{17}\) = \(0.\overline{0588235294117647}\)
Here, 17 – 1 16 gives the maximum possible number of digits in the repeating block of digits in the decimal expansion of \(\frac{1}{17}\). In some other cases, the number of digits in the repeating block of digits in the decimal expansion of \(\frac{1}{m}\) can be smaller than (m – 1), where m is a natural number.

For example, \(\frac{1}{13}\) = \(0 . \overline{076923}\) has only 6 digits (not 12) in the repeating block of digits in the decimal expansion.

Question 6.
Look at several examples of rational numbers in the form \(\frac{p}{q}\) (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?
Answer:
\(\frac{1}{2}\) = 0.5, \(\frac{1}{5}\) = 0.2, \(\frac{1}{10}\) = 0.1,
\(\frac{1}{4}\) = 0.25, \(\frac{1}{8}\) = 0.125, \(\frac{1}{16}\) = 0.0625,
\(\frac{1}{25}\) = 0.04, \(\frac{1}{125}\) = 0.008, \(\frac{1}{625}\) = 0.0016,
\(\frac{1}{20}\) = 0.05, \(\frac{1}{50}\) = 0.02 etc.
But, \(\frac{1}{3}\) = 0.\(\overline{3}\), \(\frac{1}{7}\) = \(0 . \overline{142857}\), \(\frac{1}{6}\) = 0.1\(\overline{6}\) etc.

This suggest that the decimal expansion of a rational number \(\frac{\boldsymbol{P}}{\boldsymbol{q}}\) is terminating if and only if q has no prime factors other than 2 and 5. in other words, q = 2^m5ⁿ, where m and n are whole numbers.

Question 7.
Write three numbers whose decimal expansions are non-terminating non-recurring.
Answer:
We know that the decimal expansion of an irrational number is non-terminating non recurring. There are infinitely many irrational numbers. We can state few of them as below:
o.o1001000100001 …,
0.02002000200002…., 0.50500500050000… are a few required numbers in the decimal form. The decimal expansions of numbers like √2, √3, √5, \(\sqrt[3]{10}\), etc. are also non- terminating non-recurring.

Question 8.
Find three different irrational numbers between the rational numbers \(\frac{5}{7}\) and \(\frac{9}{11}\)
Answer:
We know that \(\frac{5}{7}\) = \(0 . \overline{714285}\) and \(\frac{9}{11}\) = \(0 . \overline{81}\)
There are actually infinitely many irrational numbers between these recurring decimals. Three irrational numbers between them can be stated as below:
0.720720072000 …, 0.750750075000 …
0.780780078000….
As you see, the above numbers are non-terminating non-recurring. Hence, they are irrational numbers.

Question 9.
Classify the following numbers as rational or irrational:
(i) √23
Answer:
√23 is an irrational number.

(ii) √225
Answer:
√225 = 15 is a rational number

(iii) 0.3796
Answer:
0.3796 is a rational number.

(iv) 7.478478……..
Answer:
7.478478…… = \(7 . \overline{478}\) is a rational number.

(v) 1.101001000100001…….
Answer:
1.101001000100001……. is an irrational number.

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 1 Number Systems Ex 1.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2

Question 1.
State whether the following statements are true or false. Justify your answers:
(i) Every irrational number is a real number.
Answer:
This statement is true. The collection of real numbers contain all the rational numbers and all the irrational numbers.

(ii) Every point on the number line is of the form √m, where m is a natural number.
Answer:
This statement is false. The negative numbers represented on the number line are never of the form √m, where m is a natural number. For natural number m, √m is always a positive number.

(iii) Every real number is an irrational number.
Answer:
This statement is false. The collection of real numbers is made-up of rational numbers and irrational numbers. So, every real number is either a rational number or an irrational number.

Question 2.
Are the square roots of all positive integers irrational? if not, give an example of the square root of a number that is a rational number.
Answer:
No, The square roots of all positive integers are not irrational. The square root of any perfect square number is always a rational number.
e.g., √4 = 2, √9 = 3, √16 = 4, ……

Question 3.
Show how √5 can be represented on the number line.
Answer:

Start by taking point O on the number line which represents O. Choosing proper unit, locate point A on the number line to represent
1. Draw seg AB of unit length perpendicular to seg OA. Construct seg OB. Then, by Pythagoras’ theorem, OB = √2. Draw seg BC of unit length perpendicular to seg OB. Construct seg OC.
Then, OC = √3. Draw seg CD of unit length perpendicular to seg OC. Construct seg OD.
Then, OD = √4. Draw seg DE of unit length perpendicular to seg OD. Construct seg 0E.
Then, 0E = √5. Draw an arc with centre O and radius OE to Intersect the number line at P Then, point P on the number line represents √5.

Alternate Method:
This can be solved In fewer steps as shown in the following manner:
On the number line l, take a point O corresponding to 0. Choosing the proper unit, take a point A on l such that OA = 2 units. Construct right angled Δ OAP such that ΔOAP = 90° and AP = 1 unit.

