Class 9

Samacheer Kalvi 9th Maths Solutions Chapter 3 Algebra Ex 3.8

You can Download Samacheer Kalvi 9th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 3 Algebra Ex 3.8

Question 1.
Factorise each of the following polynomials using synthetic division:
(i) x3 – 3x2 – 10x + 24
(ii) 2x3 – 3x2 – 3x + 2
(iii) -7x + 3 + 4x3
(iv) x3 + x2 – 14x – 24
(v) x3 – 7x + 6
(vi) x3 – 10x2 – x + 10
Solution:
(i) x3 – 3x2 – 10x + 24
Let p(x) = x3 – 3x2 – 10x + 24
Sum of all the co-efficients = 1 – 3 – 10 + 24 = 25 – 13 = 12 ≠ 0
Hence (x – 1) is not a factor.
Sum of co-efficient of even powers with constant = -3 + 24 = 21
Sum of co-efficients of odd powers = 1 – 10 = – 9
21 ≠ -9
Hence (x + 1) is not a factor.
p (2) = 23 – 3 (22) – 10 × 2 + 24 = 8 – 12 – 20 + 24
= 32 – 32 = 0 ∴ (x – 2) is a factor.
Now we use synthetic division to find other factor
Samacheer Kalvi 9th Maths Chapter 3 Algebra Ex 3.8 1
Thqs (x – 2) (x + 3) (x – 4) are the factors.
∴ x3 – 3x2 – 10x + 24 = (x – 2) (x + 3) (x – 4)

The polynomial division calculator allows you to divide two polynomials to find the quotient and the remainder of the division.

(ii) 2x2 – 3x2 – 3x + 2
Let p (x) = 2x3 – 3x2 – 3x + 2
Sum of all the co-efficients are
2 – 3 – 3 + 2 = 4 – 6 = -2 ≠ 0
∴ (x – 1) is not a factor
Sum of co-efficients of even powers of x with constant = -3 + 2 = – 1
Sum of co-efficients of odd powers of x = 2- 3= -1
(-1) = (-1)
∴ (x + 1) is a factor
Let us find the other factors using synthetic division
Samacheer Kalvi 9th Maths Chapter 3 Algebra Ex 3.8 2
Quotient is 2x2 – 5x + 2 = 2x – 4x – x + 2 = 2x (x – 2) – 1 (x – 2)
= (x – 2) (2x – 1)
∴ 2x3 – 3x2 – 3x + 2 = (x + 1) (x – 2) (2x – 1)

(iii) -7x + 3 + 4x3
Let p(x) = 4x3 + 0x2 – 7x + 3
Sum of the co-efficients are = 4 + 0 – 7 + 3
= 7 – 7 = 0
∴ (x- 1) is a factor
Sum of co-efficients of even powers of x with constant = 0 + 3 = 3
Sum of co-efficients of odd powers of x with constant = 4 – 7 = -3
-3 ≠ -3
∴ (x + 1) is not a factor
Using synthetic division, let us find the other factors.
Samacheer Kalvi 9th Maths Chapter 3 Algebra Ex 3.8 3
Samacheer Kalvi 9th Maths Chapter 3 Algebra Ex 3.8 4
Quotient is 4x2 + 4x – 3
= 4x2 + 6x – 2x – 3
= 2x (2x + 3) – 1 (2x + 3)
= (2x + 3) (2x – 1)
∴ The factors are (x – 1), (2x + 3) and (2x – 1)
∴ -7x + 3 + 4x3 = (x + 1) (2x + 3) (2x – 1)

Samacheer Kalvi 9th Maths Solutions Chapter 3 Algebra Ex 3.8

(iv) x3 + x2 – 14x – 24
Let p (x) = x3 + x2 – 14x – 24
Sum of the co-efficients are = 1 + 1 – 14 – 24 = -36 ≠ 0
∴ (x – 1) is not a factor
Sum of co-efficients of even powers of x with constant = 1 – 24 = -23
Sum of co-efficients of odd powers of x = 1 – 14 = -3
-23 ≠ -13
∴ (x + 1) is also not a factor
p(2) = 23 + 22 – 14 (2) – 24 = 8 + 4 – 28 – 24
= 12 – 52 ≠ 0, (x – 2) is a not a factor
p (-2) = (-2)3 + (-2)2 – 14 (-2) – 24
= -8 + 4 + 28 – 24 = 32 – 32 = 0
∴ (x + 2) is a factor
To find the other factors let us use synthetic division.
Samacheer Kalvi 9th Maths Chapter 3 Algebra Ex 3.8 5
∴ The factors are (x + 2), (x + 3), (x + 4)
∴ x3 + x2 – 14x – 24 = (x + 2) (x + 3) (x – 4)

(v) x3 – 7x + 6
Let p (x) = x3 + 0x2 – 7x + 6
Sum of the co-efficients are = 1 + 0 – 7 + 6 = 7 – 7 = 0
∴(x- 1) is a factor
Sum of co-efficients of even powers of x with constant = 0 + 6 = 6
Sum of coefficient of odd powers of x = 1 – 7 = -7
6 ≠ -7
∴ (x + 1) is not a factor
To find the other factors, let us use synthetic division.
Samacheer Kalvi 9th Maths Chapter 3 Algebra Ex 3.8 6
∴ The factors are (x – 1), (x – 2), (x + 3)
∴ x3 + 0x2 – 7x + 6 = (x – 1) (x – 2) (x + 3)

