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Chapter 16 Probability | class 11th | revision notes maths

Class 11 Maths Notes Chapter 16 Probability

Random Experiment
An experiment whose outcomes cannot be predicted or determined in advance is called a random experiment.

Outcome
A possible result of a random experiment is called its outcome.

Sample Space
A sample space is the set of all possible outcomes of an experiment.

Events
An event is a subset of a sample space associated with a random experiment.

Types of Events
Impossible and sure events: The empty set Φ and the sample space S describes events. Intact Φ is called the impossible event and S i.e. whole sample space is called sure event.

Simple or elementary event: Each outcome of a random experiment is called an elementary event.

Compound events: If an event has more than one outcome is called compound events.

Complementary events: Given an event A, the complement of A is the event consisting of all sample space outcomes that do not correspond to the occurrence of A.

Mutually Exclusive Events
Two events A and B of a sample space S are mutually exclusive if the occurrence of any one of them excludes the occurrence of the other event. Hence, the two events A and B cannot occur simultaneously and thus P(A ∩ B) = 0.

Exhaustive Events
If E1, E2,…….., En are n events of a sample space S and if E1 ∪ E2 ∪ E3 ∪………. ∪ En = S, then E1, E2,……… E3 are called exhaustive events.

Mutually Exclusive and Exhaustive Events
If E1, E2,…… En are n events of a sample space S and if
Ei ∩ Ej = Φ for every i ≠ j i.e. Ei and Ej are pairwise disjoint and E1 ∪ E2 ∪ E3 ∪………. ∪ En = S, then the events
E1, E2,………, En are called mutually exclusive and exhaustive events.

Probability Function
Let S = (w1, w2,…… wn) be the sample space associated with a random experiment. Then, a function p which assigns every event A ⊂ S to a unique non-negative real number P(A) is called the probability function.
It follows the axioms hold

  • 0 ≤ P(wi) ≤ 1 for each Wi ∈ S
  • P(S) = 1 i.e. P(w1) + P(w2) + P(w3) + … + P(wn) = 1
  • P(A) = ΣP(wi) for any event A containing elementary event wi.

Probability of an Event
If there are n elementary events associated with a random experiment and m of them are favorable to an event A, then the probability of occurrence of A is defined as
Probability Class 11 Notes Maths Chapter 16
The odd in favour of occurrence of the event A are defined by m : (n – m).
The odd against the occurrence of A are defined by n – m : m.
The probability of non-occurrence of A is given by P(A¯) = 1 – P(A).

Addition Rule of Probabilities
If A and B are two events associated with a random experiment, then
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Similarly, for three events A, B, and C, we have
P(A ∪ B ∪ C) = P(A) + P(B) + P(C) – P(A ∩ B) – P(A ∩ C) – P(B ∩ C) + P(A ∩ B ∩ C)

Note: If A andB are mutually exclusive events, then
P(A ∪ B) = P(A) + P(B)

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Chapter 15 Statistics | class 11th | revision notes maths

 Class 11 Maths Notes Chapter 15 Statistics

Measure of Dispersion
The dispersion is the measure of variations in the values of the variable. It measures the degree of scatteredness of the observation in a distribution around the central value.

Range
The measure of dispersion which is easiest to understand and easiest to calculate is the range.
Range is defined as the difference between two extreme observation of the distribution.
Range of distribution = Largest observation – Smallest observation.

Mean Deviation
Mean deviation for ungrouped data
For n observations x1, x2, x3,…, xn, the mean deviation about their mean x¯ is given by
Statistics Class 11 Notes Maths Chapter 15 1

Mean deviation about their median M is given by
Statistics Class 11 Notes Maths Chapter 15 2

Mean deviation for discrete frequency distribution
Let the given data consist of discrete observations x1, x2, x3,……., xn occurring with frequencies f1, f2, f3,……., fn respectively in case
Statistics Class 11 Notes Maths Chapter 15 3

Mean deviation about their Median M is given by
Statistics Class 11 Notes Maths Chapter 15 4

Mean deviation for continuous frequency distribution
Statistics Class 11 Notes Maths Chapter 15 5
where xi are the mid-points of the classes, x¯ and M are respectively, the mean and median of the distribution.

Variance
Variance is the arithmetic mean of the square of the deviation about mean x¯.
Let x1, x2, ……xn be n observations with x¯ as the mean, then the variance denoted by σ2, is given by
Statistics Class 11 Notes Maths Chapter 15 6

Standard deviation
If σ2 is the variance, then σ is called the standard deviation is given by
Statistics Class 11 Notes Maths Chapter 15 7

Standard deviation of a discrete frequency distribution is given by
Statistics Class 11 Notes Maths Chapter 15 8

Standard deviation of a continuous frequency distribution is given by
Statistics Class 11 Notes Maths Chapter 15 9

Coefficient of Variation
In order to compare two or more frequency distributions, we compare their coefficient of variations. The coefficient of variation is defined as
Statistics Class 11 Notes Maths Chapter 15 10

Note: The distribution having a greater coefficient of variation has more variability around the central value, then the distribution having a smaller value of the coefficient 0f variation.

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Chapter 14 Mathematical Reasoning | class 11th | revision notes maths

Class 11 Maths Notes Chapter 14 Mathematical Reasoning

Statements
A statement is a sentence which is either true or false, but not both simultaneously.

Note:
No sentence can be called a statement if

  • It is an exclamation.
  • It is an order or request.
  • It is a question.

Simple Statements
A statement is called simple if it cannot be broken down into two or more statements.

Compound Statements
A compound statement is the one which is made up of two or more simple statement.

Connectives
The words which combine or change simple statements to form new statements or compound statements are called connectives.

Conjunction
If two simple statements p and q are connected by the word ‘and’, then the resulting compound statement “p and q” is called a conjunction of p and q is written in symbolic form as “p ∧ q”.

