Maharashtra Board Class 12 Political Science Notes Chapter 4 Contemporary India: Challenges to Peace, Stability and National Integration 

By going through these Maharashtra State Board Class 12 Political Science Notes Chapter 4 Contemporary India: Challenges to Peace, Stability and National Integration students can recall all the concepts quickly.

Maharashtra State Board Class 12 Political Science Notes Chapter 4 Contemporary India: Challenges to Peace, Stability and National Integration

Introduction:
Meaning of national integration:
Public order, peace, and stability are crucial requirements for the political, economic, and socio-cultural development of a State. The primary function of the State is maintenance law and order towards the process of national integration.

The role of the State is determined by values of nationalism, secularism, democracy, economic development, and social change. It includes –

→ Peace and Order – One of the key roles of the State is to bring about domestic and international peace and security.

→ Economic Development – The State must be a facilitator of agricultural and industrial growth and the economic well-being of the people.

→ Nation Building – The State is closely associated with the concept of nation integration i.e., diversity of ethnicity, religion, etc. It does not lead to divisive tendencies or disintegration of the State.

→ Governance – This refers to the creation of participatory democracy and good governance based on values like responsiveness, transparency, accountability, equity, etc.

→ Welfare – The State is expected to rectify imbalances in the society such as inequality, injustice, poverty, etc., by applying the principles of social justice, fairness and equality.

→ National integration refers to awareness of a common identity among the people of a nation. It means that though we belong to different races, religions, regions, castes, etc., we recognize the fact that ‘we are one. Today, most countries are facing a problem of national unity, integrity, and consolidation i.e., the problem of bringing about national integration.

National integration involves the reconciliation of socio-cultural,, religious, linguistic, economic diversities to build up a common national identity. It does not try to wipe out sectoral identities or to create a homogeneous society but instead aims to create a territorial nationality. The Indian system can be described as ‘Salad Bowl’ i.e., it is a pluralistic society, where the characteristics of every diversity are maintained but is subordinate to national identity.

Maharashtra Board Class 12 Political Science Chapter 4 Contemporary India: Challenges to Peace, Stability and National Integration

Some common values associated with national integration are –

  1. socio-economic and political justice and equality
  2. secularism and a sense of fraternity among diverse communities
  3. unity in diversity
  4. the feeling of patriotism and loyalty to the nation.
  5. common citizenship

The role of the State in national integration involves

  • evolve certain values and goals that help to maintain social order and stability
  • promote unity among socially and culturally diverse groups living in the territory
  • establish a national authority over the subordinate political units
  • establish a dialogue between the State and people to understand their living conditions, needs, and aspirations.

Indian Situation:
In 1947, when India became independent, it faced problems like social inequalities, economic underdevelopment, and poverty, illiteracy, etc. The main task was to consolidate India’s unity by recognizing India’s ethnic, religious, linguistic diversity. India had to consider two dimensions to promote national integration i.e., structural and psychological dimensions.

Structural Dimension –
This was done through the constitutional process as enumerated below.

→ The democratic system of governance with Universal Adult Franchise to encourage the participation of diverse groups.

→ Constitutional provisions

  • federal structure with a strong central government
  • specification of Fundamental Rights as well as Fundamental Duties
  • 73rd and 74th Amendments strengthened participation of urban and rural local bodies.

→ Linguistic reorganization of States in India (1956) – The 8th Schedule of the constitution lists 22 official languages.

→ At the administrative level, there are All-India Services like IAS, IPS, etc., which provide for a unified central bureaucratic system. There also exists a state-level bureaucratic system.

→ The National Integration Conference (1961) set up the National Integration Council to review issues like communalism, casteism, regionalism, etc., and make recommendations to achieve national integration, equality, justice and secularism.

(2) Psychological Dimension – A feeling of cohesiveness, oneness helps to bind people together. Psychological integration is promoted by common culture/traditions, shared history such as freedom struggle against colonial rule; symbols such as National Flag, National Anthem, National Song, National Emblem, etc.

Maharashtra Board Class 12 Political Science Chapter 4 Contemporary India: Challenges to Peace, Stability and National Integration

The Challenges To National Integration In India:

→ Princely States – There were problems with the integration of princely states of India. Eventually, even Portuguese and French colonies became part of the Indian Union.

→ The problem of North-East States – This region is ethnically very diverse. Maintenance of peace and stability, ensuring industrial and economic development has been a challenge for the Indian system. Nagaland has seen conflicts since independence with militant outfits like NSCN, etc. States like Tripura, Manipur, Mizoram have witnessed militancy. In Assam, the AASU and AGP led the ‘sons-of-the-soil’ movement.

→ Khalistan movement – In Punjab, a Sikh separatist movement for an ‘independent homeland for Sikhs.’ i.e., ‘Khalistan’ arose in the 1980s. Operation Bluestar was conducted against militants hiding in the Golden Temple. This secessionist movement also resulted in the bombing of Air India flight 182 and the assassination of then Prime Minister Smt. Indira Gandhi.

→ Communal issues can be considered as a legacy of the Partition of India. There have been hundreds of cases of religious or sectarian conflicts such as Gujarat riots (1969, 2002), Moradabad (1980). Anti-Sikh riots (1984) following the assassination of Mrs. Gandhi, riots in Mumbai and other parts of the country in 1992-93 following the demolition of Babri Masjid, Muzaffarnagar violence (2013 in UP)

→ Left-Wing Extremism (also called the Maoist movement or Naxalism) has a major support base among landless laborers, Dalits, and tribals who experience a sense of oppression, injustice, and neglect. The first attempt to promote a peasant struggle was the Telangana Movement (1946-51).

→ The Naxal movement originated in 1967 in Naxalbari (West Bengal) led by Kanu Sanyal and inspired by the writings of Charu Majumdar. Since the 1980s, the movement has taken a militant turn.

→ In 2004, CPI (M-L), People’s War Group (PWG), and Maoist Communist Centre of India (MCCI) merged to form CPI (Maoist) which aims to overthrow the government and destroy public property and attack police and officials.

→ The Red Corridor of Naxal activities extends across States like Bihar, Jharkhand, Chhattisgarh, Maharashtra, Telangana, Andhra Pradesh, etc.

Terrorism – It is the actual use or threat to use violence with an intention to disrupt life and create panic. It is called ‘asymmetric’ or ‘indirect’ warfare. It may take the form of the assassination of political figures, hijackings, bombings and attacks on civilians in public transport, etc.

Earlier, terrorism was State-centric e.g., LTTE in Sri Lanka. However, modern-day terrorism aims for abstract ideological or religious goals at the global level e.g., Taliban, Bako Haram, etc.

India has been the target of numerous terrorist attacks e.g., bomb blasts in Mumbai (1993, 2006) and LET attack on 26th Nov 2008 in Mumbai, attack on Parliament (2001), attacks on security forces at Uri (2016) and Pulwama (2019).

Jammu and Kashmir –
In October 1947, Pakistan sent militants to force Maharaja Hari Singh to join Pakistan. However, he signed the Instrument of Accession making Jammu and Kashmir a part of India. This resulted in the first India-Pakistan conflict (1947-48) as India sent troops to protect Kashmir from Pakistani raiders.

→ In 1977, Jammu Kashmir Liberation Front (JKLF) was formed to create an independent State of Kashmir. Pro-Pakistan guerilla groups like Hizbul Mujahideen and Islamic militancy in Kashmir in the 1990s have worsened the situation. Kashmiri Pandits were forced to flee and live in refugee camps. The militants try to radicalize people through social and political groups and make use of social media to incite the youth to indulge in stone-throwing, arson, etc.

→ Terrorist groups like Lashkar-e-Taiba (LeT), Jaish-e-Mohammad (JeM), Harkat ul Mujahideen (HuM), etc., have an active presence in the region. In August 2019, the ‘special’ status of Jammu and Kashmir under Article 370 was revoked and the State was bifurcated into Union Territories of Ladakh and of Jammu and Kashmir.

Maharashtra Board Class 12 Psychology Notes Chapter 5 Emotions

By going through these Maharashtra State Board Class 12 Psychology Notes Chapter 5 Emotions students can recall all the concepts quickly.

Maharashtra State Board Class 12 Psychology Notes Chapter 5 Emotions

History of Emotions:
The word emotion is derived from the Latin word ‘remover, which means to stir up or to move An emotion refers to an involuntary, aroused state of an organism involving physical, cognitive, and behavioural components.

It is described as a combination of bodily arousal, e.g., increased heart rate, thoughts, and feelings, i.e. emotional tone, and expressive behaviour, i.e., facial expression.

The main theories of emotions are –
James-Lange theory:
It was one of the earliest theories to explain emotion According to William James and Carl Lange, physiological arousal instigates the experience of emotion.

It proposes that each specific emotion is attached to a different pattern of physiological arousal. For e.g., we feel sad because we cry. The sequence of events in emotional experience is Emotion Stimulus →Physiological Response Pattern → Affective Experience.

Cannon-Bard theory:
According to Walter Cannon and Philip Bard, we may experience the same physiological arousal but emotions can be different, for e.g., we don’t cry only when we are sad but we also cry when we are angry or extremely happy.

We experience physiological arousal and feelings at the same time and independently. For e.g., seeing a man with a gun prompts the feeling of fear as well as a racing heartbeat.

Maharashtra Board Class 12 Psychology Notes Chapter 5 Emotions

Schachter and Singer’s Two Factor theory:
According to Stanley Schachter and Jerome Singer, emotion is based on two factors, i.e., physiological arousal and cognitive label, for e.g., an environmental stimulus (growling dog) elicits a physiological response (increased heart rate). We cognitively label this response (fear).

Facial Feedback hypothesis:
According to the facial feedback hypothesis, our facial expressions provide feedback to our brain about our emotions. Facial expressions are the result of our emotions but also capable of Influencing emotions.
Maharashtra Board Class 12 Psychology Notes Chapter 5 Emotions 1

Basic Emotions:
There are two primary emotions, viz. happiness and sadness. These emotions transform as our experiences change, for e.g., sadness can transform to grief or shame.

Some characteristics of emotions are –

  1. Emotions may be positive, e.g., joy or negative, e.g., anger.
  2. Emotions may occur for a brief period or may be long-lasting.
  3. Emotions may be important for our survival, e.g., fear or for our psychological well-being, e.g., love.
    Emotions differ in intensity in expression, for e.g., annoyance-anger-rage.
  4. Complex emotions (higher cognitive level emotions) result from the combination of basic emotions, for e.g., surprise and sadness lead to disappointment.