(vi) x3 – 10x2 – x + 10
Let p (x) = x3 – 10x2 – x + 10
Sum of the co-efficients = 1 – 0 – 1 + 10
= 11 – 11 = 0
∴ (x – 1) is a factor
Sum of co-efficients of even powers of x with constant = -10 + 10 = 0
Sum of co-efficients of odd powers of = 1 – 1 = 0
∴(x + 1) is a factor
Synthetic division
Samacheer Kalvi 9th Maths Chapter 3 Algebra Ex 3.8 7
∴ x3 + 10x2 – x + 10 = (x – 1) (x + 1) (x – 10)

Samacheer Kalvi 9th Science Solutions Chapter 14 Acids, Bases and Salts

You can Download Samacheer Kalvi 9th Science Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th Science Solutions Chapter 14 Acids, Bases and Salts

Samacheer Kalvi 9th Science Acids, Bases and Salts Textbook Exercises

I. Choose the correct answer.

Question 1.
Zn + 2HCl ➝ ZnCl2 + ………….. ↑
(a) H2
(b) O2
(c) CO2
Answer:
(a) H2

Question 2.
Apple contains malic acid. Orange contains ……………….
(a) citric acid
(b) ascorbic acid
Answer:
(b) ascorbic acid

Samacheer Kalvi 9th Science Solutions Chapter 14 Acids, Bases and Salts

Question 3.
Acids in plants and animals are organic acids. Whereas Acids in rocks and minerals are ………………..
(a) Inorganic acids
(b) Weak acids
Answer:
(a) Inorganic acids

Question 4.
Acids turn blue litmus paper to …………………
(a) Green
(b) Red
(c) Orange
Answer:
(b) Red

Question 5.
Since metal carbonate and metal bicarbonate are basic they react with acids to give salt and water with the liberation of ………………
(a) NO2
(b) SO2
(c) CO2
Answer:
(c) CO2

Question 6.
The hydrated salt of copper sulphate has …………….. colour
(a) Red
(b) White
(c) Blue
Answer:
(c) Blue

II. Answer in brief.

Question 1.
Name any two metals which do not react with sodium hydroxide.
Answer:
Few metals do not react with sodium hydroxide. For example: Cu, Ag, Cr.

Samacheer Kalvi 9th Science Solutions Chapter 14 Acids, Bases and Salts

Question 2.
Write any four uses of acids.

  • Sulphuric acid is called King of Chemicals because it is used in the preparation of many other compounds. It is used in car batteries also.
  • Hydrochloric acid is used as a cleansing agent in toilets.
  • Citric acid is used in the preparation of effervescent salts and as a food preservative.
  • Nitric acid is used in the manufacture of fertilizers, dyes, paints and drugs.

Question 3.
Give the significance of pH of soil in agriculture.
Answer:
In agriculture, the pH of soil is very important. Citrus fruits require slightly alkaline soil, while rice requires acidic soil and sugarcane requires neutral soil.

Question 4.
When does the acid rain occur?
Answer:
The pH of rain water is approximately 7 which means that it is neutral and also represents its high purity. If the atmospheric air is polluted with oxide gases of sulphur and nitrogen, they get dissolved in rainwater and make its pH less than 7. Thus, if the pH of rain water is less than 7, then it is called acid rain.

Question 5.
What are the uses of Plaster of Paris?
Answer:

  1. It is used for plastering bones
  2. It is used for making casts for statues.

Question 6.
Two adds ‘A’ and ‘B’ are given. Acid A gives one hydrogen ion per molecule of the acid in solution. Acid B gives two hydrogen ions per molecule of the acid in solution.

  1. Find out acid A and acid B.
  2. Which acid is called the King of Chemicals?

Answer:

  1. Acid A is HCl and Acid B is H2SO4
  2. Sulphuric acid is called the King of Chemicals.

Samacheer Kalvi 9th Science Solutions Chapter 14 Acids, Bases and Salts

Question 7.
Define aquaregia.
Answer:
Metals like gold and silver are not reactive with either HCl or HNO3. But the mixture of these two acids can dissolve gold. This mixture is called Aquaregia. It is a mixture of hydrochloric acid and nitric acid prepared optimally in a molar ratio of 3:1. It is a yellow- orange fuming liquid. It is a highly corrosive liquid, able to attack gold and other resistant substances.

Question 8.
Correct the mistakes:

  1. Washing soda is used for making cakes and bread soft, spongy.
  2. Calcium sulphate hemihydrate is used in textile industry.

Answer:

  1. Baking soda is used for making cakes and bread soft, spongy.
  2. Calcium Oxychloride hemihydrate is used in textile industry.

Question 9.
What is neutralization reaction? Give an example.
Acids and bases neutralize each other to form corresponding salts and water.
Example: Bases react with acids to form salt and water.
KOH + HCl ➝ KCl + H2O
The above reaction between a base and an acid is known as Neutralisation reaction.

III. Answer in detail.

Question 1.
Why does distilled water not conduct electricity whereas rainwater does?
Answer:
Distilled water is created through the process of distillation.

In this process, the pure water (H2O) is boiled to remove contaminants. This is done by the capturing of steam that rises after boiling of water followed by cooling. This is distilled water and is free of ions that are required for the conduction of electricity. Whereas, the pollutants present in the atmospheric air get dissolved in rainwater which provides necessary ions for the conduction of electricity.

Samacheer Kalvi 9th Science Solutions Chapter 14 Acids, Bases and Salts

Question 2.
Plaster of Paris should be stored in a moisture-proof container. Why?
Answer:
The Plaster of Paris .should be stored in a moisture-proof container as it turns into a hard substance known as gypsum on the absorption of water from moisture.

