Friday, July 29, 2022

 

NCERT Solutions – Social Science History Chapter 1

Exercise Page No. 28

1. Write a note on:

a. Guiseppe Mazzini

Answer:

During the 1830s, Giuseppe Mazzini had sought to put together a coherent programme for the unitary Italian Republic. He had also formed a secret society called ‘Young Italy’ for the dissemination of his goals.

b. Count Camillo de Cavour

Answer:

  1. Led the movement to unify Italy
  2. He was neither a revolutionary nor a democrat.
  3. Through a tactful diplomatic alliance engineered by Cavour, Sardini-Piedmont succeeded in defeating the Austrian forces in 1859.

c. The Greek war of independence

Answer:

  1. Greece had been part of the Ottoman Empire since the fifteenth century. The growth of revolutionary nationalism in Europe sparked off a struggle for independence amongst the Greeks, which began in 1821.
  2. Poets and artists lauded Greece as the cradle of European civilisation and mobilised public opinion to support its struggle against a Muslim empire.
  3. Nationalists in Greece got support from other Greeks living in exile and also from many West Europeans, who had sympathies for ancient Greek culture.
  4. Finally, the Treaty of Constantinople of 1832 recognised Greece as an independent nation.

d. Frankfurt parliament

Answer:

  1. It was an all-German National assembly formed by Middle-Class professionals, businessmen and prosperous Artisans belonging to different German regions.
  2. It was convened on 18 May 1848.
  3. It was disbanded on 31 May 1849 as it lost support.

e. The role of women in nationalist struggles

Answer:

  1. Women of the liberal middle classes combined their demands for constitutionalism with national unification. They took advantage of the growing popular unrest to push their demands for the creation of a nation-state on parliamentary principles – a constitution, freedom of the press and freedom of association.
  2. Women had formed their own political associations, founded newspapers and taken part in political meetings and demonstrations.




2. What steps did the French revolutionaries take to create a sense of collective identity among the French people?

Answer:

  1. The ideas of ‘La Patrie’ (the fatherland) and ‘Le Citoyen’ (the citizen) emphasised the notion of a united community enjoying equal rights under a constitution.
  2. A new French flag, the tricolour, was chosen to replace the former royal standard.
  3. New hymns were composed, oaths taken and martyrs commemorated, all in the name of the nation.
  4. A centralised administrative system was put in place, and it formulated uniform laws for all citizens within its territory.
  5. Internal customs duties and dues were abolished, and a uniform system of weights and measures was adopted.
  6. Regional dialects were discouraged and French, as it was spoken and written in Paris, became the common language of the nation.
  7. The revolutionaries further declared that it was the mission and the destiny of the French nation to liberate the peoples of Europe from despotism. In other words, to help other peoples of Europe to become nations.

3. Who were Marianne and Germania? What was the importance of the way in which they were portrayed?

Answer:

Female allegories were invented by artists in the nineteenth century to represent the nation.

  1. Marianne, a popular Christian name – underlined the idea of a people’s nation.
  2. Her characteristics were drawn from those of Liberty and the Republic – the red cap, the tricolour, the cockade. Statues of Marianne were erected in public squares to remind the public of the national symbol of unity and to persuade them to identify with it.
  3. The image of Marianne was marked on coins and stamps.

Germania became the allegory of the German nation. In visual representations, Germania wears a crown of oak leaves, as the German oak stands for heroism.

4. Briefly trace the process of German unification.

Answer:

  1. Nationalist sentiments were often mobilised by conservatives for promoting state power and achieving political domination over Europe. This can be observed in the process by which Germany and Italy came to be unified as nation-states.
  2. Middle-class Germans tried to unite the different regions of German Confederation, but their plans were not materialised due to actions of large landowners called Junkers of Prussia. Three wars over seven years with Austria, Denmark and France ended in a Prussian victory. In Jan 1871, Prussian King William I was proclaimed German emperor.
  3. Importance was given to modernising the currency, banking, legal and judicial systems in Germany.’