Note:

  • The statement p ∧ q has the truth value T (true) whenever both p and q have the truth value T.
  • The statement p ∧ q has the truth value F (false) whenever either p or q or both have the truth value F.

Disjunction
If two simple statements p and q are connected by the word ‘or’, then the resulting compound statement “p or q” is called disjunction of p and q and is written in symbolic form as “p ∨ q”.

Note:

  • The statement p ∨ q has the truth value F whenever both p and q have the truth value F.
  • The statement p ∨ q has the truth value T whenever either p or q or both have the truth value T.

Negation
An assertion that a statement fails or denial of a statement is called the negation of the statement. The negation of a statement p in symbolic form is written as “~p”.

Note:

  • ~p has truth value T whenever p has truth value F.
  • ~p has truth value F whenever p has truth value T.

Negation of Conjunction
The negation of a conjunction p ∧ q is the disjunction of the negation of p and the negation of q.
Equivalently we write ~ (p ∧ q) = ~p ∨ ~q.

Negation of Disjunction
The negation of a disjunction p v q is the conjunction of negation of p and the negation of q.
Equivalently, we write ~(p ∨ q) = ~p ∧ ~q.

Negation of Negation
Negation of negation of a statement is the statement itself.
Equivalently, we write ~(~p) = p

The Conditional Statement
If p and q are any two statements, then the compound statement “if p then g” formed by joining p and q by a connective ‘if-then’ is called a conditional statement or an implication and is written in symbolically p → q or p ⇒ q, here p is called hypothesis (or antecedent) and q is called conclusion (or consequent) of the conditional statement (p ⇒ q).

Contrapositive of Conditional Statement
The statement “(~q) → (~p) ” is called the contrapositive of the statement p → q.

Converse of a Conditional Statement
The conditional statement “q → p” is called the converse of the conditional statement “p → q”.

Inverse of Conditional Statement
The Conditional statement “q → p” is called inverse of p → q.

The Biconditional Statement
If two statements p and q are connected by the connective ‘if and only if’, then the resulting compound statement “p if and only if q” is called biconditional of p and q and is written in symbolic form as p ⇔ q.

Quantifier
(i) For all or for every is called universal quantifier.
(ii) There exists is called existential quantifier.

Validity of Statements
A statement is said to valid or invalid according to as it is true or false.
If p and q are two mathematical statements, then the statement
(i) “p and q” is true if both p and q are true.
(ii) “p or g” is true if p is false
⇒ q is true orq is false ⇒ p is true.
(iii) “If p, then q” is true p is true ⇒ q is true
or
q is false
⇒ p is false
or
p is true and q is false less us to a contradiction,
(iv) “p if and only if q” is true, if
(a) p is true ⇒ q is true and
(b) q is true ⇒ p is true.

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Chapter 13 Limits and Derivatives | class 11th | revision notes maths

Class 11 Maths Notes Chapter 13 Limits and Derivatives

Limit
Let y = f(x) be a function of x. If at x = a, f(x) takes indeterminate form, then we consider the values of the function which is very near to a. If these value tend to a definite unique number as x tends to a, then the unique number so obtained is called the limit of f(x) at x = a and we write it as limx→af(x).

Left Hand and Right-Hand Limits
If values of the function at the point which are very near to a on the left tends to a definite unique number as x tends to a, then the unique number so obtained is called the left-hand limit of f(x) at x = a, we write it as
Limits and Derivatives Class 11 Notes Maths Chapter 13 1

Existence of Limit
Limits and Derivatives Class 11 Notes Maths Chapter 13 2

Some Properties of Limits
Let f and g be two functions such that both limx→af(x) and lim limx→ag(x) exists, then
Limits and Derivatives Class 11 Notes Maths Chapter 13 3

Some Standard Limits
Limits and Derivatives Class 11 Notes Maths Chapter 13 4
Limits and Derivatives Class 11 Notes Maths Chapter 13 5

Derivatives
Suppose f is a real-valued function, then
Limits and Derivatives Class 11 Notes Maths Chapter 13 6

Fundamental Derivative Rules of Function
Let f and g be two functions such that their derivatives are defined in a common domain, then
Limits and Derivatives Class 11 Notes Maths Chapter 13 7

Some Standard Derivatives
Limits and Derivatives Class 11 Notes Maths Chapter 13 8

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chapter 12 Introduction to Three Dimensional Geometry | class 11th | revision notes maths

Class 11 Maths Notes Chapter 12 Introduction to Three Dimensional Geometry

Coordinate Axes
In three dimensions, the coordinate axes of a rectangular cartesian coordinate system are three mutually perpendicular lines. These axes are called the X, Y and Z axes.

Coordinate Planes
The three planes determined by the pair of axes are the coordinate planes. These planes are called XY, YZ and ZX plane and they divide the space into eight regions known as octants.

Coordinates of a Point in Space
The coordinates of a point in the space are the perpendicular distances from P on three mutually perpendicular coordinate planes YZ, ZX, and XY respectively. The coordinates of a point P are written in the form of triplet like (x, y, z).
The coordinates of any point on

  • X-axis is of the form (x, 0,0)
  • Y-axis is of the form (0, y, 0)
  • Z-axis is of the form (0, 0, z)
  • XY-plane are of the form (x, y, 0)
  • YZ-plane is of the form (0, y, z)
  • ZX-plane are of the form (x, 0, z)

Distance Formula
The distance between two points P(x1, y1, z1) and Q(x2, y2, z2) is given by
Introduction to Three Dimensional Geometry Class 11 Notes Maths Chapter 12 1

The distance of a point P(x, y, z) from the origin O(0, 0, 0) is given by
OP = x2+y2+z2−−−−−−−−−−√