Question 3.
Write any four uses of bases.
Answer:

  1. Sodium hydroxide is used in the manufacture of soap.
  2. Calcium hydroxide is used in whitewashing buildings.
  3. Magnesium hydroxide is used as a medicine for stomach disorders.
  4. Ammonium hydroxide is used to remove grease stains from clothes.

Question 4.
Write any five uses of salts.
Answer:
Common Salt (NaCl): It is used in our daily food and used as a preservative.

  1. Washing Soda (Sodium Carbonate):
    • It is used in softening hard water.
    • It is used in glass, soap and paper industries.
  2. Baking Soda (Sodium bicarbonate -NaHC03):
    • It is used in making of baking powder which is a mixture of baking soda and tartaric acid.
    • It is used in soda-acid fire extinguishers.
    • Baking powder is used to make cakes and bread, soft and spongy.
    • It neutralizes excess acid in the stomach and provides relief.
  3. Bleaching powder (Calcium Oxychloride – CaOCl2)
    • It is used as disinfectant.
    • It is used in textile industry for bleaching cotton and linen.
  4. Plaster of Paris (Calcium Sulphate Hemihydrate – CaS04 . \(\frac { 1 }{ 2 }\)H20)
    • It is used for plastering bones
    • It is used for making casts for statues

Question 5.
Sulphuric acid is called King of Chemicals. Why is it called so?
Answer:
Sulphuric acid is called King of Chemicals because it is used in the preparation of many Other compounds. It is used in car batteries also.
Acids react with metallic oxides to give salt and water.
CaO + H2S04 CaS04 + H20

Activity

Question 1.
Take about 10 ml of dilute hydrochloric acid in a test tube and add a few pieces of zinc granules into it. What do you observe? Why are bubbles formed in the solution?
Answer:
Take a burning candle near a bubble containing hydrogen gas, the flame goes off with a ‘Popping’ sound. This confirms that metal displaces hydrogen gas from the dilute acid.
Bubbles are formed as Zinc reacts with HCl to form ZnCl and Hydrogen gas is released.

Samacheer Kalvi 9th Science Solutions Chapter 14 Acids, Bases and Salts

Question 2.

  • Take solutions of hydrochloric acid or sulphuric acid.
  • Fix two nails on a cork and place the cork in a 100 ml beaker.
  • Connect the nails to the two terminals of a 6V battery through a bulb and a switch as shown in Figure.
  • Now pour some dilute HCl in the beaker and switch on the current.
  • Repeat the activity with dilute sulphuric acid, glucose and alcohol solutions. What do you observe now?
  • Does the bulb glow in all cases?

Answer:
The bulb glows when the solution in the beaker is hydrochloric acid or sulphuric acid as they ionise into H+ ions thus facilitating the flow of current.
Both hydrochloric acid and sulphuric acid readily ionise to H+, Cl and 2H+ and SO4- in solution and thus conduct electricity letting the bulb glow. Whereas glucose and alcohol do not ionise and hence the bulb doesn’t glow.

Question 3.
Collect the following samples from the science laboratory – Hydrochloric acid, sulphuric acid and Nitric acid, Sodium hydroxide, Potassium hydroxide. Take 2 ml of each solution in a test tube and test with a litmus paper and indicators phenolphthalein and Methyl orange. Tabulate your observations.

Sample Solutions Litmus Paper Indicators
Blue Red Phenolphthalein Methyl Orange
Hydrochloric acid Colourless Pink
Sulphuric acid Colourless Pink
Nitric acid Colourless Pink
Sodium hydroxide Pink Yellow
Potassium hydroxide Pink Yellow

Question 4.
Fill in the blanks in the following table based on the concept of water of crystallisation.

Salt Formula of an hydrous salt Formula of hydrated salt Name of hydrated salt
Zinc sulphate ZnSO4 ZnSO4.7H2O
Magnesium chloride MgCl2 Magnesium chloride hexahydrate
Iron (II) sulphate FeSO4.7H20 Iron (II) sulphate heptahydrate
Calcium chloride CaCl2 CaCl2.2H2O
Sodium thiosulphate Na2S2O3 Sodium thiosulphate pentahydrate

Answer:

Salt Formula of an hydrous salt Formula of hydrated salt Name of hydrated salt
Zinc sulphate ZnSO4 ZnSO4.7H2O Zinc sulphate heptahydrate
Magnesium chloride MgCl2 MgCl2. 6H2O Magnesium chloride hexahydrate
Iron (II) sulphate FeSO4 FeSO4.7H20 Iron (II) sulphate heptahydrate
Calcium chloride CaCl2 CaCl2.2H2O Calcium chloride dihydrate
Sodium thiosulphate Na2S2O3 Na2S2O3.5H2O Sodium thiosulphate pentahydrate

Question 5.
Boil about 100 ml of groundwater in a vessel to dryness. After all the water get evaporated observe the inner wall of the vessel. Can you observe any deposits?
Answer:
Yes, this is the deposit of dissolved salts present in water.

Samacheer Kalvi 9th Science Acids, Bases and Salts Additional Questions

I. Short answers questions.

Question 1.
What are acids?
Answer:
Acids are those with chemical properties that includes; turning litmus red, neutralizing alkalis, and dissolving some metals; typically, a corrosive or sour-tasting liquid present in curd, fruit juices, vinegar, etc. The word ‘acid’ is derived from the Latin name “acidus” which means sour taste.