5. What changes did Napoleon introduce to make the administrative system more efficient in the territories ruled by him?

Answer:

The Civil Code of 1804 – usually known as the Napoleonic Code – did away with all the privileges based on birth, established equality before the law and secured the right to property. This Code was exported to the regions under French control. In the Dutch Republic, in Switzerland, in Italy and Germany, Napoleon simplified the administrative divisions, abolished the feudal system and freed peasants from serfdom and manorial dues. In the towns too, guild restrictions were removed. Transport and communication systems were improved. Peasants, artisans, workers and new businessmen enjoyed new-found freedom. Businessmen and small-scale producers of goods, in particular, began to realise that uniform law, standardised weights and measures, and a common national currency would facilitate the movement and exchange of goods and capital from one region to another.

Discuss:

1. Explain what is meant by the 1848 revolution of the liberals. What were the political, social and economic ideas supported by the liberals?

Answer:

  1. In the year 1848, parallel to the revolts of the poor, another revolution was happening underway.  Led by the educated middle classes,  the unemployed, the starving peasants and workers in many European countries experienced this revolution of the liberals. Events of February 1848 in France had brought about the abdication of the monarch and a republic based on universal male suffrage had been proclaimed.
  2. In other parts of Europe where independent nation-states did not yet exist – such as Germany, Italy, Poland, the Austro-Hungarian Empire – men and women of the liberal middle classes combined their demands for constitutionalism with national unification.
  3. They took advantage of the growing popular unrest to push their demands for the creation of a nation-state on parliamentary principles – a constitution, freedom of the press and freedom of association.
  4. The issue of extending political rights to women was a controversial one within the liberal movement, in which large numbers of women had participated actively over the years. Women had formed their own political associations, founded newspapers and had taken part in political meetings and demonstrations.

2. Choose three examples to show the contribution of culture to the growth of nationalism in Europe.

Answer:

Language:

Language played a very important role. After the Russian occupation, the Polish language was forced out of schools, and the Russian language was imposed everywhere. The Clergy in Poland began using language as a weapon of national resistance. Polish was used for Church gatherings and all religious instructions. The use of Polish came to be seen as a symbol of struggle against Russian dominance.

Romanticism:

It was a cultural movement which sought to develop a particular form of nationalist sentiment. Romantic artists and poets generally criticised the glorification of reason and science and focussed instead on emotions, intuition and mystic feelings. They tried to portray a common cultural past as the basis of a nation.

Folk poetry, folk dance, folk songs:

The true spirit of the nation was popularised through the above means. So collecting and recording these forms of folk culture was an essential part of nation-building.

3. Through a focus on any two countries, explain how nations developed over the nineteenth century.

Answer:

Focus countries – Germany and Italy.

Germany

  1. Nationalist sentiments were often mobilised by conservatives for promoting state power and achieving political domination over Europe. This can be observed in the process by which Germany and Italy came to be unified as nation-states.
  2. Middle-class Germans tried to unite the different regions of German Confederation, but their plans were not materialised due to actions of large landowners called the ‘Junkers of Prussia’. Three wars over seven years with Austria, Denmark, and France ended in a Prussian victory. In Jan 1871, the Prussian King William I was proclaimed German emperor.
  3. Importance was given to modernising the currency, banking, legal and judicial systems in Germany.

Italy

  1. During the 1830s, Mazzini sought to unify Italy. He had formed a secret society called ‘Young Italy’, and It had failed. Hence, the responsibility fell on Sardinia-Piedmont under its ruler King Victor Emmanuel II, to unify Italian states through war.
  2. Austrian forces were defeated in 1859. Apart from Sardinia-Piedmont, a large number of volunteers had joined the cause under the leadership of Giuseppe Garibaldi. In 1860, they marched to South Italy and managed to defeat Spanish rulers. In 1861, Victor Emmanuel II was proclaimed as the king of Italy.