According to Paul Ekman, there are six basic (universal) types of emotions, i.e., happiness, sadness, anger, fear, surprise, disgust.

  • Happiness – It is the basic positive emotion that is associated with psychological well-being.
  • Sadness – It is characterized by related feelings of hopelessness, disappointment, etc.
  • Anger – It is a powerful, negative emotion which includes hostility, frustration, etc.
  • Fear – It is closely related to our survival from the evolutionary perspective. It is in response to some threat.
  • Surprise – It occurs in response to some unexpected event. It may be positive or negative.
  • Disgust – It is in response to some unwanted stimulus.

Maharashtra Board Class 12 Psychology Notes Chapter 5 Emotions

Physiological Changes During Emotions:
Physiological changes refer to automatic reactions that take place in our body in response to some stimulus, for e.g. if you saw a snake, the brain at the cognitive level perceived the stimulus as dangerous. This leads to physiological arousals such as dilated pupils, increased heart rate, increased pulse rate and sweating.

At the emotional level, you experience fear. The Autonomic Nervous System and glandular system signal the pituitary gland which activates the adrenal glands to secrete the cortisol hormone that triggers “the fight or flight” response. At the connection (behavioural) level there is an action plan such as running away or calling for help, etc.
Maharashtra Board Class 12 Psychology Notes Chapter 5 Emotions 2
Maharashtra Board Class 12 Psychology Notes Chapter 5 Emotions 3

Plutchik’s Model Of Emotions:
Maharashtra Board Class 12 Psychology Notes Chapter 5 Emotions 4

Robert Plutchik presented the wheel of emotions.

  1. there are eight basic emotions viz. joy, trust, fear, surprise, sadness, anticipation, anger and disgust.
  2. each primary emotion has its polar opposite such as fear is opposite of anger.
  3. primary emotions combine to produce complex emotions, for e.g., love (complex) is a combination of joy and trust.
  4. the intensity of emotions increases as we move toward the centre and decreases as we move outward. For e.g., apprehension (weak) →fear (basic) →terror (strongest). This model is important from the perspective of emotional literacy, i.e., understanding emotional levels, complexity and change as well as appropriate emotional labelling.

Maharashtra Board Class 12 Psychology Notes Chapter 5 Emotions

Emotional Well-being:
Emotional well-being is not easily observable. It can be measured on how rationally a person handles both positive and negative emotions so he/she can lead a productive, healthy life. Techniques to achieve emotional well-being are helpful at three levels viz. physical, emotional, and social.

  • Physical level, i.e., well-balanced diet, exercise.
  • Emotional level, i.e., practice mindfulness, raising levels of motivation and optimism.
  • Social level, i.e., engaging in prosocial behaviour, meaningful relationships.

The benefits of emotional after well-being give a long dash
Persons who have high emotional well-being experience benefits such as-

  • better able to deal with stress
  • better self-regulation
  • increased productivity in tasks undertaken
  • increased creativity and openness to new experiences
  • life satisfaction due to meaningful activities and relationships.

Emotional Abuse:
Emotional abuse is any kind of abuse that is emotional rather than physical in nature. It occurs when one person subjects or exposes another person to intentionally harmful behaviour that may result in anxiety, depression, and psychological trauma for the victim.

The types of emotional abuse may be-

  • verbal abuse such as blaming, insulting, labeling, threatening, swearing, etc.
  • non-verbal abuse such as ignoring, rejection, bullying, spying, etc.

Dealing with emotional abuse:

  • Accept that emotional abuse is not because of you, i.e., don’t justify the actions of the abuser.
  • Respond assertively to the abuser but seek distance from him/her.
  • Give yourself time to heal.
  • Prioritize your self-care, e.g., eating right, exercise, etc.
  • Mobilize support from family and friends. If needed, seek professional help.

Maharashtra Board Class 12 Psychology Notes Chapter 5 Emotions

Managing Emotions:
Managing of emotions is an important life skill. Managing emotions can be defined as, ‘the ability to be open to feelings and modulate them in oneself and in others, so as to promote personal understanding and growth.

Sometimes, our emotions hijack our thinking due to which we act impulsively. This is because the limbic system (emotional section) developed before the prefrontal cortex (thinking part) and is hence, an extremely strong part of the brain. Emotional management is an art as it is a form of expression as well as a science as it is a skill that needs to be learned and practiced.

Anger Management:
Anger is a common emotion that everybody experiences in life from time to time. Anger is a normal response to some real or perceived threat. It is a protective emotion that helps us to defend ourselves against physical or psychological harm.

However, anger may also be unwanted, irrational, and destructive. When we experience anger, our amygdala goes into action and overrides the cerebral cortex which is in control of thinking and evaluation.

Triggers of Anger refer to any event that signals the brain to activate the body’s anger system. The triggers of anger maybe

  • verbal, for e.g., being blamed, disrespected, or abused
  • nonverbal, for e.g., being ignored unappreciated, or rejected,
  • physical such as physical threats, sexual/ physical assault, etc.

There are three factors involved in the experience of anger: A trigger (causes of anger) → individual’s personality → particular interpretation of that situation.

As the experience of anger is subjective, it can be controlled too. If we understand the triggers of anger, we can anticipate potential anger episodes and provide an intentional/ acceptable response.

Anger management is an intervention programme to prevent anger from turning into a habit or obstacle. It enables the person to create an awareness of and responsibility for his/her emotions.

This involves two aspects

  1. managing one’s own anger
  2. learning to respond effectively to anger in others.

Maharashtra Board Class 12 Psychology Notes Chapter 5 Emotions

The 3 R’s in anger management are Relax, Reassess and Respond:
Relaxation – Relaxation, and connection with the inner self enhances thinking and concentration and helps to respond rather than react impulsively.

Reassess – helps to revisit the situation objectively. It involves

  • taking complete responsibility for your emotion
  • developing empathy for the person you perceive has wronged you
  • conduct a reality check e.g., is your anger justified given the facts of what happened.

Respond – This involves using anger as a motivation to change. It includes

  • consulting a trustworthy person to get another perspective
  • engage in talks with the other party in a calm manner
  • active listening and assertive speaking
  • cage your rage i.e. establish boundaries and moderate your anger.

Glossary:

→ Anger – A basic emotion expressing dislike or displeasure.

→ Emotions – A complex response pattern that involves physiological arousal, expression of behaviors, and conscious experience.

→ Emotional abuse – It is a non-physical form of abuse in which an individual purposely subjects another to behaviors such as intimidation, isolation humiliation, rejection, and verbal abuse.

→ Emotional well-being – It is an overall positive state of one’s emotions.

→ Trigger – An event or stimuli that cause a reaction.

Maharashtra Board 11th Commerce Maths Solutions Chapter 6 Permutations and Combinations Ex 6.1

Balbharati Maharashtra State Board 11th Commerce Maths Solution Book Pdf Chapter 6 Permutations and Combinations Ex 6.1 Questions and Answers.

Maharashtra State Board 11th Commerce Maths Solutions Chapter 6 Permutations and Combinations Ex 6.1

Question 1.
A teacher wants to select the class monitor in a class of 30 boys and 20 girls. In how many ways can he select a student if the monitor can be a boy or a girl?
Solution:
There are 30 boys and 20 girls in a class.
The teacher wants to select a class monitor from these boys and girls.
A boy can be selected in 30 ways and a girl can be selected in 20 ways.
∴ By using the fundamental principle of addition,
in a number of ways either a boy or a girl is selected as a class monitor = 30 + 20 = 50.

Question 2.
In question 1, in how many ways can the monitor be selected if the monitor must be a boy? What is the answer if the monitor must be a girl?
Solution:
(i) Since there are 30 boys in the class
∴ A boy monitor can be selected in 30 ways.
(ii) Since there are 20 girls in the class
∴ A girl monitor can be selected in 20 ways.

Maharashtra Board 11th Commerce Maths Solutions Chapter 6 Permutations and Combinations Ex 6.1

Question 3.
A Signal is generated from 2 flags by putting one flag above the other. If 4 flags of different colours are available, how many different signals can be generated?
Solution:
A signal is generated from 2 flags and there are 4 flags of different colours available.
∴ 1st flag can be any one of the available 4 flags.
∴ It can be selected in 4 ways.
Now, 2nd flag is to be selected for which 3 flags are available for a different signal.
∴ 2nd flag can be anyone from these 3 flags.
∴ It can be selected in 3 ways.
∴ By using the fundamental principle of multiplication,
Total number of ways in which a signal can be generated = 4 × 3 = 12
∴ 12 different signals can be generated.

Question 4.
How many two-letter words can be formed using letters from the word SPACE when repetition of letters
(i) is allowed
(ii) is not allowed
Solution:
A two-letter word is to be formed out of the letters of the word SPACE.
(i) When repetition of the letters is allowed
1st letter can be selected in 5 ways
2nd letter can be selected in 5 ways
∴ By using the fundamental principle of multiplication,
total number of 2-letter words = 5 × 5 = 25

(ii) When repetition of the letters is not allowed
1st letter can be selected in 5 ways
2nd letter can be selected in 4 ways
∴ By using the fundamental principle of multiplication,
total number of 2-letter words = 5 × 4 = 20

Maharashtra Board 11th Commerce Maths Solutions Chapter 6 Permutations and Combinations Ex 6.1

Question 5.
How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits
(i) are allowed
(ii) are not allowed
Solution:
The three-digit number is to be formed from the digits 0, 1, 3, 5, 6
(i) When repetition of digits is allowed:
100’s place digit should be a non-zero number.
Hence, it can be anyone from digits 1, 3, 5, 6
∴ 100’s place digit can be selected in 4 ways.
0 can appear in 10’s and unit’s place and digits can be repeated.
∴ 10’s place digit can be selected in 5 ways and the unit’s place digit can be selected in 5 ways.
∴ By using the fundamental principle of multiplication,
the total number of three-digit numbers = 4 × 5 × 5 = 100

(ii) When repetition of digits is not allowed:
100’s place digit should be a non-zero number.
Hence, it can be anyone from digits 1, 3, 5, 6
∴ 100’s place digit can be selected in 4 ways
0 can appear in 10’s and unit’s place and digits can’t be repeated.
∴ 10’s place digit can be selected in 4 ways and the unit’s place digit can be selected in 3 ways
∴ By using the fundamental principle of multiplication,
total number of three-digit numbers = 4 × 4 × 3 = 48

Question 6.
How many three-digit numbers can be formed using the digits 2, 3, 4, 5, 6 if digits can be repeated?
Solution:
A 3-digit number is to be formed from the digits 2, 3, 4, 5, 6 where digits can be repeated.
∴ The unit’s place digit can be selected in 5 ways.
10’s place digit can be selected in 5 ways.
100’s place digit can be selected in 5 ways.
∴ By using fundamental principle of multiplication,
the total number of 3-digit numbers = 5 × 5 × 5 = 125

Maharashtra Board 11th Commerce Maths Solutions Chapter 6 Permutations and Combinations Ex 6.1

Question 7.
A letter lock has 3 rings and each ring has 5 letters. Determine the maximum number of trials that may be required to open the lock.
Solution:
A letter lock has 3 rings, each ring containing 5 different letters.
∴ A letter from each ring can be selected in 5 ways.
∴ By using fundamental principle of multiplication,
the total number of trials that can be made = 5 × 5 × 5 = 125
Out of these 124 wrong attempts are made and in the 125th attempt,
the lock gets opened, for a maximum number of trials.
∴ A maximum number of trials required to open the lock is 125.