Samacheer Kalvi 9th Science Solutions Chapter 14 Acids, Bases and Salts

Question 2.
Why is the term basicity is used for acids?
Answer:
The term basicity is used for acids since they have replaceable hydrogen atoms in a molecule.

Question 3.
What are bases?
Answer:
According to Arrhenius theory, bases are substances that ionise in water to form hydroxyl ions (OH). Bases that are soluble in water are called alkalis.

Question 4.
“All alkalis are bases, but not all bases are alkalis”. Justify this statement.
Answer:
Bases react with acids to neutralise them. Some are insoluble. Soluble bases are called Alkalis. For example CuO (copper oxide) does not dissolve in water, therefore it’s a base. Generally hydroxides of alkali metals and alkaline earth metals are called alkalis.

Question 5.
What is the correct procedure of mixing an acid and water? Why?
Answer:
One has to be cautious while mixing’a concentrated inorganic acid with water. Always the acid must be added to water gently. While adding acid to water, one has to keep stirring the mixture simultaneously. Water should never be added to an acid as it generates huge amount of heat and the mixture can splash out of the container and cause harm to the person handling it, causing bums.

Question 6.
“All acids contain one or more hydrogen atoms, but not all substances containing hydrogen are acids.” Support this statement with examples.
Answer:
HCl (hydrochloric acid), H2SO4 (sulphuric acid) and HNO3 (Nitric acid) are all examples of inorganic acids. They all have the hydrogen atom in common. Most acids essentially contain one or more hydrogen atoms. Whereas water (H20) also contains hydrogen, but it is not an acid. Similarly, molecules of methane and ammonia also contain hydrogen, but all these do not produce H+ ions in aqueous solutions. Therefore it can be said that “all acids contain hydrogen, but all substances containing hydrogen are not acids.”

Samacheer Kalvi 9th Science Solutions Chapter 14 Acids, Bases and Salts

Question 7.
Explain the role of pH in our digestive system.
Answer:
The pH of saliva is usually between 6.5 – 7.5.
pH of stomach fluid is approximately 2.0. This is because it produces hydrochloric acid which helps in the digestion of food without harming the stomach. pH in the small and large intestine ranges from 4.0 to 7.0.

II. Long answers questions.

Question 1.
Explain water of crystallisation.
Answer:
Many salts are found as crystals with water molecules they contain. These water molecules are known as water of crystallisation. Salts that contain water of crystallisation are called ‘ hydrated salts. The number of molecules of water hydrated to a salt is indicated after the dot in its chemical formula. For example, copper sulphate crystal have five molecules of water for each molecule of copper sulphate. It is written as CuS04.5H20 and named as copper sulphate pentahydrate. This water of crystallisation makes the copper sulphate blue.

When it is heated, it loses its water molecules and becomes white. Salts that do not contain water of crystallisation is called anhydrous salt.

Question 2.
What are four types of salts?
Answer:
Types of Salts

1. Normal Salts
A normal salt is obtained by complete neutralization of an acid by a base.
NaOH + HCl ➝ NaCl + H2O

2. Acid Salts
It is derived from the partial replacement of hydrogen ions of an acid by a metal. When a calculated amount of a base is added to a polybasic acid, acid salt is obtained.
NaOH + H2S02 ➝ NaHS04 + H20

3. Basic Salts
Basic salts are formed by the partial replacement of hydroxide ions of a diacidic or triacidic base with an acid radical.
Pb(OH)2 + HCl ➝ Pb(OH)Cl + H2O

4. Double Salts
Double salts are formed by the combination of the saturated solution of two simple salts in equimolar ratio followed by crystallization. For example, Potash alum is a mixture of potassium sulphate and aluminium sulphate.
KAI(SO4)2·12H2O

Question 3.
Classify acids based on their sources and basicity.
Answer:
Acids are classified in different ways as follows:
Based on their sources:

  1. Organic acids: Acids present in plants and animals (living things) are organic acids. Example: HCOOH, CH3COOH
  2. Inorganic acids: Acids prepared from rocks and minerals are inorganic acids or mineral acids. Example: HCl, HNO3, H2SO4

Based on their Basicity:

  1. Monobasic Acid: Acid that contain only one replaceable hydrogen atom per molecule is called monobasic acid. It gives one hydrogen ion per molecule of the acid in solution. Example: HCl, HNO3
  2. Dibasic Acid: An acid which gives two hydrogen ions per molecule of the acid in solution. Example: H3SO4, H2CO3
  3. Tribasic Acid: An acid which gives three hydrogen ions per molecule of the acid in solution. Example: H3P04

Samacheer Kalvi 9th Science Solutions Chapter 14 Acids, Bases and Salts

Question 4.
Name the acid present in the given table.
Answer:
Acid and its source

SOURCE ACID PRESENT
Apple Malic acid
Lemon Citric acid
Grape Tartaric acid
Tomato Oxalic acid
Vinegar Acetic acid
Curd Lactic acid
Orange Ascorbic acid
Tea Tannic acid
Ant, Bee Formic acid
Stomach juice Hydrochloric acid

Question 5.
Describe the tests used to determine acids and bases.
Answer:
Take 10 ml of solution in a test tube and test with a litmus paper or indicators like phenolphthalein and methyl orange.

  1. Test with a litmus paper: An acid turns blue litmus paper into red. A base turns red litmus paper into blue.
  2. Test with an indicator Phenolphthalein: In acid medium, phenolphthalein is colourless.
    In basic medium, phenolphthalein is pink in colour.
  3. Test with an indicator Methyl orange: In acid medium, methyl orange is pink in colour. In basic medium, methyl orange is yellow in colour.