4. How was the history of nationalism in Britain unlike the rest of Europe?

Answer:

  1. Formation of the nation-state was not due to sudden upheaval or revolution. It was the result of a long-drawn-out process.
  2. The primary identities of people who inhabited the British Isles were ethnic ones such as English, Welsh, Scot or Irish.
  3. The Act of Union between England and Scotland resulted in the formation of the United Kingdom of Great Britain. Scottish people were forbidden from speaking their Gaelic language and from wearing their national dress. Many were driven out of their homeland.
  4. Ireland was forcibly incorporated into the UK in 1801. This was achieved by the English helping the Protestants of Ireland to establish their dominance over the Catholics.
  5. The symbols of the new Britain – the British flag (Union Jack), the national anthem (God save our Noble King) and the English language were actively promoted, and the older nations survived only as subordinate partners in this union.

5. Why did nationalist tensions emerge in the Balkans?

Answer:

  1. It was a region of geographical and ethnic variation comprising modern-day Romania, Bulgaria, Albania, Greece, Macedonia, Croatia, Bosnia-Herzegovina, Slovenia, Serbia and Montenegro who were broadly known as Slavs.
  2. A large part was under the control of the Ottoman Empire. Gradually independence was declared from them.
  3. The spread of the ideas of romantic nationalism in the Balkans, together with disintegration of the Ottoman Empire made this region very explosive.

Monday, July 25, 2022

 

Access Answers to NCERT Class 9 Maths Chapter 1 – Number Systems

Exercise 1.1 Page: 5

1. Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0?

Solution:

We know that, a number is said to be rational if it can be written in the form p/q , where p and q are integers and q ≠ 0.

Taking the case of ‘0’,

Zero can be written in the form 0/1, 0/2, 0/3 … as well as , 0/1, 0/2, 0/3 ..

Since it satisfies the necessary condition, we can conclude that 0 can be written in the p/q form, where q can either be positive or negative number.

Hence, 0 is a rational number.

2. Find six rational numbers between 3 and 4.

Solution:

There are infinite rational numbers between 3 and 4.

As we have to find 6 rational numbers between 3 and 4, we will multiply both the numbers, 3 and 4, with 6+1 = 7 (or any number greater than 6)

i.e., 3 × (7/7) = 21/7

and, 4 × (7/7) = 28/7. The numbers in between 21/7 and 28/7 will be rational and will fall between 3 and 4.

Hence, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7 are the 6 rational numbers between 3 and 4.

3. Find five rational numbers between 3/5 and 4/5.

Solution:

There are infinite rational numbers between 3/5 and 4/5.

To find out 5 rational numbers between 3/5 and 4/5, we will multiply both the numbers 3/5 and 4/5

with 5+1=6 (or any number greater than 5)

i.e., (3/5) × (6/6) = 18/30

and, (4/5) × (6/6) = 24/30

The numbers in between18/30 and 24/30 will be rational and will fall between 3/5 and 4/5.

Hence,19/30, 20/30, 21/30, 22/30, 23/30 are the 5 rational numbers between 3/5 and 4/5

4. State whether the following statements are true or false. Give reasons for your answers.

(i) Every natural number is a whole number.

Solution:

True

Natural numbers- Numbers starting from 1 to infinity (without fractions or decimals)

i.e., Natural numbers= 1,2,3,4…

Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)

i.e., Whole numbers= 0,1,2,3…

Or, we can say that whole numbers have all the elements of natural numbers and zero.

Every natural number is a whole number; however, every whole number is not a natural number.

(ii) Every integer is a whole number.

Solution:

False

Integers- Integers are set of numbers that contain positive, negative and 0; excluding fractional and decimal numbers.

i.e., integers= {…-4,-3,-2,-1,0,1,2,3,4…}

Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)

i.e., Whole numbers= 0,1,2,3….

Hence, we can say that integers include whole numbers as well as negative numbers.

Every whole number is an integer; however, every integer is not a whole number.

(iii) Every rational number is a whole number.

Solution:

False

Rational numbers- All numbers in the form p/q, where p and q are integers and q≠0.

i.e., Rational numbers = 0, 19/30 , 2, 9/-3, -12/7…

Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)

i.e., Whole numbers= 0,1,2,3….

Hence, we can say that integers includes whole numbers as well as negative numbers.

Every whole numbers are rational, however, every rational numbers are not whole numbers.