Question 8.
In a test that has 5 true/false questions, no student has got all correct answers and no sequence of answers is repeated. What is the maximum number of students for this to be possible?
Solution:
For a set of 5 true/false questions, each question can be answered in 2 ways.
∴ By using fundamental principle of multiplication,
the total number of possible sequences of answers = 2 × 2 × 2 × 2 × 2 = 32
Since no student has written all the correct answers.
∴ Total number of sequences of answers given by the students in the class = 32 – 1 = 31
Also, no student has given the same sequence of answers.
∴ Maximum number of students in the class = Number of sequences of answers given by the students = 31

Question 9.
How many numbers between 100 and 1000 have 4 in the unit’s place?
Solution:
Numbers between 100 and 1000 are 3-digit numbers.
A 3-digit number is to be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 where the unit place digit is 4.
Since Unit’s place digit is 4.
∴ it can be selected in 1 way only.
10’s place digit can be selected in 10 ways.
For 3-digit number 100’s place digit should be a non-zero number.
∴ 100’s place digit can be selected in 9 ways.
∴ By using fundamental principle of multiplication,
total number of numbers between 100 and 1000 which have 4 in the units place = 1 × 10 × 9 = 90

Maharashtra Board 11th Commerce Maths Solutions Chapter 6 Permutations and Combinations Ex 6.1

Question 10.
How many numbers between 100 and 1000 have the digit 7 exactly once?
Solution:
Numbers between 100 and 1000 are 3-digit numbers.
A 3-digit number is to be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, where exactly one of the digits is 7.
When 7 is in the unit’s place
The unit’s place digit is 7.
∴ it can be selected in 1 way only.
10’s place digit can be selected in 9 ways.
100’s place digit can be selected in 8 ways.
∴ total number of numbers which have 7 in the unit’s place = 1 × 9 × 8 = 72
When 7 is in 10’s place
The unit’s place digit can be selected in 9 ways.
10’s place digit is 7
∴ it can be selected in 1 way only.
100’s place digit can be selected in 8 ways.
∴ total number of numbers which have 7 in 10’s place = 9 × 1 × 8 = 72
When 7 is in 100’s place
The unit’s place digit can be selected in 9 ways.
10’s place digit can be selected in 9 ways.
100’s place digit is 7
∴ it can be selected in 1 way.
∴ total numbers which have 7 in 100’s place = 9 × 9 × 1 = 81
∴ total number of numbers between 100 and 1000 having digit 7 exactly once = 72 + 72 + 81 = 225.

Question 11.
How many four-digit numbers will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?
Solution:
Among many set’s of digits, the greatest number is possible when digits are arranged in descending order.
∴ 7432 is the greatest number, formed from the digits 2, 3, 4, 7.
∴ Since a 4-digit number is to be formed from the digits 2, 3, 4, 7, where repetition of the digit is not allowed.
∴ 1000’s place digit can be selected in 4 ways.
100’s place digit can be selected in 3 ways.
10’s place digit can be selected in 2 ways.
The unit’s place digit can be selected in 1 way.
∴ Total number of numbers not exceeding 7432 that can be formed from the digits 2, 3, 4, 7
= Total number of four-digit numbers formed from the digits 2, 3, 4, 7
= 4 × 3 × 2 × 1
= 24

Maharashtra Board 11th Commerce Maths Solutions Chapter 6 Permutations and Combinations Ex 6.1

Question 12.
If numbers are formed using digits 2, 3, 4, 5, 6 without repetition, how many of them will exceed 400?
Solution:
Case I: Three-digit numbers with 4 occurring in hundred’s place:
100’s place digit can be selected in 1 way.
Ten’s place can be filled by any one of the numbers 2, 3, 5, 6.
∴ 10’s place digit can be selected in 4 ways.
The unit’s place digit can be selected in 3 ways.
∴ total number of numbers which have 4 in 100’s place = 1 × 4 × 3 = 12

Case II: Three-digit numbers more than 500
100’s place digit can be selected in 2 ways.
10’s place digit can be selected in 4 ways.
Unit’s place digit can be selected in 3 ways.
∴ total number of three digit numbers more than 500 = 2 × 4 × 3 = 24

Case III: Number of four digit numbers formed from 2, 3, 4, 5, 6
Since, repetition of digits is not allowed
∴ total four digit numbers formed = 5 × 4 × 3 × 2 = 120

Case IV: Number of five digit numbers formed from 2, 3, 4, 5, 6
Since, repetition of digits is not allowed
∴ total five digit numbers formed = 5 × 4 × 3 × 2 × 1 = 120
∴ total number of numbers that exceed 400 = 12 + 24 + 120 + 120 = 276

Question 13.
How many numbers formed with the digits 0, 1, 2, 5, 7, 8 will fall between 13 and 1000 if digits can be repeated?
Solution:
Case I: 2-digit numbers more than 13, less than 20, formed from the digits 0, 1, 2, 5, 7, 8
Number of such numbers = 3

Case II: 2-digit numbers more than 20 formed from 0, 1, 2, 5, 7, 8
Ten’s place digit is selected from 2, 5, 7, 8.
∴ Ten’s place digit can be selected in 4 ways.
Unit’s place digit is anyone from 0, 1, 2, 5, 7, 8
∴ The unit’s place digit can be selected in 6 ways.
Using the multiplication principle,
the number of such numbers (repetition allowed) = 4 × 6 = 24

Case III: 3-digit numbers formed from 0, 1, 2, 5, 7, 8
100’s place digit is anyone from 1, 2, 5, 7, 8.
∴ 100’s place digit can be selected in 5 ways.
As digits can be repeated, the 10’s place and unit’s place digits are selected from 0, 1, 2, 5, 7, 8
∴ 10’s place and unit’s place digits can be selected in 6 ways each.
Using multiplication principle,
the number of such numbers (repetition allowed) = 5 × 6 × 6 = 180
All cases are mutually exclusive and exhaustive.
∴ Required number = 3 + 24 + 180 = 207

Question 14.
A school has three gates and four staircases from the first floor to the second floor. How many ways does a student have to go from outside the school to his classroom on the second floor?
Solution:
A student can go inside the school from outside in 3 ways and from the first floor to the second floor in 4 ways.
∴ Number of ways to choose gates = 3
Number of ways to choose staircase = 4
∴ By using fundamental principle of multiplication,
number of ways in which a student has to go from outside the school to his classroom = 4 × 3 = 12

Maharashtra Board 11th Commerce Maths Solutions Chapter 6 Permutations and Combinations Ex 6.1

Question 15.
How many five-digit numbers formed using the digit 0, 1, 2, 3, 4, 5 are divisible by 3 if digits are not repeated?
Solution:
For a number to be divisible by 3.
The sum of digits must be divisible by 3.
Given 6 digits are 0, 1,2, 3, 4, 5.
Sum of 1, 2, 3, 4, 5 = 15, which is divisible by 3.
∴ There are two cases of 5 digit numbers formed from 0, 1, 2, 3, 4, 5 and divisible by 3.
Either 3 is selected in 5 digits (and 0 not selected) or 3 is not selected in 5 digits (and 0 is selected)
Case I:
3 is not selected (and 0 is selected) i.e., the digits are 0, 1, 2, 4, 5.
10000’s place digit can be selected in 4 ways (as 0 cannot appear).
As digits are not repeated, 1000’s place digit can be selected in 4 ways.
100’s place digit can be selected in 3 ways.
10’s place digit can be selected in 2 ways.
The unit’s place digit can be selected in 1 way.
∴ Using multiplication theorem,
Number of 5-digit number formed from 0, 1, 2, 4, 5 (with no repetition of digits) = 4 × 4 × 3 × 2 × 1 = 96

Case II:
3 is selected (and 0 is not selected) i.e., 1, 2, 3, 4, 5
10000’s place digit can be selected in 5 ways.
1000’s place digit can be selected in 4 ways.
100’s place digit can be selected in 3 ways.
10’s place digit can be selected in 2 ways.
The unit’s place digit can be selected in 1 way.
Using multiplication theorem,
Number of 5-digit numbers formed from 1, 2, 3, 4, 5 = 5 × 4 × 3 × 2 × 1 = 120
Both the cases are mutually exclusive and exhaustive.
∴ Required number = 96 + 120 = 216

Maharashtra Board Class 12 Political Science Notes Chapter 2 Key Concepts and Issues Since 1991: Globalisation 

By going through these Maharashtra State Board Class 12 Political Science Notes Chapter 2 Key Concepts and Issues Since 1991: Globalisation students can recall all the concepts quickly.

Maharashtra State Board Class 12 Political Science Notes Chapter 2 Key Concepts and Issues Since 1991: Globalisation

Introduction Meaning of Globalisation:
Globalisation refers to the rapid spread of goods and services, technology and information, ideas and culture, trade and interactions across the world. It is the connection of different parts of the world, resulting in the expansion of international cultural, informational, economic and political activities.

In the early 1990s, the term globalisation was used to include economic, political, sociocultural, technological and ideological changes that occurred in the world in the post-Cold War era. The world has become more interconnected due to advances in technology and communication. Events in one part of the world have an impact on other parts of the world. Changes have taken place economically and culturally.