Samacheer Kalvi 9th Science Solutions Chapter 14 Acids, Bases and Salts

Question 6.
Differentiate between Acids and Bases.
Answer:

Acids Bases
Acids are proton donors or electron acceptors Bases are proton acceptor or electron donors
Acids are able to increase the H+ ion concentration in aqueous solution. Bases are able to increase the OH” ion concentration in an aqueous solution
Acids have a pH value < 7. Bases have a pH value > 7.
Acids turn blue litmus paper red. Bases turn red litmus paper blue.
Acids react with bases to form salts in an aqueous medium. Bases react with acids to form salts.
Acids are sour to taste. Bases are soapy to touch.

Samacheer Kalvi 9th Maths Solutions Chapter 8 Statistics Additional Questions

You can Download Samacheer Kalvi 9th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 8 Statistics Additional Questions

Exercise 8.1

Question 1.
The following data gives the number of residents in an area based on their age. Find the average age of the residents.
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 1
Solution:
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 2
Samacheer Kalvi 9th Maths Solutions Chapter 8 Statistics Additional Questions
Question 2.
Find the mean for the following frequency table :
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 3
Solution:
Let Assumed mean A = 170
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 4

Median Calculator Instructions. This calculator computes the median from a data set: To calculate the median from a set of values, enter the observed values.

Question 3.
Find the mean for the following distribution using step Deviation Method.
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 5
Solution:
Let Assumed mean A = 28, Class width C = 8
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 6

Exercise 8.2

Question 1.
For the following up grouped data 8, 15, 14, 19, 11, 16, 10, 8, 17, 20. Find the median.
Solution:
Arrange the values in ascending order 8, 8, 10, 11, 14, 15, 16, 17, 19, 20
The number of values = 10
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 7

Question 2.
The following table gives the weekly expenditure of 200 families. Find the median of the weekly expenditure.
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 8
Solution:
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 9
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 10
Question 3.
The median of the following data is 24. Find the value of x.
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 11
Solution:
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 12
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 13

Question 4.
The following are the scores obtained by 11 players in a cricket match 7, 21, 45, 12, 56, 35, 25, 0, 58, 66, 29. Find the median score.
Solution:
Let us arrange the values in ascending order 0, 7, 12, 21, 25, 29, 35, 45, 56, 58, 66
The number of values = 11 which is odd.
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 60

Exercise 8.3
Samacheer Kalvi 9th Maths Solutions Chapter 8 Statistics Additional Questions
Question 1.
Find the mode of the given data : 65, 65, 71, 71, 72, 75, 82, 72, 47, 72.
Solution:
In the given data 72 occurs thrice. Hence the mode is 72.

Question 2.
Find the mode:
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 61
Solution:
7 has the maximum frequency 21. Therefore 7 is the mode.

Question 3.
Find the mode for the following data.
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 62
Solution:
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 63

Question 4.
In a distribution, the mean and mode are 46 and 40 respectively. Calculate the median.
Solution:
Given, Mean = 46 and mode = 40
Using mode ≈ 3 median – 2 mean ,
40 ≈ 3 Median – 2 (46)
3 Median ≈ 40 + 92
Therefore, Median ≈ \(\frac{132}{3}\) = 44

Exercise 8.4
Samacheer Kalvi 9th Maths Solutions Chapter 8 Statistics Additional Questions
Multiple Choice Questions :

Question 1.
The mean of first 10 natural numbers.
(1) 25
(2) 55
(3) 5.5
(4) 2.5
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 71
Solution:
(3) 5.5

Question 2.
The mean of a distribution is 23, the median is 24 and the mode is 25.5. It is most likely that this distribution is :
(1) Positively skewed
(2) Symmetrical
(3) Asymptotic
(4) Negatively skewed
Hint: For Negatively skewed means is likely to be less than mode and median
Solution:
(4) Negatively skewed

Question 3.
The middle value of an ordered array of numbers is the
(1) Mode
(2) Mean
(3) Median
(4) Mid point
Solution:
(3) Median

Question 4.
The weights of students in a school is a :
(1) Discrete variable
(2) Continuous variable
(3) Qualitative variable
(4) None of these
Solution:
(2) Continuous variable
Samacheer Kalvi 9th Maths Solutions Chapter 8 Statistics Additional Questions
Question 5.
The first hand and unorganized form data is called
(1) Secondary data
(2) Organised data
(3) Primary data
(4) None of these
Solution:
(3) Primary data

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

You can Download Samacheer Kalvi 6th Science Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

Samacheer Kalvi 6th Science Force and Motion Textual Evaluation

I. Choose the correct answer.

Question 1.
Unit of speed is
(a) m
(b) s
(c) kg
(d) m/s
Answer:
(d) m/s

Question 2.
Oscillatory motion among the following is
a. Rotation of the earth about its axis
b. Revolution of the moon about the earth
c. To and fro movement of a vibrating string
d. All of these.
Answer:
c. To and fro movement of a vibrating string

Question 3.
The correct relation among the following is
(a) Speed = distance × time
(b) speed = distance / time
(c) Speed = time / distance
(d) speed = 1/ (distance × time)
Answer:
(b) speed = distance / time

Question 4.
Gita rides with her father’s bike to her uncle’s house which is 40 km away from her home. She takes 40 minutes to reach there.
Statement 1 : She travels with a speed of 1 km/minute
Statement 2: She travels with a speed of 1 km/hour
a. Statement 1 alone is correct.
b. Statement 2 alone is correct
c. Both statement 1 and 2 are correct.
d. Neither statement 1 nor statement 2 is correct.
Answer:
a. Statement 1 alone is correct.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

II. Find whether the following statements are true or false. – if false give the correct answer.

Question 1.
To and fro motion is called oscillatory motion.
Answer:
True.