Section Formula
The coordinates of the point R which divides the line segment joining two points P(x1, y1, z1) and Q(x2, y2, z2) internally or externally in the ratio m : n are given by
Introduction to Three Dimensional Geometry Class 11 Notes Maths Chapter 12 2

The coordinates of the mid-point of the line segment joining two points P(x1, y1, z1) and Q(x2, y2, z2) are
Introduction to Three Dimensional Geometry Class 11 Notes Maths Chapter 12 3

The coordinates of the centroid of the triangle, whose vertices are (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) are
Introduction to Three Dimensional Geometry Class 11 Notes Maths Chapter 12 4

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Chapter 11 Conic Sections | class 11th | revision notes maths

Class 11 Maths Notes Chapter 11 Conic Sections

Circle
A circle is the set of all points in a plane, which are at a fixed distance from a fixed point in the plane. The fixed point is called the centre of the circle and the distance from centre to any point on the circle is called the radius of the circle.
The equation of a circle with radius r having centre (h, k) is given by (x – h)2 + (y – k)2 = r2.

The general equation of the circle is given by x2 + y2 + 2gx + 2fy + c = 0 , where, g, f and c are constants.

  • The centre of the circle is (-g, -f).
  • The radius of the circle is r = g2+f2−c−−−−−−−−−√

The general equation of the circle passing through origin is x2 + y2 + 2gx + 2fy = 0.

The parametric equation of the circle x2 + y2 = r2 are given by x = r cos θ, y = r sin θ, where θ is the parametre and the parametric equation of the circle (x – h)2 + (y – k)2 = r2 are given by x = h + r cos θ, y = k + r sin θ.

Note: The general equation of the circle involves three constants which implies that at least three conditions are required to determine a circle uniquely.

Parabola
A parabola is the set of points P whose distances from a fixed point F in the plane are equal to their distance from a fixed line l in the plane. The fixed point F is called focus and the fixed line l is the directrix of the parabola.

Main Facts About the Parabola

Forms of parabolay2= 4axy2 = -4axx2 = 4ayx2 = -4ay
Axis of parabolay = 0y = 0x = 0x = 0
Directrix of parabolax = -ax = ay = -ay = a
Vertex(0, 0)(0, 0)(0, 0)(0, 0)
Focus(a, 0)(-a, 0)(0, a)(0, -a)
Length of latus rectum4a4a4a4a
Focal length|x + a||x – a||y + a||y – a|

Ellipse
An ellipse is the set of all points in a plane such that the sum of whose distances from two fixed points is constant.
or
An ellipse is the set of all points in the plane whose distances from a fixed point in the plane bears a constant ratio, less than to their distance from a fixed point in the plane. The fixed point is called focus, the fixed line a directrix and the constant ratio(e) the eccentricity of the ellipse. We have two standard forms of ellipse i.e.
Conic Sections Class 11 Notes Maths Chapter 11

Main Facts about the Ellipse
Conic Sections Class 11 Notes Maths Chapter 11

Hyperbola
A hyperbola is the locus of a point in a plane which moves in such a way that the ratio of its distance from a fixed point in the same plane to its distance from a fixed line is always constant which is always greater than unity. The fixed point is called the focus, the fixed line is called the directrix and the constant ratio, generally denoted bye, is known as the eccentricity of the hyperbola.
We have two standard forms of hyperbola i.e.
Conic Sections Class 11 Notes Maths Chapter 11

Main Facts About Hyperbola
Conic Sections Class 11 Notes Maths Chapter 11

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Chapter 12 Buildings, Paintings and Books Class 6 Important Questions history

Class 6 History Chapter 12 Buildings, Paintings, and Books Important Questions

1. Fill in the blanks.

(i) _________ was a great astronomer.

(ii) Stories about gods and goddesses are found in the ________.

(iii) ________ is recognised as the author of the Sanskrit Ramayana.

(iv) ________ and ________ are two Tamil epics.

(v) Both the Puranas and the Mahabharata are supposed to have been compiled by ________.

(vi) Stories from the ______ were often shown on the railings of stupas and in paintings in places such as Ajanta.

Answer:
(i) Aryabhata
(ii) Puranas
(iii) Valmiki 
(iv) Silappadikaram and Manimekalai 
(v) Vyasa
(vi) Jatakas 

2. Write True/False against each of the following

(i) The Mahabharata is about a war fought between the Kauravas and Pandavas, who were cousins.

(ii) Bhagavad Gita was included in the Ramayana. 

(iii) Kannagi, the wife of Kovalan, mentioned in the Silappadikara, destroyed the city of Madurai. 

(iv) Devotees walked around the stupa, in an anticlockwise direction, as a mark of devotion. 

Answer:
(i) True
(ii) False
(iii) True
(iv) False

Answer the following questions

1. What does the word stupa mean?

Answer: The word stupa means a mound.

2. Who wrote Ramayana?

Answer: Valmiki wrote Ramayana.

3. Who composed Silapadikaram?

Answer: It was composed by a poet named Ilango.

4. What was the capital of Kosala?

Answer: Ayodhya was the capital of Kosala.

5. What are the two great sanskrit epics of India?

Answer: The two Sanskrit epics are Mahabharata and Ramayana.

6. Name two Tamil epics.

Answer: The two Tamil epics are Silappadikaram and Manimekalai.

7. What do you understand by Mandapa?

Answer: Mandapa is place in temples where people could assemble.

8. Who use to decide to build the stupas and temples?

Answer: Kings or queens decided to build these as it was an expensive affair.

9. What do you understand by the term Garbhagriha?

Answer: Garbhagriha is a place where the image of the deity is installed.

10. What is Pradakshina patha?

Answer: Pradakshina patha is a circular path around the stupa.

11. In which language were Puranas written?

Answer: The Puranas were written in simple Sanskrit verse.

12. Who wrote Meghaduta?

Answer: Kalidasa wrote Meghaduta.