Economic Issues:
Some economic changes that have occurred due to globalisation are –

Free flow of finance and capital – Investments provide finance and help to build industries. Indian companies, both private for e.g., Tatas and government e.g., ONGC have invested in many countries in Asia, Africa and Europe. Foreign companies have also invested in India in sectors like power plants, infrastructure projects, consumer food chains, etc. This free flow of capital is both ways i.e., India to foreign countries and vice-versa. Foreign investment especially in the infrastructure sector is essential.

Change in the concept of trade

→ WTO – It was established in 1995 to replace GATT. WTO is the only agency that oversees the rules of international trade, settles trade disputes and organises trade negotiations and agreements.

→ The scope of the term ‘trade’ has widened to include not only traditional commodities like fruits, grains, minerals, oil, etc. but also services like banking, insurance and intellectual property like trademarks.

→ Use of container cargo ships to carry huge amount of goods all over the world.

→ Rise of Transnational companies for e.g., Nestle, Unilever are transnational companies that operate in India. Even Indian multinational companies like Wipro, Bajaj, etc., are doing well.

This affects the economy as follows –

→ Labour market – MNC’s recruit skilled and semi-skilled employees for e.g., Indian labour is employed in West Asia, Europe, USA, etc., in industrial and service sectors.

→ Small shops and industries – Those stores which are efficient, continue to thrive while some industries either sell out to MNC’s or shut down.

→ Agricultural sector- Many MNC’s have introduced new technology and opened up direct markets for Indian agricultural products for e.g., India exports spices, fish, etc., to many nations.

Maharashtra Board Class 12 Political Science Chapter 2 Key Concepts and Issues Since 1991: Globalisation

Idealogical Issues:
During the Cold War, East European nations, Soviet Union and China followed socialist ideology where the public sector was important. USA and West European countries were capitalist and so the private sector was important. India followed Democratic Socialism and a ‘Mixed Economy’ where both public and private sector co-existed in the economic system.

Today, there is only one dominant ideological and economic system i.e., market economy. However, the nature of the market economy is determined by the ideology of that country for e.g., USA has ‘capitalist market economy, many West European countries have ‘welfare market economy’, China has ‘socialist market economy. The Indian system is based on ‘economic liberalism’

Technological Issues:
Rapid advances in global communication such as internet, satellite communication etc., brought in revolutionary changes in our lives. The internet has provided search engines like ‘Google’ to find out information and has enabled social networking through micro media like Instagram, Skype, etc.

All these technologies are transnational and may be positively inclined e.g., NGO’s working for humanitarian issues or negatively inclined such as terrorist organisations.

Social and Cultural Issues:
Today, a ‘global cosmopolitan culture’ has emerged i.e., movement of people across the world and public awareness of global issues. This is noticed in matters like values e.g., secularism, clothing, food choices, ways of celebrating festivals, etc. There is international awareness of India’s rich cultural and historical heritage.

Similarly, westernisation and urbanisation have influenced Indian society e.g., breakup of the traditional joint family and rise of individualism and materialism in the country.

Maharashtra Board Class 12 Political Science Chapter 2 Key Concepts and Issues Since 1991: Globalisation

Political Issues:

Importance of Democracy – Disintegration of Soviet Union and the revolutions in East European countries signified the end of communism and a move towards democratic systems. Today, concepts like Participatory State, Good Governance, etc., have become important.

A participatory State indicates that all sections of society participate in policymaking and in the democratic process. Good governance focuses on the role of civil society in the functioning of an accountable, responsible and responsive government.

Position of the State – Under globalisation, sovereignty of the State, which is closely linked to its jurisdiction appears to be challenged internally and externally. Internal challenges include activism of non-state actors, rise of divisive factors, decline of national consensus, etc while external challenges include rise Of regional economic organisations, growing humanitarian concerns, etc.

Non-State actors – Today, not only States but also non-state actors like NGO’s, pressure groups, etc. Play a significant role in international affairs and in promoting humanitarian issues.

Human Rights – Protection and promotion of human rights is an important issue in the age of globalisation. Countries interpret human rights in accordance with their history, culture, economy and polity, Many nations, including India lay stress on social justice before full enjoyment of civil and political rights.

It is often argued that the role and importance of the State is slowly reducing, However, the State is still the pivot in domestic and international spheres.

Maharashtra Board Class 12 Political Science Chapter 2 Key Concepts and Issues Since 1991: Globalisation

Evaluation Of Globalisation:

Positive aspects

  • Better communication and interconnection.
  • New employment opportunities.
  • Better choice of goods and services to the consumer.
  • Wider investments and scope of expansion of industries.

Negative aspects

  • A fear that the State’s welfare activities in fields like education, health, etc. will be diminished.
  • Fear that international competition will cripple small, local businesses.

Maharashtra Board Class 11 History Notes Chapter 3 Chalcolithic Villages in India

By going through these Maharashtra State Board Class 11 History Notes Chapter 3 Chalcolithic Villages in India students can recall all the concepts quickly.

Maharashtra State Board Class 11 History Notes Chapter 3 Chalcolithic Villages in India

Chalcolithic Period in India:
The people of Late Harappan cultures who had settled on the ruins of Mature Harappan cities had to migrate elsewhere. The urban Harappans and the Late Harappans dispersed. Wherever these people reached, new rural cultures came into being.

The discipline of architecture, town planning of the Mature Harappan period was absent in the Late Harappan settlements, established on the ruins of the Harappan cities. The designs found on the burial pots in ‘Cemetery H’ at Harappa were different. In brief, the characteristics of the Late Harappan culture were different.

Rajasthan
‘Ahar’ or ‘Banas’ Culture: The chalcolithic cultures in India generally belong to the post-Harappan period. However, the ‘Ahar’ or ‘Banas’ culture in the Mewad region of Rajasthan was contemporary to the Harappan civilisation. Balathal and Gilund near Udaipur are the important sites of Ahar culture. ‘Ahar’ culture at Balathal is dated to 4000 B.C.E and was first discovered at Ahar near Udaipur, so it was named as ‘Ahar’ culture.

Ganeshwar-Jodhpura Culture: Many sites of the culture known as ‘Ganeshwar-Jodhpura’ culture have been found in the vicinity of the copper mines at Khetri. The settlements there are earlier than the Harappan civilisation. During the excavations at Ganeshwar copper artefacts like arrowheads, spearheads, harpoons, bangles, chisels and also pottery was found. The people of Ganeshwar-Jodhpur culture supplied copper objects to the Harappans.

Maharashtra Board Class 11 History Notes Chapter 3 Chalcolithic Villages in India

The Ganga Valley
Ochre Coloured Pottery and Copper Hoards: Initially, the Ochre Coloured Pottery (OCP) was mostly found in river beds. Now, a number of sites of the OCP culture are found in Punjab, Haryana, Rajasthan and the Western region of Uttar Pradesh. House floors of these people were made by ramming. On the house floors were found traces of hearths, terracotta male figurines and bull figurines. Remains of cattle bones, rice and barley were also found.

Bihar, Bengal, Odisha: Copper hoards have been found in Bihar, Bengal, Odisha and Madhya Pradesh. However, OCP is not found in these regions. Chalcolithic sites have been discovered in these regions. In Bengal and Odisha also, some chalcolithic sites have yielded pottery that shows Harappan influence as far their shapes are concerned. They include bowls and troughs of various sizes.

Madhya Pradesh
Kayatha Culture:
Kayatha is a site situated on the bank of the river known as Chhoti Kali Sindh, at a distance of 25 kilometres from Ujjain in Madhya Pradesh. Kayatha culture was contemporary to the Harappan civilisation. The people of Kayatha culture subsisted on agriculture and animal husbandry.

Malwa Culture: The name ‘Malwa’ obviously tells us that this culture originated and spread first in the Malwa region. It existed in Madhya Pradesh during 1800- 1200 B.C.E. ‘Navadatoli’ situated on the river Narmada, on the opposite bank of Maheshwar, is an important site of Malwa culture. The other important sites are Eran (District Sagar) and Nagda (District Ujjain). They were surrounded by protective walls.

Gujarat: The chalcolithic settlements in Gujarat coincide with the following phases of the Harappan culture:
Early Harappan phase (3950-2600 B.C.E.) (2) Mature (urban) phase (2600-1900 B.C.E.) (3) Post- Harappan phase (1900-900 B.C.E.) There are ample sources of semi-precious stones in Gujarat. Making beads of these stones was a big industry during Harappan times.

The Neolithic settlements in Gujarat played a major role in procuring these stones. People residing in the neolithic settlements of Gujarat were mainly pastoral, that is people whose primary occupation was animal husbandry. Probably, some of these pastoral people were semi-nomadic.

There are regional variations in the characteristics of chalcolithic cultures of Gujarat. The chalcolithic pottery of Kutch Saurashtra and Northern Gujarat are distinct from each other. The chalcolithic villages in Kutch-Saurashtra were abandoned by 1900 B.C.E.

In the post-Harappan period, there were two chalcolithic cultures in Gujarat. The culture in south Gujarat was known as ‘Prabhas’ culture and the one in northeastern Gujarat was known as ‘Rangpur’ culture. The pottery of these chalcolithic cultures was akin to Late Harappan pottery with regards to the colour, shapes and designs. These cultures existed till 1800-1200 B.C.E.

Maharashtra Board Class 11 History Notes Chapter 3 Chalcolithic Villages in India

Chalcolithic Maharashtra:
The chalcolithic culture before the arrival of the Late Harappans at Daimabad is known as ‘Savalda’ culture.

Savalda Culture: Savalda is in Dhule district. It is situated on the banks of the river Tapi Savalda culture is dated to 2000-1800 B.C.E. This culture seems to have arisen by the cultural contact between the Mesolithic people in northern Maharashtra and the Harappan people in Saurashtra. People of Savalda culture at Daimabad used wheel-made pottery. The designs on their earthen pots included arrowheads, harpoons and figures of various animals.

Malwa and Jorwe Cultures: The First Farmers of Maharashtra. The people of Malwa culture reached Maharashtra around 1600 B.C.E. Permanent villages of farmers were first established in Maharashtra by the Malwa people. They were the first farmers of Maharashtra. After arriving in Maharashtra, they came into contact with the neolithic people in Karnataka. It resulted into a few changes in the pot making technology of Malwa people as far as shapes of the pots and designs are concerned.

Megalithic Period in India: At about 700 B.C.E. Inamgaon was completely abandoned by the Jorwe people. Thereafter it was never occupied till the historic period. This situation prevailed in most of the Maharashtra. However, a nomadic people of this period erected stone circles by using huge slabs of rock. The – space within these circles was used to bury dead people. Because of the huge stone slabs used in their erection, these circles are known as megaliths. The period of these megaliths is known as the ‘Megalithic Age’.