Question 2.
Vibratory motion and rotatory motion are periodic motions.
Answer:
False.
Vibratory motion and oscillatory motion are periodic motions.

Question 3.
Vehicles moving with varying speeds are said to be in uniform motion.
Answer:
False.
Vehicles moving with varying speeds are said to be in non-uniform motion.
(OR)
Vehicles moving with uniform speeds are said to be in uniform motion.

Question 4.
Robots will replace humans in the future.
Answer:
False. Robots will not replace humans in the future.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

III. Fill in the blanks.

  1. A bike moving on a straight road is an example of _______ motion.
  2. Gravitational force is a _______ force.
  3. The motion of a potter’s wheel is an example of _______ motion.
  4. When an object covers equal distances in equal interval of time, it is said to be in _______ motion.

Answers:

  1. Linear
  2. Non-Contact Force
  3. rotatory
  4. uniform

IV. Match the following
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 1
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 25
Answers:

  1. c
  2. d
  3. b
  4. a
  5. e

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

V. Analogy

Question 1.
kicking a ball: contact force :: falling of leaf: ________?
Answer:
Noncontact force.

Question 2.
Distance : metre :: speed : _______ ?
Answer:
metre/second.

Question 3.
circulatory motion :: a spinning top :: oscillatory motion : _______ ?
Answer:
Swinging of a pendulum.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

VI. Given below Is the distance-traveled by an elephant across a forest with uniform speed. Complete the data of the table given below with the idea of uniform speed.
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 2
Answer:
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 3
(i) Distance/Time = \(\frac { 4 }{ 2 } \) × 4 = \(\frac { 16 }{ 22 } \) = 8
(ii) Distance / Time = \(\frac { 4 }{ 2 } \) × 8 = \(\frac { 32 }{ 2 } \) = 16
(iii) Time/Distance = \(\frac{1 \emptyset}{2 \emptyset}\) × 12 = \(\frac { 12 }{ 2 } \) = 6

VII. Complete the web chart.
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 4
Answer:
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 5

VIII. Give one word for the following statements.

Question 1.
The force acts on an object without physical contact with it.
Answer:
non-contact forces.

Question 2.
A change in the position of an object with time.
Answer:
Motion.

Question 3.
The motion repeats itself after a fixed interval of time.
Answer:
Oscillatory motion.

Question 4.
The motion of an object travels equal distances in equal intervals of time.
Answer:
Uniform motion.

Question 5.
A machine capable of carrying out a complex series of actions automatically.
Answer:
Artificial intelligence.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

IX. Answer the following in a sentence or two.

Question 1.
Define force.
Answer:
Force is a push or pull by an animate or inanimate agency.

Question 2.
Name different types of motion based on the path.
Answer:

  1. Linear motion;
  2. Curvilinear;
  3. Circular motion;
  4. Rotatory motion;
  5. Oscillatory motion
  6. Irregular motion.

Question 3.
If you are sitting in a moving car, will you be at rest or motion with respect to your friend sitting next to you?
Answer:
I will be at rest with respect to my friend sitting with me in a moving car.

Question 4.
The rotation of the earth is a periodic motion. Justify
Answer:
Rotation of the earth is a periodic motion because it takes an equal interval of time for all rotations.

Question 5.
Differentiate between rotational and curvilinear motion.
Answer:
Rotational motion:
The movement of a body about its own axis
Ex: Rotating tape

Curvilinear motion:
Movement of a body along a curved path
Ex. Throwing a ball.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

X. Calculate

Question 1.
A vehicle covers a distance of 400 km in 5 hours. Calculate its average speed.
Answer:
Distance covered by the vehicle = 400 km
Time taken = 5 hour
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 6

XI. Answer in detail.

Question 1.
What is motion? Classify different types of motion with examples.
Answer:
Motion is a change in the position of an object with respect to time.
Types of motion based on the path:

  1. Linear motion: moving in a straight line, like a person walking on a straight path.
  2. Curvilinear motion: moving ahead by changing direction like a throwing ball.
  3. Circular motion: moving in a circular path. Ex. Swirling store tied to the rope.
  4. Rotatory motion: The movement of a body about its own axis. Ex. Revolution of the earth around the sun.
  5. Oscillatory motion: Coming back to the same position after a fixed time interval. Ex pendulum.
  6. Zigzag (irregular): like the motion of a bee or people walking in a crowded street.

Motion-based on duration:
Periodic motion: motion repeated in equal intervals of time. Ex. Revolution of the moon around the earth.
Nonperiodic motion: motion is not repeated in equal interval Ex. Sabing swing.

Motion-based on speed :
Uniform motion: The object covers the uniform distance in uniform intervals.
Non- uniform motion: if an object covers different distances at different intervals of times. Ex. The motion of a vehicle.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

XII. Fill with examples.
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 7
Answer:
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 8

Samacheer Kalvi 6th Science Force and Motion Intext Activities

Activity – 1

Can you identify whether it is push or pull that results in motion in the following cases?
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 9
Event 2:
The girl on the swing is moving with respect to the seat of the swing.
She is at rest with respect to the garden.

Event 3:
Nisha is going to her grandmother’s house by bicycle The girl on the bicycle is moving with respect to the road.
She is at rest with respect to the bicycle.