Exercise 1.2 Page: 8

1. State whether the following statements are true or false. Justify your answers.

(i) Every irrational number is a real number.

Solution:

True

Irrational Numbers – A number is said to be irrational, if it cannot be written in the p/q, where p and q are integers and q ≠ 0.

i.e., Irrational numbers = π, e, √3, 5+√2, 6.23146…. , 0.101001001000….

Real numbers – The collection of both rational and irrational numbers are known as real numbers.

i.e., Real numbers = √2, √5, , 0.102…

Every irrational number is a real number, however, every real numbers are not irrational numbers.

(ii) Every point on the number line is of the form √m where m is a natural number.

Solution:

False

The statement is false since as per the rule, a negative number cannot be expressed as square roots.

E.g., √9 =3 is a natural number.

But √2 = 1.414 is not a natural number.

Similarly, we know that there are negative numbers on the number line but when we take the root of a negative number it becomes a complex number and not a natural number.

E.g., √-7 = 7i, where i = √-1

The statement that every point on the number line is of the form √m, where m is a natural number is false.

(iii) Every real number is an irrational number.

Solution:

False

The statement is false, the real numbers include both irrational and rational numbers. Therefore, every real number cannot be an irrational number.

Real numbers – The collection of both rational and irrational numbers are known as real numbers.

i.e., Real numbers = √2, √5, , 0.102…

Irrational Numbers – A number is said to be irrational, if it cannot be written in the p/q, where p and q are integers and q ≠ 0.

i.e., Irrational numbers = π, e, √3, 5+√2, 6.23146…. , 0.101001001000….

Every irrational number is a real number, however, every real number is not irrational.

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.

 

Solution:

No, the square roots of all positive integers are not irrational.

For example,

√4 = 2 is rational.

√9 = 3 is rational.

Hence, the square roots of positive integers 4 and 9 are not irrational. ( 2 and 3, respectively).

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

Solution:

Step 1: Let line AB be of 2 unit on a number line.

Step 2: At B, draw a perpendicular line BC of length 1 unit.

Step 3: Join CA

Step 4: Now, ABC is a right angled triangle. Applying Pythagoras theorem,

AB2+BC2 = CA2

22+12 = CA2 = 5

⇒ CA = √5 . Thus, CA is a line of length √5 unit.

Step 4: Taking CA as a radius and A as a center draw an arc touching

the number line. The point at which number line get intersected by

arc is at √5 distance from 0 because it is a radius of the circle

whose center was A.

Thus, √5 is represented on the number line as shown in the figure.

Ncert solution class 9 chapter 1-1

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 Fig. 1.9 :

Ncert solution class 9 chapter 1-2

Constructing this manner, you can get the line segment Pn-1Pn by square root spiral drawing a line segment of unit length perpendicular to OPn-1. In this manner, you will have created the points P2, P3,….,Pn,… ., and joined them to create a beautiful spiral depicting √2, √3, √4, …

Solution:

Ncert solution class 9 chapter 1-3

Step 1: Mark a point O on the paper. Here, O will be the center of the square root spiral.

Step 2: From O, draw a straight line, OA, of 1cm horizontally.

Step 3: From A, draw a perpendicular line, AB, of 1 cm.

Step 4: Join OB. Here, OB will be of √2

Step 5: Now, from B, draw a perpendicular line of 1 cm and mark the end point C.

Step 6: Join OC. Here, OC will be of √3

Step 7: Repeat the steps to draw √4, √5, √6….





Exercise 1.3 Page: 14

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

(i) 36/100

Solution:

NCERT Solution For Class 9 Maths Ex-1.3-1

= 0.36 (Terminating)

(ii)1/11

Solution:

NCERT Solution For Class 9 Maths Ex-1.3-2

Ncert solution class 9 chapter 1-4

Ncert solution class 9 chapter 1-5

Solution:

Ncert solution class 9 chapter 1-6

NCERT Solution For Class 9 Maths Ex-1.3-3

= 4.125 (Terminating)

(iv) 3/13

Solution:

NCERT Solution For Class 9 Maths Ex-1.3-4

Ncert solution class 9 chapter 1-7

(v) 2/11

Solution:

NCERT Solution For Class 9 Maths Ex-1.3-5

Ncert solution class 9 chapter 1-8

(vi) 329/400

Solution:

NCERT Solution For Class 9 Maths Ex-1.3-6

= 0.8225 (Terminating)

2. You know that 1/7 = 0.142857. Can you predict what the decimal expansions of 2/7, 3/7, 4/7, 5/7, 6/7 are, without actually doing the long division? If so, how?