13. Where and by whom paper was invented?

Answer: Paper was invented in China about 1900 years ago, by a man named Cai Lun.

14. What colors were used in Ajanta cave paintings?

Answer: The colours used in Ajanta cave paintings were made of plants and minerals.

15. Whose name is inscribed on the iron pillar at Mehrauli, Delhi?

Answer: There is an inscription on the pillar mentioning a ruler named Chandra, who probably belonged to the Gupta dynasty.

16. What is Bhitargaon Temple known for?

Answer: It is an early temple at Bhitargaon, Uttar Pradesh. This was built about 1500 years ago, and was made of baked brick and stone.

17. What is Shikhara?

Answer: A tower-like structure built on top of the garbhagriha, to mark this out as a sacred place is known as the shikhara.

18. What are the various kinds of stupas?

Answer: There are several kinds of stupas, round and tall, big and small, these have certain common features.

19. Who wrote Aryabhatiyam?

Answer: Aryabhata, a mathematician and astronomer, wrote a book in Sanskrit known as the Aryabhatiyam.

20. What are epics?

Answer: Epics are grand, long compositions, about heroic men and women, and include stories about gods.

21. What is the historical importance of Amaravati?

Answer: This was a place where a magnificent stupa once existed. Many of the stone carvings for decorating the stupa were made about 2000 years ago.

22. What is Manimekalai?

Answer: Manimekalai is a Tamil epic which was composed by Sattanar around 1400 years ago. This describes the story of the daughter of Kovalan and Madhavi.

23. Describe the poem Meghaduta written by Kalidasa?

Answer: Meghaduta is a poem written by Kalidasa, in which a monsoon cloud is imagined to be a messenger between lovers who are separated from one another.

24. What is stated in Aryabhatiyam?

Answer: In Aryabhatiyam, Aryabhata stated that day and night were caused by the rotation of the earth on its axis, even though it seems as if the sun is rising and setting every day.

25. Write about Monolithic temples.

Answer: There are Monolithic temples at Mahabalipuram. Each of these was carved out of a huge, single piece of stone. While brick structures are built up by adding layers of bricks from the bottom upwards.

26. Where are the stories told by ordinary people preserved?

Answer: Ordinary people also told stories, composed poems and songs, sang, danced, and performed plays. Some of these are preserved in collections of stories such as the Jatakas and the Panchatantra.

27. What do you know about ‘zero’?

Answer: While numerals had been used earlier, mathematicians in India now invented a special symbol for zero. This system of counting was adapted by the Arabs and then spread to Europe. It continues to be in use throughout the world.

28. What is relic casket?

Answer: Generally, there is a small box placed at the centre or heart of the stupa. This may contain bodily remains (such as teeth, bone or ashes) of the Buddha or his followers, or things they used, as well as precious stones, and coins. This box, known as a relic casket, was covered with earth.

29. What are Puranas?

Answer: Purana literally mean old. The Puranas contain stories about gods and goddesses, such as Vishnu, Shiva, Durga or Parvati. They also contain details on how they were to be worshipped. Besides, there are accounts about the creation of the world, and about kings.

30. What is Silappadikaram?

Answer: Silappadikaram is a Tamil epic. It was composed by a poet named Ilango, around 1800 years ago. It is the story of a merchant named Kovalan, who lived in Puhar and fell in love with a courtesan named Madhavi, neglecting his wife Kannagi.

31. How the technique of making paper spread around the world?

Answer: The technique of making paper was a closely guarded secret for centuries. It reached Korea about 1400 years ago, and spread to Japan soon after. It was known in Baghdad about 1800 years ago. From Baghdad it spread to Europe, Africa, and other parts of Asia including the subcontinent.

32. Discuss several stages in building a stupa or a temple.

Answer: First, good quality stone had to be found, quarried, and transported to the place that was often carefully chosen for the new building. Here, these rough blocks of stone had to be shaped and carved into pillars, and panels for walls, floors and ceilings. And then these had to be placed in precisely the right position.

33. What is the Mahabharata all about?

Answer: The Mahabharata is about a war fought between the Kauravas and Pandavas, who were cousins. This was a war to gain control of the throne of the Kurus, and their capital, Hastinapur. The story itself was an old one, but was written down in the form in which we know it today, about 1500 years ago. The Mahabharata are supposed to have been compiled by Vyasa. The Bhagavad Gita was also included in the Mahabharata.

34. What do you know about iron pillar at Mehrauli?

Answer: 

  • The iron pillar at Mehrauli, Delhi, is a remarkable example of the skill of Indian crafts persons.
  • It is made of iron, 7.2. m high, and weighs over 3 tonnes.
  • It was made about 1500 years ago. We know the date because there is an inscription on the pillar mentioning a ruler named Chandra, who probably belonged to the Gupta dynasty.

35. Who was Aryabhatta? What was he known for?

Answer: Aryabhata was a mathematician and astronomer, wrote a book in Sanskrit known as the Aryabhatiyam.

His contribution are:

  • He stated that day and night were caused by the rotation of the earth on its axis, even though it seems as if the sun is rising and setting every day.
  • He developed a scientific explanation for eclipses as well.
  • He also found a way of calculating the circumference of a circle, which is nearly as accurate as the formula we use today.

36. Highlight the chief features of stupa architecture.

Answer: Features of stupa architecture

  • Generally, there is a small box placed at the centre or heart of the stupa. This may contain bodily remains of the Buddha or his followers, or things they used, as well as precious stones, and coins.
  • Often, a path, known as the pradakshina patha, was laid around the stupa. This was surrounded with railings.
  • Entrance to the path was through gateways.
  • Both railings and gateways were often decorated with sculpture.