Activity – 2

Moon or Cloud?
Observe the moon on a windy night with a fair bit of cloud cover in the sky. As a cloud passes in front of the moon you sometimes think it is the moon which is moving behind the cloud. What would you think if you were to observe a tree at the same time?
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 10
Answer:
Activity to be done by the students themselves

Activity – 3

Fill in the empty spaces.
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 11
Answer:
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 12

Can you give example for contact and non-contact forces?
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 13
Answer:
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 14

Activity – 4
Play with a pencil
Please do what Shanthi did…

  1. Shanthi took a pencil and sharpened it with a sharpener.
  2. Then she drew a circle using the pencil and a compass.
  3. Later she took her ruler (scale) and drew a straight line in another paper.
  4. Then she kept the pencil between her finger and moved it back and forth.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 15

Now, look at the motion of the pencil in all these four cases. How was it?

  1. In the first case, the pencil rotated in its axis.
  2. In the second case, it went in a circle.
  3. In the third case, the pencil travelled in a straight line.
  4. The fourth case, the pencil tip moved back and forth, that is it oscillated like a swing.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

Activity – 5
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 16

Activity – 6
Classify the following according to the path it takes.

Linear, Curvilinear, Circular, Rotatory, Oscillatory, Zigzag (irregular)

  • A sprinter running a 100 m race – Linear Motion
  • A coconut falling from a tree – Linear Motion
  • striking a coin in a carom board game – Zigzag Motion
  • Motion of flies and mosquitoes – Zigzag Motion
  • Beating of heart – Oscillatory Motion
  • Children playing in a swing – Oscillatory Motion
  • The tip of hands of a clock – Rotatory Motion
  • Flapping of elephant’s ears – Oscillatory Motion
  • A stone is thrown into the air at an angle – Curvilinear Motion
  • Movement of people in a bazaar – Zigzag Motion
  • Athlete running around a track – Circular Motion
  • Revolution of the moon around the earth – Circular Motion
  • The movement of a ball kicked in a football match – Curvilinear Motion
  • Motion of a spinning top – Rotatory Motion
  • Revolution of the earth around the sun – Circular Motion
  • Swinging of a pendulum – Oscillatory Motion
  • Children skidding on a sliding board – Linear Motion
  • Skidding down a playground slide – Zigzag Motion
  • Wagging tail of a dog – Oscillatory Motion
  • Flapping of a flag in wind – Oscillatory Motion
  • A car driving around a curve – Circular Motion
  • Woodcutter cutting with a saw – Linear Motion
  • Motion of water wave – Oscillatory Motion
  • Motion of piston inside a syringe – Linear Motion
  • Bouncing ball – Oscillatory Motion

add five motions you observe to this list:

  • Falling fruits from the tree – Linear Motion
  • Ceiling fan running – Rotatory Motion
  • Car running on the straight road – Linear Motion
  • Swirling stone tied to the rope – Circular Motion
  • Motion of sewing machine needle – Oscillatory Motion

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

Activity
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 17
Answer:
The Taxi driver travelled at the highest speed.

How do we say? Let us calculate how long they travelled in One Hour?
Distance travelled by Car in One Hour = 80 km (160 ÷ 2)
Distance travelled by the Bus in One Hour = 50 km (200 ÷ 4)
Distance travelled by Truck in One Hour = 60 km (300 ÷ 5)

Have you found out? say now.
Fastest Taxi, Slowest Bus.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

Our speed…

Let us play a small game. Go to the playground with your friends. Mark 100 metre distance for a race. Conduct a friendly running race and calculate the time they took to complete the distance by stopwatch. Now fill up the following table.
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 20

Compute the following Numerical Problems.

  1. If you travel 10 kilometres in 2 hours, your speed is 5 km per hour. (10 km/2 hours)
  2. If you travel 15 kilometres in 1/2 hour, you would travel 30 km in one hour, and your speed is 30 km per hour. (15 km × 2/1 hours)
  3. If you run fast at 20 kilometres per hour for 2 hours, you will cover 40 km. (20 km × 2 hours)

Activity

Multiple Motion to a Sewing Machine
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 21

The motion of the needle
Periodic (or) Oscillatory motion

The motion of the wheel
Rotatory motion

Motion of footrest
Oscillatory motion

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

Activity – 7

Simple Spinner

Let us enjoy by making a simple spinner. Make it by the following instruction.

Cut a 2cm long piece from an old ball-pen refill and make a hole in its center with a divider point (Fig 1).
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 22
Take a thin wire of length 9cm and fold it into a U-shape (Fig 2).

Weave the refill spinner in the U-shaped wire (Fig 3).

Wrap the two ends of the wire on the plastic refill, leaving enough clearance for the spinner to rotate (Fig 4).

On blowing through the refill, the spinner rotates (Fig 5).

For obtaining maximum speed – adjust the wires so that air is directed towards the ends of the spinner.

Have you enjoyed with a simple spinner? Do you observe the motions in the toy? Can you answer the following question?

  1. Motion of the air in tube is _____________ motion.
  2. Motion of the refill stick _____________ motion.
  3. The toy converts _____________ motion into _____________ motion.