Glossary:

→ Chalcolithic Relating to or denoting a period when tools and weapons were made of copper.

→ Harpoons – A long thin weapon with a sharp pointed end and a rope tied to it that is used to catch large sea animals.

→ Contemporary – Belonging to the same time as somebody/something else.

→ Farmstead A farm and its buildings.

→ Pegging – Controlling.

→ Fanning – To cause a current of air to blow upon.

Maharashtra Board Class 12 Political Science Notes Chapter 6 India and the World 

By going through these Maharashtra State Board Class 12 Political Science Notes Chapter 6 India and the World students can recall all the concepts quickly.

Maharashtra State Board Class 12 Political Science Notes Chapter 6 India and the World

Introduction
India has played an active role in international relations even before independence for e.g. India was a signatory at the San Francisco Conference that gave shape to the United Nations Charter.

The primary objectives of India’s Foreign Policy are –

  • maintenance of international peace and security.
  • protection of the sovereignty and integrity of the country.
  • maintaining good relations with neighbouring countries and with regional groups such as ASEAN.
  • greater integration with the world economy to sustain a high growth rate.

The principles of India’s foreign policy are –

→ respect for the sovereignty and territorial integrity of all States.

→ non-intervention in the internal affairs of any other States.

→ respect for international law.

→ belief in peaceful coexistence and peaceful resolution of international disputes.

→ active participation in international and regional organisations.

→ Pandit Jawaharlal Nehru is called the ‘architect of India’s foreign policy.

Factors Influencing India’s Foreign Policy:

Geography – The extensive coastline of the Indian peninsula and the Himalayan mountain ranges have shaped India’s security and foreign policy. India shares a border with all neighbouring countries of South Asia. It also holds a dominant position in the Indian Ocean.

History – It includes the influence of traditional cultural values, cultural ties as well as values like anti-colonialism which were imbibed during the freedom struggle.

Economy – The strong urge to come out of poverty and economic backwardness created by the colonial period as well as the policy of Non-Alignment shaped India’s foreign policy. India followed democratic socialism through the policy of import substitution and importance to the public sector. Post-1991, after adopting the policy of Liberalisation, Privatisation and Globalisation many changes have occurred in India’s foreign policy.

Polity – Political leadership has a significant impact on India’s foreign policy for e.g., Prime Ministers Jawaharlal Nehru, Lai Bahadur Shastri, Indira Gandhi, Atal Bihari Vajpayee, Narendra Modi have played a decisive role in determining India’s foreign policy. Ministry of External Affairs and National Security Advisor play an important role in formulating foreign policy.

International situation – During the Cold War, superpower politics had impacted India’s foreign policy e.g., adopting Non-Alignment. Similarly, conditions such as end of the Cold War, Indo-US dialogues, China-Pakistan relations, growth of regional organisations, etc., have impacted the foreign policy of India.

Maharashtra Board Class 12 Political Science Chapter 6 India and the World

India’s Relations With The World:
→  Relations with major powers in the world During the Cold War, USA and Soviet Union were the superpowers. In the 21st century, Russia and China have emerged as major powers. ‘

United States of America (USA):
US President Franklin D. Roosevelt had supported the cause of India’s independence, However, relations between USA and India remained strained for most of the Cold War period. Close relations of the USA with Pakistan and its position on the Kashmir issue have been irritants in Indo-US relations. Following India’s second nuclear tests (1998) the US imposed sanctions on India.

→ However, from the start of this century Indo- US ties have improved due to the following reasons –

Anti-terrorism stance: India supported President George W. Bush’s war on terrorism. Similarly, after the 2001 terrorist attack on Indian Parliament by Pakistan-supported terrorist groups, US demanded that Pakistan should stop sponsoring cross-border terrorism.

Partnership and Agreements: The US regards India as a major partner in the Indo- Pacific region. India regards the USA as a major source of investment and partner in trade and defence as well as in multilateral fora like India-US-Japan. In 2008, the India- US Civil Nuclear Cooperation Agreement was signed by which India became the only country outside NPT that has nuclear capabilities.

Soviet Union / Russia:
During the Cold War era, Soviet Union provided aid to India in the form of technology, weapons and low-interest credit to India’s heavy industry projects in the public sector. Indo-Soviet Friendship Treaty (1971) is considered a milestone in their bilateral relations.

After the disintegration of the Soviet Union, Russia agreed to provide reactors for India’s Kudankulam nuclear power plant and for joint ventures to produce Sukhoi fighter aircraft and Brahmos missiles. Both India and Russia have major stakes in Russia oil fields such as Sakhalin-1 highlighting the importance of energy security.

Maharashtra Board Class 12 Political Science Chapter 6 India and the World

China: In 1949, the Communist revolution took place in China. India was among the first nations to recognize the People’s Republic of China. In 1954, India and China signed the Panchsheel Agreement and India also recognised Chinese suzerainty on Tibet.

The main hindrances in Sino-Indian relations are –

  • 1962 Indo-China war, 2017 Doklam skirmish
  • Border disputes in Aksai Chin and NEFA region
  • China has been critical of India offering political asylum to the Dalai Lama
  • Chinese support to Pakistan
  • India’s apprehensions against China’s Belt and Road Initiative.

On the positive side, India-China relationship has improved due to –

→ Agreement on maintenance of peace and tranquillity along the LOC

→ China has become among the largest trading partners of India

→ India and China are part of BRICS and SCO

→ In the late 1990s, Russia mooted the idea of a Trilateral Summit of Russia, China, India which was a recognition of India’s status as a major regional power.

Relations with Africa:
In the first few decades after independence, India supported the fight against apartheid and provided financial and material aid to liberation struggles in Africa for eg., the AFRICA Fund created at the NAM Summit (Harare)
There are several issues in the context of India-African relations

→ The India-Africa summit was held in 2015.

→ About 24 per cent of Indian crude oil imports are sourced from the African continent eg., ONGC Videsh has invested in Sudan and Egypt.

→ About two million people in Eastern and Southern Africa constitute the India diaspora which is considered as an asset by the Indian government.

→ Indian industries are interested in offering technological and material services to developing African nations.

→ India continues to be one of the military training destinations e.g., National Defence Academy, Pune has the ‘Sudan Block’ as a symbol of cooperation between India and Sudan.

→ Countries from Somalia to South Africa fall under the India maritime strategic perspective. Hence, cases of terrorism and piracy in Somalian waters have made this region sensitive to Indian concerns.

Relations with the Neighbourhood:
All South Asian countries share a border with India. Bangladesh, China, Indonesia, Myanmar, Pakistan, Thailand and Sri Lanka are regarded as India’s neighbours. Countries in the India Ocean Region (IOR), from East Africa, Persian Gulf to Malaysia, Vietnam as well as countries in the Central Asian hinterland of IOR form India’s extended neighbourhood.

India’s first Prime Minister Jawaharlal Nehru promoted the idea of Asian-African regionalism. This led to initiatives like Asian Relations Conference (1947) and Bandung conference (1955)

Relations with Pakistan: The main cause of the tensions between India and Pakistan has been the status of Kashmir. This led to the 1947-48 conflict and 1965 war. Efforts to improve Indo-Pak relations include 1972 Shimla Agreement, 1999 Lahore Agreement, etc.

Himalayan Kingdoms: Nepal, Bhutan and Sikkim were British protectorates. Sikkim opted to integrate with India (1975). Relations with Bhutan have been cordial. However, relations with Nepal have seen ups and downs.

Bangladesh: India played a major role in securing independence for Bangladesh in 1971. Major issues in Indo – Bangladesh relations were about distribution of waters of Teesta river, land and maritime boundaries, Chakma refugees, etc. Cross border terrorism is a concern for both countries.

Sri Lanka: India and Sri Lanka had a disputed maritime boundary. The main issue here is Sri Lanka had accused India of supporting the LTTE.

Myanmar: It was a co-convener at the Bandung Conference. However, after the military coup in 1962 there was a cooling off in Indo-Burma relations. India extended support to the pro-democracy movement in Myanmar under its leader Mrs. Aung San Suu Kyi. The support of Myanmar is vital in India’s action against militant groups hiding in Myanmar

West Asia: India has been a supporter of the Palestine Liberation Organisation (PLO) and yet ensured that it maintains good relations with Israel. Similarly, India has shared cordial historical and cultural ties with Iran and Saudi Arabia.

Maharashtra Board Class 12 Political Science Chapter 6 India and the World

South-East Asia: Indonesia under Sukarno had co-founded the Non-Aligned Movement. Relations with Vietnam have always been good. India had openly criticised US intervention in Viet Minh. As part of its “Look East” and “Act East” policy, India has improved relations with countries like Japan, Thailand, Singapore, Malaysia, Indonesia, etc., The areas of cooperation include security of trade routes, anti-piracy operations, etc.,

India has a Free Trade Agreement with ASEAN and is also a partner in ASEAN promoted ARF. India has been an active partner in SCO, BIMSTEC, etc.,

India Ocean Region: The coastline presents both challenge and opportunity to India due to its trade and security perspectives. The Naval Plans Paper (1948) expressed India’s maritime vision. In the 1971 war with Pakistan, the Indian Navy played a significant role. Bharatmala and Sagarmala projects are significant. The Indian Ocean Rim Association for Regional Cooperation was created in 1997 to promote sustained and balanced growth of the region. It has 22 Member States and 9 Dialogue Partners.

Maharashtra Board Class 11 History Notes Chapter 2 First Cities of India

By going through these Maharashtra State Board Class 11 History Notes Chapter 2 First Cities of India students can recall all the concepts quickly.

Maharashtra State Board Class 11 History Notes Chapter 2 First Cities of India

Characteristics of Harrapan Civilisation:
A few years ago, it was strongly believed that the Vedic Aryans arrived in India at about 1500 B.C.E. However, no information was available regarding the period before that. This situation continued till the discovery of Harappa in 1921 and Mohenjodaro in 1922.