37. What are main features of the Hindu temples built around 1800 years ago?

Answer: Main features of the Hindu temples

  • Deities such as Vishnu, Shiva, and Durga were worshipped in these shrines. The most important part of the temple was the room known as the garbhagriha, where the image of the chief deity was placed.
  • It was here that priests performed religious rituals, and devotees offered worship to the deity.
  • Often, as at Bhitargaon, a tower, known as the shikhara, was built on top of the garbhagriha, to mark this out as a sacred place.
  • Most temples also had a space known as the mandapa. It was a hall where people could assemble.
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Chapter 11 New Empires and Kingdoms Class 6 Important Questions history

Class 6 History Chapter 11 New Empires and Kingdoms Important Questions

1. Fill in the blanks.

(i) We can learn about the Gupta rulers from their ________ and _______.

(ii) Kumara devi, mother of Samudragupta belonged to the ________.

(iii) _______ checked the advance of Harsha.

(iv) The _____ and ______ were the most important ruling dynasties in south India during this period.

Answer:
(i) inscriptions and coins
(ii) Lichchhavi gana
(iii) Pulakeshin II 
(iv) Pallavas and Chalukyas 

2. Write True/False against each of the following

(i) His brother-in-law was the ruler of Kanauj. 

(ii) Harishena composed a prashasti in praise of Gautamiputra Shri Satakarni. 

(iii) The rulers of Aryavarta brought tribute for Samudragupta. 

(iv) There were twelve rulers in Dakshinapatha. 

(v) Taxila and Madurai were important centres under the control of the Gupta rulers. 

(vi) Local assemblies functioned for several centuries in south India. 

Answer:
(i) True
(ii) False
(iii) False
(iv) True
(v) False
(vi) True

Answer the following questions

1. Whose court poet was Ravikriti?

Answer: Pulakeshin II

2. What do genealogies mean?

Answer: Genealogies mean lists of ancestors.

3. Name an Indian king who was known as ’musician king’.  

Answer: Samudragupta

4. In ancient period, who was called sarthavaha?

Answer: Leader of the merchant caravans was called as Sarthavaha.

5. Who was the best-known Chalukya ruler?

Answer: The best-known Chalukya ruler was Pulakeshin II.

6. In which language is Harshacharita written?

Answer: Harshacharita is written in Sanskrit.

7. What was the capital of Chalukyas?

Answer: Aihole was the capital of the Chalukyas.

8. Which ruler was described as equal as gods?

Answer: Samudragupta

9. How many rulers were there in dakshinapatha?

Answer: There were twelve rulers in dakshinapatha.

10. Who composed the Prashasti of Chalukya king Pulakeshin II?

Answer: Ravikirti the Prashasti of Chalukya king Pulakeshin II.

11. Who led an expedition to western India against Shakas?

Answer: Chandragupta II led an expedition to western India against Shakas.

12. Who wrote the biography of king Harshavardhana?

Answer: Banabhatta wrote the biography of king Harshavardhana.

13. What do you know about the mother of the greatest Gupta emperor Samudragupta?

Answer: His mother was Kumara devi and she belonged to the Lichchhavi gana.

14. What were the functions of assemblies in southern kingdom?

Answer: These assemblies looked after irrigation, agricultural operations, making roads, local temples, etc.

15. What was Ur?

Answer: The ur was a village assembly found in areas where the land owners were not brahmins.

16. Who was Fa Xian and what did he notice during his visit to India?

Answer: Fa Xian was a Chinese pilgrim. He noticed the plight of those who were treated as untouchables by the high and mighty.

17. Who was Banabhatta?

Answer: Banabhatta was the court poet of King Harshvardhana. He wrote Harshcharita, a biography of Harshavardhana.

18. Write about the kingdom of the Pallavas.

Answer: The kingdom of the Pallavas spread from the region around their capital, Kanchipuram, to the Kaveri delta.

19. What is a prashasti?

Answer: Inscription of a special kind is known as a prashasti, a Sanskrit word, meaning ‘in praise of’.

20. Mention three authors who wrote about Harshavardhana.

Answer: Ravikirti, Banabhatta and Xuan Zang were the three authors who wrote about Harshavardhana.

21. Write the meaning of kumar-amatya and sandhi-vigrahika.

Answer: kumar-amatya – an important minister
sandhi-vigrahika – a minister of war and peace.

22. Who was Harishena?

Answer: Harishena was a poet, a maha-danda-nayaka, a kumar-amatya and a sandhi-vigrahika.

23. Write a note on rulers of Dakshinapatha.

Answer: There were twelve rulers in dakshinapatha. They surrendered to Samudragupta after being defeated and he then allowed them to rule again.

24. Who was the first ruler of Gupta Dynasty who adopted the grand title of maharaj-adhiraja?

Answer: Chandragupta was the first ruler of the Gupta dynasty to adopt the grand title of maharaj-adhiraja.

25. What is Abhijana Shakuntalam?

Answer: Abhijnana Shakuntalam is the most famous play of Kalidasa. It is the story of the love between a king named Dushyanta and a young woman named Shakuntala.

26. How did poet praise the king Samudragupta?

Answer: The poet praised the king in glowing terms — as a warrior, as a king who won victories in battle, who was learned and the best of poets. He is also described as equal to the gods.

27. How did the Sabha function in ancient India?

Answer: Sabha was an assembly of brahmin land owners and this assembly functioned through subcommittees, which looked after irrigation, agricultural operations, making roads, local temples, etc.

28. How do we come to know about Harshavardhana?

Answer: We can find out about Harshavardhana from:

  • his biography, the Harshacharita written by his court poet, Banabhatta
  • a detailed account left by Xuan Zang, who spent a lot of time at Harsha’s court.

29. What changes do you find in the army at this time?

Answer: Some kings maintained a well-organised army. Besides, there were military leaders who provided the king with troops whenever he needed them. They were not paid regular salaries. Instead, some of them received grants of land. They collected revenue from the land and used this to maintain soldiers and horses, and provide equipment for warfare.