Answers:

  1. Linear
  2. Rotatory
  3. Linear, Rotatory

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

Samacheer Kalvi 6th Science Force and Motion Additional Questions

I. Choose the correct answer:

Question 1.
_______ is an ancient Indian astronomer.
(a) C.V. Raman
(b) Aryabhata
(c) Usain Bolt
(d) Edison
Answer:
(b) Aryabhata

Question 2.
What is the path of the housefly buzzing around the room?
(a) Periodic motion
(b) Non- Periodic motion
(c) circular motion
(d) None of the above
Answer:
(b) Non- Periodic motion

Question 3.
Identify the Periodic motion among the following :
(a) a horse running in a race
(b) the revolution of the moon around the earth
(c) a coconut falling from a tree
(d) paper flight moving
Answer:
(b) the revolution of the moon around the earth

Question 4.
The cheetah the fastest animal among terrestrial animals run with an average speed of
(a) 100 km /hr
(b) 200 km/hr
(c) 112 km/hr
(d) 10 km /hr.
Answer:
(c) 112 km/hr

Question 5.
_______ are robots scaled down to microscopic size in order to put them into very small spaces to perform a function.
(a) Car robots
(b) Home robots
(c) Game robots
(d) Nanobots
Answer:
(d) Nanobots

Question 6.
A _______ is the fastest land animal.
(a) Horse
(b) Lion
(c) Cheetah
(d) Tiger
Answer:
(c) Cheetah

Question 7.
A cheetah can run with an average speed of _______
(a) 112 km/h
(b) 121 km/h
(c) 211 km/h
(d) 122 km/h
Answer:
(a) 112 km/h

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

II. Find whether the following sentences are true or false. If false Correct the statement.

Question 1.
Motion occurs when the object is pulled or pushed by an agency.
Answer:
True.

Question 2.
Force executed by touching the body is called non – contact force.
Answer:
False. Force executed by touching the body is called contact force.

Question 3.
Gravity pushes the ripen coconut from the tree to the ground.
Answer:
False. Gravity pulls the ripen coconut from the tree to the ground.

Question 4.
Throwing paper aeroplane is the best example of linear motion.
Answer:
False. Throwing paper aeroplane is the best example of curvilinear motion.

Question 5.
The movement of a body about its own axis like a rotating top is linear motion.
Answer:
False. The movement of a body about its own axis like a rotating top is Rotatory

Question 6.
Motion repeated in equal intervals of time is called as periodic motion.
Answer:
True.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

III. Fill in the blanks.

  1. _________ are push or pull by an animate or inanimate agency.
  2. Application of force in an object results in motion from a state of _________
  3. Fast oscillations are referred to as _________
  4. Motion repeated in equal intervals of time is called _________
  5. _________ are automatic machines.
  6. The term Robots comes from a tech word _________
  7. _________ is die study of robots in science.

Answers:

  1. Forces
  2. rest
  3. vibrations
  4. periodic motion
  5. Robots
  6. robota
  7. Robotics

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

IV. Complete the web chart.
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 23
Answer:

  • A – In animate factors,
  • B – Contact forces.

V. Answer the following in one or two sentences.

Question 1.
What is meant by the State of Rest?
Answer:
When there is no change of position of an object with respect to time and if it remains stationary it is called rest.

Question 2.
What is a non-contact force?
Answer:
The force applied without touching the object is known as non-contact force.

Question 3.
What is the contact force?
Answer:
When the force is in contact with the object then it is known as contact force.

Question 4.
Give the properties of force.
Answer:

  1. Forces can change the state of a body from rest to motion or motion to rest.
  2. Forces can change the shape of the body.

Question 5.
A bus moves with a speed of 40 km and crosses 200 km and then how many hours has that bus taken to travel?
Answer:
Time (t) = \(\frac{distence}{AverageSpeed}\)
Time (t) = \(\frac{200 km}{400 km/h}\) = 5 hours

Question 6.
Define Average speed.
Answer:
The distance travelled by an object in unit time is called average speed.
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion 24

Question 7.
List out the types of motion on the basis of speed.
Answer:
There are two types:

  1. Uniform motion,
  2. Non-uniform motion.

Question 8.
Define uniform motion.
Answer:
If an object covers uniform distances in uniform intervals, then the motion of the object is called uniform motion.

Question 9.
Why robots are used in many places?
Answer:
Robots can perform mechanical and repetitive jobs faster, more accurately than human beings. It can also handle dangerous materials and explore distant planets.

Question 10.
What are the important parts of a robot?
Answer:
Electronic sensors are a robot’s eyes and ears. These are the important parts.

Question 11.
What are nanobots?
Answer:
Nanobots are robots scaled down to microscopic size in order to put them into very small places to perform a function.

Question 12.
What are the uses of future robots?
Answer:

  1. It could be placed in the bloodstream to perform surgical procedures.
  2. It could target cancer cells and destroy them without touching healthy cells nearby.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 2 Force and Motion

VI. Answer in Detail.

Question 1.
Classify the following motions according to the path it takes.

  1. A coconut falling from a tree
  2. Heartbeat
  3. A stone is thrown into the air at an angle
  4. Movement of people in a bazaar
  5. The motion of a spinning top

Answers:

  1. A coconut falling from a tree – Linear Motion
  2. Heartbeat – Oscillatory Motion
  3. A stone is thrown into the air at an angle – Curvilinear Motion
  4. Movement of people in a Bazar – Zigzag Motion
  5. The motion of a spinning top – Rotatory Motion

Question 2.
Classify the following motions based on duration and speed.

  1. Coconut falls to the ground
  2. A cart pulled by a bullock
  3. Train journey
  4. A bouncing ball
  5. Revolution of the Moon around the earth

Answers:

  1. Non-periodic Motion
  2. Non-periodic Motion
  3. Non-uniform Motion
  4. Periodic Motion
  5. Uniform Motion