The discovery of the Harappan Civilisation at these two places stretched the antiquity of Indian history to 3500-3000 B.C.E. Harappan civilisation belonged to ‘Bronze Age’. So far, more than 2000 sites of the Harappan civilisation have been recorded. The history of these cities had three stages viz:

  • Early Harappan period
  • Mature Harappan (Urban) period
  • Late Harappan period
  • Some of the main characteristics of the Harappan cities are
  • Systematic Town Planning
  • Central Administration
  • Social Organisation
  • Economy
  • Use of Developed Writing System
  • Some cities of Harrapan Civilisation:

Harappa: Harappa is situated on the banks of the river Ravi (District Sahiwal in Punjab, Pakistan). The v ancient site of Harappa had spread on 150 Hectares. The first excavation at Harappa began in 1921. The first settlement of the Early Harappan period was established around 3300 B.C.E. It evolved to the Mature Harappan (urban) phase around 2600 B.C.E. It reached its peak during 2450-1900 B.C.E.

Maharashtra Board Class 11 History Notes Chapter 2 First Cities of India

Mohenjodaro: Mohenjodaro was built on the banks of the river Sindhu (Indus) in Pakistan (District Larkana, Sindh). Area wise, Mohenjodaro is the biggest city, among those discovered in Pakistan so far. It was thought that the city was divided into two fortified sections, namely the ‘Citadel’ and the ‘Lower Town’.

The excavations at Mohenjodaro by Rakhaldas Banerjee began in 1921-22. In 1923- 24 to gather more information about Mohenjodaro Madho Sarup Vats, Kashinath Narayan Dikshit, Earnest Mackay and others conducted further excavations under Sir John Marshall’s direction. He was the Director-General of the Archaeological Survey of India at that time. During these excavations, various artefacts, houses and public monuments were unearthed.

Kalibangan: The site of Kalibangan is 205 kilometres away from Bikaner. It is located in the Hanumangarh district of Rajasthan. It was one of the important urban centres of the Harappan civilisation, situated on the banks of the river Ghaggar. L. P. Tessitore, an Italian linguist had visited Kalibangan during his study tour of the region.

It was conducted under the direction of Brijabasi Lai, the then Director-General of the Archaeological Survey of India and Balkrishna Thapar. At Kalibangan two settlements, one of the Mature Harappan period and the other of the Early Harappan period, were found. Kalibangan was a small city compared to Harappa and Mohenjodaro.

Lothal: Lothal was established on the banks of the river Bhogao. The centre of the Harappan civilisation at Lothal was situated near the Gulf of Kutch, in Gujarat, 80 kilometres away from Ahmedabad. It is known for the remains of Harappan dock. Lothal was excavated from 1955 to 1960 under the supervision of S.R. Rao. The ‘Citadel’ and the ‘Lower Town’ at Lothal do not have separate fortification walls. Rather they are surrounded by a single fortification wall.

Dholavira: Dholavira was discovered by J.P. Joshi, the Director-General of Archaeological Survey of India. The site is in ‘Khadirbet’ in Gujarat (Dist. Kutch). Excavations at the site were started by R.S. Bisht in 1990. Among the excavated Harappan sites, extent wise Dholavira is the fifth-largest city. An Early Harappan settlement was discovered at Dholavira. There was a protective wall built around it by using mud bricks (unbaked bricks) and dressed stones. It was surrounded by an outer fortification wall.

The settlement within the outer fortification was divided into four sections.

  1. Citadel
  2. The adjacent section reserved for high officials
  3. Lower Town – These three sections had walls, which separated them from each other.
  4. The fourth section inside the outer fortification did not have any additional separating walls.

Maharashtra Board Class 11 History Notes Chapter 2 First Cities of India

Rakhigarhi: In the Hissar district of Haryana is situated the site of Rakhigarhi, a Harappan city. It is on the distance of 150 kilometres from Delhi. It is located on the banks of Chautang (ancient Drishdvati river). Rakhigarhi is the largest Harappan site, among all the sites from India and Pakistan.

Its total area was more than 350 Hectares. The excavations at Rakhigarhi started in 1963. It continued in 1997-2000. Later, Dr Vasant Shinde of the Deccan College, Pune also conducted excavations at the site.

Inter-relationship between Cities and Villages:
The city people are dependent on the natural resources and villages in their vicinity in order, to meet the needs of urban way of life and urban administration. The raw material needed for Harappan industrial production included clay, various siliceous and semi-precious stones, metals, etc.

The inter-relationship between Harappan cities and villages was dependent on the mechanism of making available, things like food grains and the raw materials.

Production, Trade, Organisation and Administration:
During the Mature (urban) Harappan period the sphere of commodity exchange expanded and their import-export increased to a great extent. The internal and distant trade received momentum. Trade with distant places like Mesopotamia became regular. Trade with Mesopotamia had begun during Early Harappan times.

The Akkadian empire was founded in 2334 B.C.E. by Emperor Sargon I. During his reign the Harappan trade with Mesopotamia flourished and the Harappan cities reached their peak. Harappan period and the sea trade had become the preferred mode. ‘Dilmun’, ‘Makan’ and ‘Meluhha’ are mentioned as three important centres on the sea route. Harappan traders are likely to have received wool, gold and silver in exchange other commodities.

Maharashtra Board Class 11 History Notes Chapter 2 First Cities of India

Decline of the Cities:
When Harappan civilisation was discovered, it was presumed that its cities were destroyed by invading tribes who came from outside. Indra is described as ‘Purandara’ meaning the destroyer of fortified cities. The Harappan cities were fortified, thus befitting the definition of ‘pura’. Deteriorating environment was the main reason of the decline of Mesopotamia. Similarly, climatic changes and deteriorating environment were the main reasons of the decline of the Harappan civilisation too. Around 2000 B.C.E. the climate became increasingly arid and there were frequent famines. Degradation of cultivable land was on the increase.

Glossary:

→ Fortification – Walls, towers etc. built especially in the past to protect a plact’ against attack.

→ Artefacts – An object that is made by a person.

→ Citadel – A castle on high ground or near a city where people could go when the rity is attacked.

→ Granary – A large building for storing grains.

→ Linguist Someone who studies the structure and development of language.

→ Furrow – A trench in the earth made by a plough.

→ Dock – An area of a port where ships stop to be loaded, repaired etc.

→ Dwindled – To become smaller or weaker.

Maharashtra Board Class 11 Economics Notes Chapter 4 The Economy of Maharashtra

By going through these Maharashtra State Board Class 11 Economics Notes Chapter 4 The Economy of Maharashtra students can recall all the concepts quickly.

Maharashtra State Board Class 11 Economics Notes Chapter 4 The Economy of Maharashtra

→ Maharashtra State has been divided into 36 districts.

Maharashtra Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics 1

6 Revenue Divisions of Maharashtra

  1. Mumbai
  2. Pune
  3. Nasik
  4. Aurangabad
  5. Amravati
  6. Nagpur

Maharashtra Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics 2

Maharashtra Board Class 11 Economics Notes Chapter 4 The Economy of Maharashtra

Features Of Maharashtra Economy

  • Abundant natural resource, skilled manpower, technologically advanced infrastructure, etc.
  • Highest GSDP & SPCI as compared to other states.
  • Literacy rate 82.3% – 2011 Census
  • Most favoured destination for creativity, skill, development, tourism and investment.
  • Sex Ratio L929 females per 1000 males
  • 2nd 1arges populated F4ate country (11.24 crores- Census 2011)
  • 3rd largest state in country in terms of geographical area. (3.08 lacs sq. km)
  • Most urbanised state

Maharashtra Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics 3

Problems In Economic Development Of Mahakashtra

  1. Agricultural Sector
  2. Industrial Sector

1. Agricultural Sector:

  • Decrease in average size of land holdings
  • Increase in number of small and marginal farmers
  • Excessive use of chemical fertilizers and pesticides (soil degradation)
  • Agricultural indebtedness
  • Poor implementation of land reforms
  • Inadequate irrigation facilities
  • Lack of capital and marketing facilities
  • Improper implementation of rural development plans
  • Impact of climatic change

2. Industrial Sector:

  • Delays in Government procedure
  • Lack of opportunities for skill development
  • Lack of updated technology
  • Lack of infrastructure facilities
  • Lack of motivation to new enterpreneurs
  • Lack of development programmes
  • Regional imbalance

Maharashtra Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics 4

Maharashtra Board Class 11 Economics Notes Chapter 4 The Economy of Maharashtra

Measures Undertaken By The Govt. For – Agricultural Development:

  • Distribution of quality seeds at reasonable rates.
  • Number of outlets increased for fertilizer and pesticide distribution. Development of irrigation facilities.
  • Electrification of agricultural pumps and to provide electricity on demand.
  • Provide financial assistance.
  • Setting up of APMC, Establishment of agro export zones, horticultural training centres, grading and packing facilities.
  • Create awareness by use of mass media for making agriculture a profit making business.

Maharashtra Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics 5

Industry : Maharashtra is an industrially advanced state.
The share of industry in Net Value Added (NVA) is about 18%. Maharashtra is the first choice of domestic and foreign investor.
Maharashtra is ranked as number one investment destination in India.
Maharashtra is in forefront in terms of FDI inflow in India.

Problems In Industrial Sector:

  • Lack of opportunities for skill development
  • Delays in Government procedure
  • Lack of updated technology
  • Regional imbalance
  • Lack of infrastrucLural facilities
  • Lack of development programmes
  • Lack of motivation to new enterprises

Maharashtra Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics 6

Measures Undertaken By ‘The Government For Industrial Development:

  • Introduction of MAITRI (Maharashtra Industry, Trade and Investment Facilitation Cell)
  • Awards for export performance space rent subsidies to small scale industries
  • Introduction of MAITRI (Maharashtra Industry, Trade and Investment Facilitation Cell)
  • Initiation of Single window cell
  • Creation of (SEZ) Special: Economic Zones
  • Implementation of Maharashtra State Industrial Cluster Development Programme (MSICDP)

Maharashtra Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics 7

Maharashtra Board Class 11 Economics Notes Chapter 4 The Economy of Maharashtra

Service Sector :

  • It consists of – insurance, tourism, retail banking, education and social services.
  • It provides services to business sector as well as final consumers.
  • It is largest employment generating and fastest growing sector.
  • Core area of service sector includes – Fintech, IT/ITES, start ups, cloud computing, electric vehicles, defence, tourism and private universities.