30. What do you know about Chalukyas kingdom?

Answer: Chalukyas was one of the most important ruling dynasties in south India. Chalukyas was centred around the Raichur Doab, between the rivers Krishna and Tungabhadra. Aihole, the capital of the Chalukyas, was an important trading centre. It developed as a religious centre, with a number of temples.

31. What were the new administrative arrangements during this period?

Answer: There were some new developments. Kings adopted a number of steps to win the support of men who were powerful, either economically, or socially, or because of their political and military strength. For instance:

  • Some important administrative posts were made hereditary.
  • Sometimes, one person held many offices.
  • Besides, important men probably had a say in local administration.

32. Write a note on Pulakeshin II.

Answer: The best-known Chalukya ruler was Pulakeshin II. We know about him from a prashasti, composed by his court poet Ravikirti. This tells us about his ancestors, who are traced back through four generations from father to son. Pulakeshin evidently got the kingdom from his uncle. According to Ravikirti, he led expeditions along both the west and the east coasts. Besides, he checked the advance of Harsha.

33. Write a short note on Harshavardhana?

Answer: Harsha was not the eldest son of his father, but became king of Thanesar after both his father and elder brother died. His brother-in-law was the ruler of Kanauj and he was killed by the ruler of Bengal. Harsha took over the kingdom of Kanauj, and then led an army against the ruler of Bengal. Although he was successful in the east, and conquered both Magadha and Bengal, he was not as successful elsewhere. He tried to cross the Narmada to march into the Deccan, but was stopped by a ruler belonging to the Chalukya dynasty, Pulakeshin II.

34. Write about assemblies in the southern kingdoms.

Answer: The inscriptions of the Pallavas mention a number of local assemblies. These included the sabha, which was an assembly of brahmin land owners. This assembly functioned through subcommittees, which looked after irrigation, agricultural operations, making roads, local temples, etc. The ur was a village assembly found in areas where the land owners were not brahmins. And the nagaram was an organisation of merchants. It is likely that these assemblies were controlled by rich and powerful landowners and merchants. Many of these local assemblies continued to function for centuries.

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Chapter 10 Traders, Kings and Pilgrims Class 6 Important Questions history

Class 6 History Chapter 10 Traders, Kings and Pilgrims Important Questions

1. Fill in the blanks.

(i) Puhar was an important port on the _________.

(ii) Around 200 years later a dynasty known as the Satavahanas became powerful in ________.

(iii) South India was famous for ___________.

(iv) Fa Xian began his journey back home from __________.

(v) Statues of the Buddha were made in ______ and ______.

(vi) About 2000 years ago, wearing _______ became the fashion amongst rulers and rich people in Rome.

Answer:
(i) east coast
(ii) western India
(iii) gold, spices and precious stones
(iv) Bengal
(v) Mathura and Taxila
(vi) silk 

2. Write True/False against each of the following statements

(i) Amongst the river valleys, that of the Kaveri is the most fertile. 

(ii) Only rich, belonging to the so-called ‘high’ castes, man could follow the path of Bhakti. 

(iii) Nalanda, (Bihar) was the most famous Buddhist monastery of the period. 

(iv) Muvendar is a Sanskrit word meaning three chiefs.

(v) Sometimes, Chinese rulers sent gifts of silk to rulers in Iran and west Asia. 

Satavahanas became powerful in eastern India. 

(vi) At Taxila a new form of Buddhist art influenced by the Greek style was developed.

Answer:
(i) True
(ii) False
(iii) True
(iv) False
(v) True
(vi) False
(vii) True

Answer the following questions

1. Name the ruler who controlled silk route effectively.

Answer: Kushanas

2. Where is the site of Eran located?

Answer: Madhya Pradesh

3. Which was the capital kingdom of Pandyas?

Answer: Madurai was the capital of the Pandyas.

4. Where was Jesus Christ born?

Answer: Jesus Christ was born in Bethlehem.

5. Which port was under the cholas?

Answer: Puhar or Kaveripattinam port was under the Cholas.

6. What is Buddhacharita?

Answer: Buddhacharita is a biography of the Buddha.

7. Which Kushana ruler organized a Buddhist council?

Answer: The most famous Kushana ruler, Kanishka organized a Buddhist council.

8. Where can evidences of trade be found?

Answer: Evidence of trade can be found in the Sangam poems.

9. Which is the oldest form of Buddhism?

Answer: Theravada is believed to be the oldest form of Buddhism.

10. What was the most valued export commodity to the Roman Empire from India?

Answer: Pepper

11. Name the three chiefs mentioned in Sangam poems.

Answer: Cholas, Cheras and Pandyas

12. Which form of Buddhism was popular in South-Eastern countries?

Answer: Theravada Buddhism

13. Where the philosophy of the Bodhisattvas was most popular?

Answer: China

14. Where we find discussions between Krishna and Arjuna?

Answer: Bhagavad Gita

15. From which word the term Bhakti has been derived.

Answer: Bhakti comes from the Sanskrit term bhaj meaning ‘to divide or share.’

16. In which sacred book the idea of bhakti presented?

Answer: The idea of Bhakti is present in the Bhagavad Gita, a sacred book of the Hindus, which is included in the Mahabharata.

17. What was South India famous for?

Answer: South India was famous for gold, spices, especially pepper, and precious stones.

18. Name the most important ruler of the Satavahanas.  

Answer: The most important ruler of the Satavahanas was Gautamiputra Shri Satakarni.

19. Name the three powerful ruling families of South India.

Answer: The three powerful ruling families of South India were the Cholas, Cheras, and Pandyas.

20. What were items given by chiefs to the poets as rewards?

Answer: Chiefs rewarded them with precious stones, gold, horses, elephants, chariots, and fine cloth.