Then, by Pythagoras theorem,
OP² = OA² + AP²
= (2)² + (1)² = 4 + 1 = 5
∴ OP = √5
Draw an arc with centre O and radius OP to intersect l at B. B is the point corresponding to Draw an arc with centre O and radius OP to intersect I at B. B is the point corresponding to √5.

Question 4.
Classroom activity (Constructing the ‘square root spiral’): Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion. Start with a point O and draw a line segment OP₁ of unit length. Draw a line segment P₁P₂ perpendicular to OP₁ of unit length (see Fig. 1.9). Now draw a line segment P₂P₃ perpendicular to OP₂. Then draw a line segment P₃P₄ perpendicular to OP₃. Continuing in this manner, you can get the line segment P_n-1P_n by drawing a line segment of unit length perpendicular to OP_n-1. In this manner, you will have created the points P₂, P₃, …………, P_n, ………, and joined them to create a beautiful spiral depicting √2, √3, √4, ………..

Answer:
Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion:

Start with a point O and draw a line segment OP₁ of unit length. Draw a line segment P₁P₂ perpendicular to OP₁ of unit length (see Fig. 1.9). Now draw a line segment P₂P₃ perpendicular to OP₂. Then draw a line segment P₃P₄ perpendicular to OP₃. Continuing in this manner, you can get the line segment P_n-1P_n by drawing a line segment of unit length perpendicular to OP_n-1. In this manner, you will have created the points P₂, P₃, …………, P_n, ………, and joined them to create a beautiful spiral depicting √2, √3, √4, ………..

Punjab State Board PSEB 9th Class Science Book Solutions Chapter 14 Natural Resources Textbook ExerciseQuestions and Answers.

PSEB Solutions for Class 9 Science Chapter 14 Natural Resources

PSEB 9th Class Science Guide Natural Resources Textbook Questions and Answers

Question 1.
Why is atmosphere essential for life?
Answer:
Importance of atmosphere:

1. Role of atmosphere in climate control. Atmosphere acts as a blanket and keeps the average temperature of earth steady during day and even during course of year.
2. Movement of air causes winds.
3. Rain and rainfall pattern are decided by wind pattern.
4. Air provides oxygen for breathing.
5. Atmosphere absorbs the harmful ultrovoilet rays thus protects the living organisms.

Question 2.
Why is water essential for life?
Answer:
Water is a wonder liquid and is essential for life due to the following reasons:

1. Life is not possible without water.
2. Water makes up 60-70 per cent of body weight.
3. All the reactions that take place in our body and within the cells occur between substances that are dissolved in water.
4. Water is required for transport of materials in living organisms.
5. The density of water is similar to that of protoplasm.
6. Water is a universal solvent.

Question 3.
How are living organisms dependent on the soil? Are organisms that live in water totally independent of soil as a resource?
Answer:
Functions of Soil:

Soil plays an important role in plant growth by providing water, nutrients and anchorage i.e. fixation of plant in it.

1. Soil also supports the growth of crops, grassland and forests which provide us food, fibre, wood and building material.
2. Soil is an important resource and decides the diversity of life in an area. Plants living in water are also dependent on soil.

Question 4.
You have seen weather reports on television and in newspapers. How do you think that we are able to predict the weather?
Answer:
Weather can be predicted on the basis of the study of the following:

• Movement of air resulting in diverse phenomena caused by uneven heating of the atmosphere in different regions of the earth.
• Rainfall pattern is decided by the prevailing wind pattern.

Question 5.
We know that many human activities lead to increasing levels of pollution of the air, water bodies and soil. Do you think that isolating these activities to specific and limited areas would help in reducing pollution?
Answer:
Pollution of air, water and soil is caused by human activities such as:

1. Combustion of fossil fuels for energy used for industries, automobiles.
2. Further use of insecticides and fertilizers cause pollution of soil and water.
3. Release of chemicals from industries also cause pollution.
4. If separate industrial zones are created, it will help in reducing pollution.
5. Controlled release of pollutants from automobiles.

Question 6.
Write a note on how forests influence the quality of air, soil and water resources.
Answer:

1. Roots of plants have important role in preventing soil erosion.
2. Forests have moderating effects on climates.
3. Forests prevent floods.
4. Forests release O₂ evolved during photosynthesis into atmosphere, thus renewing the oxygen.

Science Guide for Class 9 PSEB Natural Resources InText Questions and Answers

Question 1.
How is our atmosphere different from atmosphere on Venus and Mars?
Answer:
In planets such as Venus and Mars the major component of atmosphere is 95-97% of C0₂ and it does not support life. Atmosphere on planet Earth is a mixture of nitrogen (78.08%), oxygen (20.95%), C0₂ (0.03%) and water vapours that help life to exist here.