[Hint: Study the remainders while finding the value of 1/7 carefully.]

Solution:

Ncert solution class 9 chapter 1-9

3. Express the following in the form p/q, where p and q are integers and q 0.

(i) Ncert solution class 9 chapter 1-10

Solution:

Ncert solution class 9 chapter 1-11

Assume that  x = 0.666…

Then,10x = 6.666…

10x = 6 + x

9x = 6

x = 2/3

(ii) 0.4\overline{7}

Solution:

0.4\overline{7} = 0.4777..

= (4/10)+(0.777/10)

Assume that x = 0.777…

Then, 10x = 7.777…

10x = 7 + x

x = 7/9

(4/10)+(0.777../10) = (4/10)+(7/90) ( x = 7/9 and x = 0.777…0.777…/10 = 7/(9×10) = 7/90 )

= (36/90)+(7/90) = 43/90

Ncert solution class 9 chapter 1-14

Solution:

Ncert solution class 9 chapter 1-15

Assume that  x = 0.001001…

Then, 1000x = 1.001001…

1000x = 1 + x

999x = 1

x = 1/999

4. Express 0.99999…. in the form p/q . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

Solution:

Assume that x = 0.9999…..Eq (a)

Multiplying both sides by 10,

10x = 9.9999…. Eq. (b)

Eq.(b) – Eq.(a), we get

10x = 9.9999

x = -0.9999…

_____________

9x = 9

x = 1

The difference between 1 and 0.999999 is 0.000001 which is negligible.

Hence, we can conclude that, 0.999 is too much near 1, therefore, 1 as the answer can be justified.

5. What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17 ? Perform the division to check your answer.

Solution:

1/17

Dividing 1 by 17:

NCERT Solution For Class 9 Maths Ex-1.3-7

Ncert solution class 9 chapter 1-16

There are 16 digits in the repeating block of the decimal expansion of 1/17.

6. Look at several examples of rational numbers in the form 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?

Solution:

We observe that when q is 2, 4, 5, 8, 10… Then the decimal expansion is terminating. For example:

1/2 = 0. 5, denominator q = 21

7/8 = 0. 875, denominator q =23

4/5 = 0. 8, denominator q = 51

We can observe that the terminating decimal may be obtained in the situation where prime factorization of the denominator of the given fractions has the power of only 2 or only 5 or both.

7. Write three numbers whose decimal expansions are non-terminating non-recurring.

Solution:

We know that all irrational numbers are non-terminating non-recurring. three numbers with decimal expansions that are non-terminating non-recurring are:

  1. √3 = 1.732050807568
  2. √26 =5.099019513592
  3. √101 = 10.04987562112

8. Find three different irrational numbers between the rational numbers 5/7 and 9/11.

Solution:

Ncert solution class 9 chapter 1-17

Three different irrational numbers are:

  1. 0.73073007300073000073…
  2. 0.75075007300075000075…
  3. 0.76076007600076000076…

9.  Classify the following numbers as rational or irrational according to their type:

(i)√23

Solution:

√23 = 4.79583152331…

Since the number is non-terminating non-recurring therefore, it is an irrational number.

(ii)√225

Solution:

√225 = 15 = 15/1

Since the number can be represented in p/q form, it is a rational number.

(iii) 0.3796

Solution:

Since the number,0.3796, is terminating, it is a rational number.

(iv) 7.478478

Solution:

The number,7.478478, is non-terminating but recurring, it is a rational number.

(v) 1.101001000100001…

Solution:

Since the number,1.101001000100001…, is non-terminating non-repeating (non-recurring), it is an irrational number.