21. Who were the earliest rulers of the subcontinent to issue gold coins?

Answer: The Kushanas were amongst the earliest rulers of the subcontinent to issue gold coins.

22. How do we come to know about the dangers faced by the piligrims in their travels?

Answer: Chinese Buddhists pilgrims wrote about the dangers they encountered on their travels.

23. Who were known as lords of the dakshinapatha?

Answer: Gautamiputra Shri Satakarni and other Satavahana rulers were known as lords of the dakshinapatha.

24. What makes silk highly valued fabric in most societies?

Answer: The rich, glossy colours of silk, as well as its smooth texture, make it a highly valued fabric in most societies.

25. Discuss the reasons why the Chinese pilgrims came to India.

Answer: They came to visit places associated with the life of the Buddha as well as famous monasteries.

26. Who was Appar? Which community he belonged to?

Answer: Appar was Tamil poet-saint and a devotee of Shiva. He belonged to vellala community.

27. Who were the rulers, who ruled over central Asia and north-west India around 2000 years ago?

Answer: Kushanas were the rulers, who ruled over central Asia and north-west India around 2000 years ago.

28. Name the regions where Bodhisattvas became very popular.

Answer: The worship of Bodhisattvas became very popular, and spread throughout Central Asia, China, and later to Korea and Japan.

29. How did the chiefs use the tribute that they collected from neighbouring areas?

Answer: They kept some of the wealth and distributed the rest amongst their supporters, including members of their family, soldiers, and poets.

30. What do you know about Syrian Christians?

Answer: The Christians of Kerala, known as Syrian Christians because they probably came from West Asia, are amongst the oldest Christian communities in the world.

31. Why do you think ordinary people were attracted to Bhakti?

Answer: Ordinary people were attracted to Bhakti because it emphasised devotion and individual worship of a god or goddess, rather than the performance of elaborate sacrifices.

32. Making silk is a complicated process. Why?

Answer: Making silk is a complicated process because raw silk has to be extracted from the cocoons of silk worms, spun into thread and then woven into cloth.

33. From where is the word ‘Hindu’ derived?

Answer: The word ‘Hindu’, like the term ‘India’ is derived from the river Indus. It was used by Arabs and Iranians to refer to people who lived to the east of the river, and to their cultural practices, including religious beliefs.

34. Why did kings want to control the Silk Route?

Answer: The kings want to control the Silk Route because they could benefit from taxes, tributes and gifts that were brought by traders travelling along the route.

35. Who was Kanishka?

Answer: The most famous Kushana ruler was Kanishka, who ruled around 1900 years ago. He organized a Buddhist council, where scholars met and discussed important matters.

36. Who were bodhisattvas in Buddhism?

Answer: Bodhisattvas were supposed to be persons who had attained enlightenment. Once they attained enlightenment, they could live in complete  isolation and meditate in peace.

37. What was emphasized under the system of bhakti?

Answer: Those who followed the system of Bhakti emphasised devotion and individual worship of a god or goddess, rather than the performance of elaborate sacrifices.

38. Who was Gautamiputra Shri Satakarni? How did we come to know about him?

Answer: The most important ruler of the Satavahanas was Gautamiputra Shri Satakarni. We know about him from an inscription composed by his mother, Gautami Balashri.

39. What is Bhakti? Who could follow Bhakti?

Answer: Bhakti is generally understood as a person’s devotion to his or her chosen deity. Anybody, whether rich or poor, belonging to the so-called ‘high’ or ‘low’ castes, man or woman, could follow the path of Bhakti.

40. Why was silk so expensive?

Answer: It was very expensive, as it had to be brought all the way from China, along dangerous roads, through mountains and deserts. People living along the route often demanded payments for allowing traders to pass through.

41. What were the main features of Bhakti?

Answer: 

  • Those who followed the system of Bhakti emphasised devotion and individual worship of a god or goddess, rather than the performance of elaborate sacrifices.
  • According to this system of belief, if a devotee worships the chosen deity with a pure heart, the deity will appear in the form in which he or she may desire.

42. Write about the Chinese Buddhist pilgrims.

Answer: The best-known of these are the Chinese Buddhist pilgrims, Fa Xian, who came to the subcontinent about 1600 years ago, Xuan Zang (who came around 1400 years ago) and I-Qing, who came about 50 years after Xuan Zang. They came to visit places associated with the life of the Buddha as well as famous monasteries. Each of these pilgrims left an account of his journey.

43. What kinds of evidence do historians use to find out about trade and trade routes?

Answer: Fine pottery, especially bowls and plates, were found from several archaeological sites throughout the subcontinent. Traders may have carried them from the places where they were made, to sell them at other places.

South India was famous for gold, spices, especially pepper, and precious stones. Pepper was particularly valued in the Roman Empire, so much so that it was known as black gold. So, traders carried many of these goods to Rome in ships, across the sea, and by land in caravans. There must have been quite a lot of trade as many Roman gold coins have been found in south India.

44. How did Buddhism grow during Kushana dynasty?

Answer: 

  • The most famous Kushana ruler was Kanishka, who ruled around 1900 years ago.
  • He organized a Buddhist council, where scholars met and discussed important matters.
  • Ashvaghosha, a poet who composed a biography of the Buddha, the Buddhacharita, lived in his court.
  • A new form of Buddhism, known as Mahayana Buddhism, developed.
  • The worship of Bodhisattvas became very popular, and spread throughout Central Asia, China, and later to Korea and Japan.
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Chapter 9 Vital Villages, Thriving Towns Class 6 Important Questions history

Class 6 History Chapter 9 Vital Villages, Thriving Towns Important Questions

1. Fill in the blanks.

(i) _________ was a word used for large landowners in Tamil.

(ii) The gramabhojaka often got his land cultivated by the _______ and ________.

(iii) Ploughmen were known as ________ in Tamil.