Core Area Of Service Sector:

  • Infrastructure
  • Tourism
  • Hospitality
  • Entertainment Industry

Infrastructure:

  1. Economic Infrastructure
  2. Social Infrastructure

Economic Infrastructure:

  • Energy
  • Transport
  • Communication

Social Infrastructure:

  • Health
  • Education

Maharashtra Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics 8

Measures for development of Economic Infrastructure:

  • Increase in installed capacity of electricity generation.
  • Rural electrification, network improvement and energy conservation programmes.
  • Direct benefit transfer scheme to LPG consumers.
  • Implementation of Road development pIan. (2001 .2021).
    (Target – 3.37 lakh kms of road)
  • Metro Railway – at Mumbai and Nagpur.
  • Constitution of Maharashtra Port Development Policy,
    (Sagarmala Programme- by Central Government)

Maharashtra Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics 9

Maharashtra Board Class 11 Economics Notes Chapter 4 The Economy of Maharashtra

4 Levels of Education:

  1. Primary Education (STD. I To VIII)
  2. Secondary and Higher Secondary Education (STD. IX to XII)
  3. Higher Education
  4. Others:

1. Primary Education (STD. I To VIII)

  • Scheme: Right to Education (RTE) (6-14 yrs)
  • Sarva Shiksha Abhiyan(SSA)
  • Expenditure: ‘19,486 Crores (2016-17)

2. Secondary and Higher Secondary Education (STD. IX to XII)

  • Schemes: Rashtriya Madhyamik Shiksha Abhiyan (RMSA)
  • Expenditure : Rs. 16,089 Crores (2016-17)

3. Higher Education:

  • 22 State Universities
  • Maharashtra Public Universities Act, 2016
  • Scheme : Rashtriya LJchchatar Shiksha Abhiyan (RUSA)

4. Others:

  1. Inclusive Education
  2. Girls Education
  3. Adult Literacy
  4. Tribal Education

Inclusive Education:
For Differently abled children

Girls Education:

  • Free education till higher secondary level
  • Free of cost S.T. bus service
  • Bicycles to near living within 5 kms from schools.

Adult Literacy:

  • ‘Each one Teach one’
  • ‘Sakshar Bharat Abhiyan

Tribal Education:

  • Residential Ashram Schools
  • Hostel facility
  • Free uniform, food, educational materials, etc.

Maharashtra Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics 10

Maharashtra Board Class 11 Economics Notes Chapter 4 The Economy of Maharashtra

Health Services:

  • 1814 Primary health centres
  • 360 Community health centres
  • Health programme by Government of Maharashtra
  • National Rural Health Mission (NRHM)
  • National Urban Health Mission (NUHM) include programme like
    • Sanitation and Hygiene (common points in both NRHM and NUHM)
    • Nutrition (common points in both NRHM and NUHM)
    • Safe drinking water

3 Tier”Health Infrastructure:

  1. Primary Tier
  2. Secondary Tier
  3. Tertiary Tier

Primary Tier

  • Primary Health Centres
  • Community Health Centres

Secondary Tier

  • Sub-district hospitals
  • District hospitals

Tertiary Tier

  • Well Equipped Medical Colleges
  • Super specialty hospitals

Maharashtra Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics 11

Tourism (Maharashtra Tourism Policy, 2016)

Objectives:

  • to make Maharashtra a leading tourist destination by 2025.
  • to attract investments of ? 30,000 Crore.
  • to create additional jobs

Nodal Agency: → Maharashtra Tourism Development Corporation (MTDC)
“Mahabhraman” → (agro tourism, village tourism, food tourism, safaris, etc.)

Maharashtra Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics 12

Maharashtra Board Class 11 Economics Notes Chapter 4 The Economy of Maharashtra

Hospitality:

  • Hotel Industry
  • Transportation
  • Event Management
  • General Tourism
  • Restaurants

Transportation

  • Airlines
  • Mumbai – Goa Cruiseship
  • Fancier Trains (Deccan Odyssey)

Maharashtra Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics 13

Entertainment Industry:

  • Largest number of films in world Generates
  • Generates employment opportunities
  • Koihapur – well known for regional films
  • Mumbai – Popularly called as ‘Bollywood’.

Maharashtra Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics 14

Co-operative Movement in Maharashtra:
Objectives:

  • To develop rural areas.
  • To improve socio-economic conditions of under-privileged
  • To develop agro-processing and agro marketing.
  • To support sugar co-operatives, fisheries co-operative and dairy co-operatives.

Maharashtra Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics 15

Word Meaning:

revenue divisions – administrative division to collect government revenue and lower its expenses, geographical area – physical features of an area, urbanized – people staying in city or town, census – a survey of counting of population, literacy rate – percentage of population who can read and write, characterised – features, abundant- plenty, resources – stock of something, infrastructure – basic structure like buildings, roads, bridges, etc. destination – place to visit, allied – joined, declining – decreasing, trend – direction, average – mean, marginal – very small, excessive – more, degradation – low in quality, indebtness – to owe something, implement – to do it / to carry out, adverse – poor, inadequate – not sufficient, reasonable – low cost, electrification – use of electricity, assistance – to help, agro – agriculture based, awareness – to make understand/ to bring to notice, mass media – communication to people through TV, Radio, Newspaper, etc, potential – capable possibility, diversification – to change the line of business, amend – to make changes, liberalisation – removal of restrictions, opportunities – chances, motivation – willingness to do something, clearances – to clear/ to give pass away, consolidate – to combine, subsidies – grant/allowaness, retail banking – banking services provided to general /public, core – important/essential/significant, expand – to enlarge, rapid – fast, sustainable – to maintain, achievement – to do something successfully, energy conservation – preventing the waste of energy, integrated – linked together, subscriber – member, components – a part of something, stimulate – to encourage, backbone – to support, scenario – situation, priority – more important, compulsory – essential, universalization – through out, veterinary- study related to animal diseases and it treatments, autonomous – independent, privatization – transfer of public company to private ownership, globalization – all over the world, concession – discount, emphasizes – to give special attention, strengthen- to build up, sanitation – to provide clean drinking water and sewage disposal, hygiene – cleanliness, nutrition – obtaining necessary food for health, three tier – three level, comprehensive – inclusive, tertiary – service sector, abroad – foreign, agro tourism – agriculture based tourism, manifold – numbers /multiple, cruiseship – passenger ship used for travelling with amenities within it, impact – effect, underprivileged – needy, solidarity – mutual support, subsequently – afterward.

Maharashtra Board Class 11 History Notes Chapter 1 First Farmers

By going through these Maharashtra State Board Class 11 History Notes Chapter 1 First Farmers students can recall all the concepts quickly.

Maharashtra State Board Class 11 History Notes Chapter 1 First Farmers

River Valley Civilisations:
Homo habilis made the first stone tools. These tools were useful only for simple jobs like scraping meat from the hides of dead animals, breaking nuts, etc. The later species of mankind after Homo habilis were more advanced. It resulted into the rise of the ‘Neolithic Age’. After that, settled villages came into being. The archaeological evidence shows that systematic agriculture began some 12000-11000 years ago.

The progress in the techniques of systematic cultivation resulted in the rise of the most ancient river valley civilisations of the Neolithic age. The river valley civilisations grew in four regions of the world. Those regions were Mesopotamia, Egypt, Indian Subcontinent and China.

The Valley of Euphrates and Tigris – Mesopotamia: Mesopotamia is the Greek name of the region between the two rivers, Tigris and Euphrates. Mesos means the ‘middle one’. Potamos means ‘river’. The region between two rivers is ‘Mesopotamia’. The Mesolithic people began to stay in this region for longer times because of the availability of ample water.

Ancient Mesopotamia included modern Iraq, Syria as well as the western regions of Iran and south-eastern regions of Turkey. The camps of Mesolithic people developed into the first settled neolithic villages. These first villages are dated to 10000 years B.C.E.

Maharashtra Board Class 11 History Notes Chapter 1 First Farmers

The Valley of Nile – Egypt: Napoleon Bonaparte had taken along many scholars from various fields during his invasion of Egypt in 1798. They studied the ancient remains in Egypt and published it. These studies received a momentum because of the decipherment of the Rosetta inscriptions. The first neolithic villages in Egypt came into being at about 6000 B.C.E. The beginning of agriculture in Egypt coincides with the same time.

The Valley of the Huang He – China: The Valley of Huang He River is considered to be the region of origin of the Chinese culture. The Chinese culture evolved here. Agriculture in the neolithic villages of China began at about 7000 B.C.E. Wheat, foxtail millet and rice were grown by the farmers in these villages.

The Valleys of Sindhu (Indus) and Saraswati – Indian Subcontinent: The region of the valleys of Sindhu and Saraswati is now divided between India and Pakistan. The archaeological excavations at Harappa on the banks of Ravi in Punjab and Mohenjo Daro on the banks of Sindhu in Sindh indicate the existence of a fully developed civilisation in the Indian subcontinent which was dated to circa 3000 B.C.E.

It proves that there were well-settled villages in the Indian subcontinent as early as 8000 B.C.E. There is a general consensus among the scholars that the Harappan cities evolved from these early villages.

Beginning of Cultivation: Agricultural Production:
Beginning of cultivation is also the beginning of the neolithic age. It spans through 10000 – 8700 B.C.E. It may vary to some extent from place to place. This period marked the beginning of domestication of animals along with the beginning of cultivation.

Barley was the main crop in this period. Other crops were wheat and flaxseed. Thus, the technology evolved; the techniques of hunting and obtaining food improved; food became available in plenty.
This resulted in making the Mesolithic people stay at one place for a longer time of the year. This is how the villages were settled on a permanent basis.

Maharashtra Board Class 11 History Notes Chapter 1 First Farmers

First Farmers of India:
Neo means ‘new’ and lithic means ‘of stone neolithic’ age got its name because of the stone tools of completely new types. The site is of great importance among the neolithic villages in the Indian subcontinent established by the first farmers. The Mehrgarh farmers cultivated barley and wheat. There is another site of a neolithic village that is contemporary to Mehrgarh.

The site was found at ‘Lahuradeva’ in Sant Kabir Nagar district of Uttar Pradesh. In Maharashtra, the mesolithic man existed during 10000-4000 B.C.E. The Chalcolithic people were the first farmers of Maharashtra. Inamgaon, in the Shirur taluka of Pune district, is an important site of the village of Chalcolithic farmers in Maharashtra.

Agricultural Settlements:
A village with at least a population of 100 could meet the needs of individual members who would be completely dependent on agriculture and animal husbandry. Neolithic villages were small in size. Permanently occupied dwellings (mostly round huts) were characteristic of these villages.

Other than these dwellings, some places in the central part of the village were perhaps used as common storage places of food-grains and other things. This internal settlement pattern of the village indicates that the transactions related to food production were centrally controlled.