Question 2.
How does atmosphere acts as a blanket?
Answer:
Atmosphere acts as a blanket because of following reasons:

1. Air is a bad conductor of heat.
2. The atmosphere keeps the average temperature of earth fairly steady during the day and even during the course of whole year.
3. The atmosphere prevents the sudden increase or decrease in temperature.

Question 3.
What causes winds?
Answer:
All movements of air are caused by the uneven heating of the atmosphere in different regions of earth. Air above the land gets heated faster and being light starts rising. As the air rises, a region of low pressure is created. Due to this, air over the sea moves into this area of pressure.

Factors which control the movement of wind:

1. The rotation of earth and presence of mountain ranges are other factors which cause winds.
2. Uneven heating of land in different parts of earth.
3. Differences in heating and cooling of land and water.

Question 4.
How are clouds formed?
Answer:
Clouds are formed by the condensation of water droplets in air. It occurs as large amount of water evaporates and goes into air. Air rises up, it expands and cools. The cooling causes the water vapours in the air to condense in the form of tiny droplets. These water droplets get bigger by more and more condensation of other droplets and form clouds.

Question 5.
List any three human activities that you think would lead to air pollution.
Answer:

1. Combustion of fossil fuels. Excessive use and burning of fossil fuels like coal and petroleum by man in industries and automobiles produce different oxides of nitrogen and sulphur.
2. These are not only dangerous to our respiratory system but also leads to acid rain.
3. Deforestation i.e. cutting of trees leads to deterioration of atmosphere. The pollutants also come from industries.
4. Forest fires, excessive mining and ore refining, excessive use of chloro-fluoro carbons and excessive industrialisation leads to air pollution.

Question 6.
Why do organisms need water?
Answer:
Importance of water:

1. All cellular processes take place in water medium.
2. All reactions that take place within our body and within the cells occur between substances that are dissolved in water.
3. Substances are also transported from one part of the body to the other in a dissolved form.
4. Organisms need to maintain the level of water within their bodies in order to survive.
5. Water is a universal solvent and helps the organism in many ways.
6. Water is required by organisms for many of their activities such as agriculture, production of hydropower, drinking, cooking etc.
7. Terrestrial life forms require freshwater because their bodies cannot tolerate high amount of dissolved salts in saline water.
8. The availability of water is the major resource which determines the diversity of life on land.
9. Thus, water is essential for maintenance and very existence of life.

Question 7.
What is the major source of fresh water in the city/town/village where you live?
Answer:
Freshwater is found in ice-caps and on snow-covered mountains. The underground water and the water in rivers, lakes and ponds is also fresh. This water is available for human use.

Question 8.
Do you know any activity which may be polluting the water sources?
Answer:

1. Sewage from towns and cities and waste from factories released into water bodies.
2. Discharging hot water from cooling towers into water bodies affects the living organisms.

Question 9.
How is soil formed?
Answer:
The weathering of rocks at or near the surface of earth over long period of time results in soil formation. They are broken down by various physical, chemical and biological processes. The end products of this breaking down are the fine particles of soil.

Soil: There are many other factors which play a vital role in the formation of soil. These factors are:

1. The Sun: It causes heating of rocks which Causes cracking and ultimately breaking up into smaller pieces.
2. Water: It breaks rocks both by freezing and fast flow.
3. Wind: It causes erosion of rocks.
4. Living Organisms: Lichens and mosses growing dn rock surface form cracks in them and result in their breakdown.

Question 10.
What is soil erosion?
Answer:
Removal of useful components from the topsoil which affects the fertility of soil is called soil erosion.

Question 11.
What are the methods of preventing or reducing soil erosion?
Answer:
Prevention of Soil Erosion:

1. It can be prevented by intensive cropping.
2. It can be prevented by providing proper drainage canals around the fields.
3. Soil erosion in hilly areas can be prevented by practising terrace farming.
4. It can be prevented by planting trees and sowing grasses.
5. It can be prevented by constructing strong embankments along the river banks.

Question 12.
What are the different states in which water is found during water cycle?
Answer:
Groundwater, surface water, water vapours, water droplets, clouds. Water is found in gaseous state, liquid state and solid state during water cycle.

Question 13.
Name two biological important compounds that contain both oxygen and nitrogen.
Answer:
Proteins and Nucleic acids (DNA and RNA).

Question 14.
List any three human activities which would lead to an increase in CO, in air.
Answer:

1. Combustion of fossil fuel to provide energy for various needs like heating, cooking transportation etc.
2. Respiration.
3. Deforestation.

Question 15.
What is greenhouse effect?
Answer:
Greenhouse effect. The increase in global temperature due to rise in CO-, is called greenhouse effect. It causes global warming.

Question 16.
What are the two forms of oxygen found in the atmosphere?
Answer:

1. Oxygen (0₂), about 21%.
2. Ozone: In the upper region such as stratosphere oxygen is found in the form of ozone.