(iv) Most grihapatis were _______ landowners.

(v) Punch marked coins were made of _________.

(vi) _________ are tall double-handled jars that contained liquids such as wine or oil.

Answer:
(i) Vellalar
(ii) slaves and hired workers
(iii) uzhavar
(iv) smaller
(v) silver
(vi) Amphorae 

2. Write True/False against each of the following statement

(i) Grama Bhojaka also functioned as a judge, and sometimes as a policeman. 

(ii) Mathura was an important centre for the worship of Lord Shiva. 

(iii) The Tamil terms are found in Sangam literature. 

(iv) Ring wells were used for bathing. 

(v) Stamped red-glazed pottery, known as Arretine Ware.

Answer:
(i) True
(ii) False
(iii) True
(iv) False
(v) True

Answer the following questions

1. When did the use of iron begin in the subcontinent?

Answer: Use of iron in the subcontinent began about 3000 years ago.

2. What does vellalar mean?

Answer: In the Tamil region, large landowners were known as vellalar.

3. Why were Varanasi and Madurai famous?

Answer: Both were famous centres for manufacturing of cloth.

4. Where were some of the largest collections of iron tools found?

Answer: These were found in the megalithic burials.

5. How wealth is measured during early times?

Answer: Wealth is measured in terms of coins.

6. What were Shrenis?

Answer: Many crafts persons and merchants formed associations known as shrenis.

7. How did Dasa Karmakara earn a living?

Answer: Dasa Karmakara had to earn a living working on the fields owned by others.

8. Who was called Grama Bhojaka?

Answer: In the northern part of the country, the village headman was known as the grama bhojaka.

9. Who was Dasa Karmakara?

Answer: There were men and women who did not own land were known as the dasa karmakara.

10. What is Sangam literature?

Answer: Some of the earliest works in Tamil, known as Sangam literature, were composed around 2300 years ago.

11. What was Arikamedu during ancient India?

Answer: Between 2200 and 1900 years ago, Arikamedu was a coastal settlement where ships unloaded goods from distant lands.

12. What were aqueducts?

Answer: Huge aqueducts were the channels to supply water which were built to bring water to the city for the baths, fountains and toilets.

 13. What do you understand by Jatakas?

Answer: These were stories that were probably composed by ordinary people, and then written down and preserved by Buddhist monks.

14. What are ring wells?

Answer: In many cities, archaeologists have found rows of pots, or ceramic rings arranged one on top of the other. These are known as ring wells.

15. Make a list of the occupations of people who lived in Mathura.

Answer: The main occupations of the people were goldsmiths, blacksmiths, weavers, basket makers, garland makers, perfumers.

16. What were ring wells used for?

Answer: These seem to have been used as toilets in some cases, and as drains and garbage dumps. These ring wells are usually found in individual houses.

17. Why the earliest coins which were in use for about 500 years were called punch marked coins?

Answer: They have been given this name because the designs were punched on to the metal — silver or copper.

18. Why some of the earliest works in Tamil, known as Sangam literature?

Answer: These texts were called Sangam because they were supposed to have been composed and compiled in assemblies (known as sangams) of poets that were held in the city of Madurai.

19. List all the women who could be employed by the superintendent.

Answer: Widows, young women who are differently abled, nuns, mothers of courtesans, retired women servants of the king, women who have retired from service in temples, may be employed by the superintendent.

20. What kinds of inscription have been found in Mathura?

Answer: Generally, these are short inscriptions, recording gifts made by men (and sometimes women) to monasteries and shrines. These were made by kings and queens, officers, merchants, and crafts persons who lived in the city.

21. Who lived in the village?

Answer: There were at least three different kinds of people living in most villages in the southern and northern parts of the subcontinent. In the Tamil region, large landowners were known as vellalar, ordinary ploughmen were known as uzhavar, and landless labourers, including slaves, were known as kadaisiyar and adimai.

22. What are the ways of finding out about early cities?

Answer: Ways of finding out about early cities are:

  • Sculptors carved scenes depicting peoples’ lives in towns and villages, as well as in the forest.
  • Archaeologists’ findings such as found rows of pots, or ceramic rings arranged one on top of the other.
  • Accounts of sailors and travellers who visited them.

23. What has been found in the archaeological excavations at Arikamedu?

Answer: Findings in the archaeological excavations at Arikamedu were:

  • A massive brick structure, which may have been a warehouse, was found at the site.
  • Other finds include pottery from the Mediterranean region, such as amphorae and stamped red-glazed pottery, known as Arretine Ware, which was named after a city in Italy.
  • Roman lamps, glassware and gems have also been found at the site.

24. What were the functions performed by Shrenis?

Answer: Functions performed by Shrenis were:

  • These shrenis of crafts persons provided training, procured raw material, and distributed the finished product.
  • Then shrenis of merchants organised the trade.
  • Shrenis also served as banks, where rich men and women deposited money. This was invested, and part of the interest was returned or used to support religious institutions such as monasteries.

25. Mathura has been an important settlement for more than 2500 years. Give reasons.

Answer: 

  • It was important because it was located at the cross roads of two major routes of travel and trade – from the northwest to the east and from north to south.
  • There were fortifications around the city, and several shrines.
  • Farmers and herders from adjoining areas provided food for people in the city.
  • Mathura was also a centre where some extremely fine sculpture was produced.

26. Write a short note on Grama Bhojaka.

Answer: 

  • In the northern part of the country, the village headman was known as the grama bhojaka.
  • Usually, men from the same family held the position for generations. In other words, the post was hereditary.
  • The grama bhojaka was often the largest landowner.
  • Generally, he had slaves and hired workers to cultivate the land.
  • Besides, as he was powerful, the king often used him to collect taxes from the village.
  • He also functioned as a judge, and sometimes as a policeman.
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