Trade and Transport:
The nomadic-semi nomadic groups of Mesolithic people had a system of barter among themselves. The wheel was not yet invented. It means that the means of mechanical transport were not available to them. The neolithic people invented the wheel and the technology they had developed so far, underwent a revolution. The neolithic people began to produce wheel-made pottery.

The wheel technology made it possible to produce pottery on a mass scale. The invention of the wheel also made it possible to obtain the raw material from distant places in much lesser time. It helped to develop trade and transport on a greater scale.

Maharashtra Board Class 11 History Notes Chapter 1 First Farmers

Beginning of Urbanisation:
After settling down at one place for a long time, a feeling of ownership arose among the Neolithic people. This feeling was focused on their individual dwellings and the piece of land cultivated by them. Eventually, the villages expanded. Along with it, awareness of collective landholdings and the village boundaries became prominent.

It gave rise to administrative centers. Such administrative centers attract a large population that includes officials, people from various occupations. As a result, the periphery of the original settlement kept expanding and cities came into being. Thus, began the process of urbanization in the Neolithic age.

Glossary:

→ Civilization – The process by which a society or place reaches an advanced stage of social and cultural development and organization.

→ Homo habilis – Extinct species, ancestor of modern human.

→Nomadic – Moving from one place to another rather than living in one place all of the time.

→ Pastoralism – Animal Husbandry.

→ Decipherment – To discover the meaning of.

→ Hieroglyphs – Pictorial script.

→ Archaeology – Study of ancient evidence of the past.

→ Excavation – To remove the earth from a place in order to find old objects buried there.

→ Monochrome – Single colour.

→ Burnished – Polished by rubbing with a wooden or stone tool.

→ Applique work – Pasting wet clay ribbons and making patterns on them.

Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9

Balbharti Maharashtra State Board 11th Maths Book Solutions Pdf Chapter 9 Differentiation Miscellaneous Exercise 9 Questions and Answers.

Maharashtra State Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9

(I) Select the appropriate option from the given alternatives.

Question 1.
If y = \(\frac{x-4}{\sqrt{x+2}}\), then \(\frac{d y}{d x}\) is
(A) \(\frac{1}{x+4}\)
(B) \(\frac{\sqrt{x}}{\left(\sqrt{x+2)^{2}}\right.}\)
(C) \(\frac{1}{2 \sqrt{x}}\)
(D) \(\frac{x}{(\sqrt{x}+2)^{2}}\)
Answer:
(C) \(\frac{1}{2 \sqrt{x}}\)
Hint:
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 I Q1

Question 2.
If y = \(\frac{a x+b}{c x+d}\),then \(\frac{d y}{d x}\) =
(A) \(\frac{a b-c d}{(c x+d)^{2}}\)
(B) \(\frac{a x-c}{(c x+d)^{2}}\)
(C) \(\frac{a c-b d}{(c x+d)^{2}}\)
(D) \(\frac{a d-b c}{(c x+d)^{2}}\)
Answer:
(D) \(\frac{a d-b c}{(c x+d)^{2}}\)
Hint:
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 I Q2

Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9

Question 3.
If y = \(\frac{3 x+5}{4 x+5}\), then \(\frac{d y}{d x}\) =
(A) \(-\frac{15}{(3 x+5)^{2}}\)
(B) \(-\frac{15}{(4 x+5)^{2}}\)
(C) \(-\frac{5}{(4 x+5)^{2}}\)
(D) \(-\frac{13}{(4 x+5)^{2}}\)
Answer:
(C) \(-\frac{5}{(4 x+5)^{2}}\)
Hint:
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 I Q3

Question 4.
If y = \(\frac{5 \sin x-2}{4 \sin x+3}\), then \(\frac{d y}{d x}\) =
(A) \(\frac{7 \cos x}{(4 \sin x+3)^{2}}\)
(B) \(\frac{23 \cos x}{(4 \sin x+3)^{2}}\)
(C) \(-\frac{7 \cos x}{(4 \sin x+3)^{2}}\)
(D) \(-\frac{15 \cos x}{(4 \sin x+3)^{2}}\)
Answer:
(B) \(\frac{23 \cos x}{(4 \sin x+3)^{2}}\)
Hint:
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 I Q4

Question 5.
Suppose f(x) is the derivative of g(x) and g(x) is the derivative of h(x).
If h(x) = a sin x + b cos x + c, then f(x) + h(x) =
(A) 0
(B) c
(C) -c
(D) -2(a sin x + b cos x)
Answer:
(B) c
Hint:
h(x) = a sin x + b cos x + c
Differentiating w.r.t. x, we get
h'(x) = a cos x – b sin x = g(x) …..[given]
Differentiating w.r.t. x, we get
g'(x) = -a sin x – b cos x = f(x) …..[given]
∴ f(x) + h(x) = -a sin x – b cos x + a sin x + b cos x + c
∴ f(x) + h(x) = c

Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9

Question 6.
If f(x) = 2x + 6, for 0 ≤ x ≤ 2
= ax2 + bx, for 2 < x ≤ 4
is differentiable at x = 2, then the values of a and b are
(A) a = \(-\frac{3}{2}\), b = 3
(B) a = \(\frac{3}{2}\), b = 8
(C) a = \(\frac{1}{2}\), b = 8
(D) a = \(-\frac{3}{2}\), b = 8
Answer:
(D) a = \(-\frac{3}{2}\), b = 8
Hint:
f(x) = 2x + 6, 0 ≤ x ≤ 2
= ax2 + bx, 2 < x ≤ 4
Lf'(2) = 2, Rf'(2) = 4a + b
Since f is differentiable at x = 2,
Lf'(2) = Rf'(2)
∴ 2 = 4a + b …..(i)
f is continuous at x = 2.
∴ \(\lim _{x \rightarrow 2^{+}} f(x)=f(2)=\lim _{x \rightarrow 2^{-}} f(x)\)
∴ 4a + 2b = 2(2) + 6
∴ 4a + 2b = 10
∴ 2a + b = 5 …..(ii)
Solving (i) and (ii), we get
a = \(-\frac{3}{2}\), b = 8

Question 7.
If f(x) = x2 + sin x + 1, for x ≤ 0
= x2 – 2x + 1, for x ≤ 0, then
(A) f is continuous at x = 0, but not differentiable at x = 0
(B) f is neither continuous nor differentiable at x = 0
(C) f is not continuous at x = 0, but differentiable at x = 0
(D) f is both continuous and differentiable at x = 0
Answer:
(A) f is continuous at x = 0, but not differentiable at x = 0
Hint:
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 I Q7

Question 8.
If f(x) = \(\frac{x^{50}}{50}+\frac{x^{49}}{49}+\frac{x^{48}}{48}+\ldots .+\frac{x^{2}}{2}+x+1\), then f'(1) =
(A) 48
(B) 49
(C) 50
(D) 51
Answer:
(C) 50
Hint:
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 I Q8

Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9

(II).

Question 1.
Determine whether the following function is differentiable at x = 3 where,
f(x) = x2 + 2, for x ≥ 3
= 6x – 7, for x < 3.
Solution:
f(x) = x2 + 2, x ≥ 3
= 6x – 7, x < 3
Differentiability at x = 3
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 II Q1
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 II Q1.1
Here, Lf'(3) = Rf'(3)
∴ f is differentiable at x = 3.

Question 2.
Find the values of p and q that make function f(x) differentiable everywhere on R.
f(x) = 3 – x, for x < 1
= px2 + qx, for x ≥ 1.
Solution:
f(x) is differentiable everywhere on R.
∴ f(x) is differentiable at x = 1.
∴ f(x) is continuous at x = 1.
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 II Q2
f(x) is differentiable at x = 1.
∴ Lf'(1) = Rf'(1)
∴ -1 = 2p + q …..(ii)
Subtracting (i) from (ii), we get
p = -3
Substituting p = -3 in (i), we get
p + q = 2
∴ -3 + q = 2
∴ q = 5

Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9

Question 3.
Determine the values of p and q that make the function f(x) differentiable on R where
f(x) = px3, for x < 2
= x2 + q, for x ≥ 2
Solution:
f(x) is differentiable on R.
∴ f(x) is differentiable at x = 2.
∴ f(x) is continuous at x = 2.
Continuity at x = 2:
f(x) is continuous at x = 2.
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 II Q3
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 II Q3.1
f(x) is differentiable at x = 2.
∴ Lf'(2) = Rf'(2)
∴ 12p = 4
∴ p = \(\frac{1}{3}\)
Substituting p = \(\frac{1}{3}\) in (i), we get
8(\(\frac{1}{3}\) – q = 4
∴ q = \(\frac{8}{3}\) – 4 = \(\frac{-4}{3}\)

Question 4.
Determine all real values of p and q that ensure the function
f(x) = px + q, for x ≤ 1
= tan(\(\frac{\pi x}{4}\)), for 1 < x < 2
is differentiable at x = 1.
Solution:
f(x) is differentiable at x = 1.
∴ f(x) is continuous at x = 1.
Continuity at x= 1:
f(x) is continuous at x = 1.
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 II Q4
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 II Q4.1

Question 5.
Discuss whether the function f(x) = |x + 1| + |x – 1| is differentiable ∀ x ∈ R.
Solution:
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 II Q5
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 II Q5.1
Here, Lf'(1) ≠ Rf'(1)
∴ f is not differentiable at x = 1.
∴ f is not differentiable at x = -1 and x = 1.
∴ f is not differentiable ∀ x ∈ R.

Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9

Question 6.
Test whether the function
f(x) = 2x – 3, for x ≥ 2
= x – 1, for x < 2
is differentiable at x = 2.
Solution:
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 II Q6

Question 7.
Test whether the function
f(x) = x2 + 1, for x ≥ 2
= 2x + 1, for x < 2
is differentiable at x = 2.
Solution:
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 II Q7
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 II Q7.1

Question 8.
Test whether the function
f(x) = 5x – 3x2, for x ≥ 1
= 3 – x, for x < 1
is differentiable at x = 1.
Solution:
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 II Q8
Here, Lf'(1) = Rf'(1)
∴ f(x) is differentiable at x = 1.

Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9

Question 9.
If f(2) = 4, f'(2) = 1, then find \(\lim _{x \rightarrow 2}\left[\frac{x f(2)-2 f(x)}{x-2}\right]\)
Solution:
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 II Q9

Question 10.
If y = \(\frac{\mathbf{e}^{x}}{\sqrt{x}}\), find \(\frac{d y}{d x}\) when x = 1.
Solution:
Maharashtra Board 11th Maths Solutions Chapter 9 Differentiation Miscellaneous Exercise 9 II Q10