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Trigonometrical Identities Part 1 - Lecture 25
Trigonometrical Identities : Here we will discuss about some Trigonometrical Identities and their uses to prove another identities like :
(i) sin² A+ cos² A = 1
(ii) 1+ tan² A = sec² A
(iii) 1+ cot2 A = cosec² A
Trigonometrical Ratios of Complementary Angles like:
For an acute angle A,
(a) sin (90° - A) = cos A
(b) cos (90°- A) = sin A
(c) tan (90°- A) = cot A
(d) cot (90°- A) = tan A
(e) sec (90°- A) = cosec A
(f) cosec (90° - A) = sec A
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27min
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Trigonometrical Identities Part 2 - Lecture 26
Trigonometrical Identities : Here we will discuss about some Trigonometrical Identities and their uses to prove another identities like :
(i) sin² A+ cos² A = 1
(ii) 1+ tan² A = sec² A
(iii) 1+ cot2 A = cosec² A
Trigonometrical Ratios of Complementary Angles like:
For an acute angle A,
(a) sin (90° - A) = cos A
(b) cos (90°- A) = sin A
(c) tan (90°- A) = cot A
(d) cot (90°- A) = tan A
(e) sec (90°- A) = cosec A
(f) cosec (90° - A) = sec A
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29min
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Trigonometrical Identities Part 3 - Lecture 27
Trigonometrical Identities : Here we will discuss about some Trigonometrical Identities and their uses to prove another identities like :
(i) sin² A+ cos² A = 1
(ii) 1+ tan² A = sec² A
(iii) 1+ cot2 A = cosec² A
Trigonometrical Ratios of Complementary Angles like:
For an acute angle A,
(a) sin (90° - A) = cos A
(b) cos (90°- A) = sin A
(c) tan (90°- A) = cot A
(d) cot (90°- A) = tan A
(e) sec (90°- A) = cosec A
(f) cosec (90° - A) = sec A
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25min
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Trigonometrical Identities Part 4 - Lecture 28
Trigonometrical Identities : Here we will discuss about some Trigonometrical Identities and their uses to prove another identities like :
(i) sin² A+ cos² A = 1
(ii) 1+ tan² A = sec² A
(iii) 1+ cot2 A = cosec² A
Trigonometrical Ratios of Complementary Angles like:
For an acute angle A,
(a) sin (90° - A) = cos A
(b) cos (90°- A) = sin A
(c) tan (90°- A) = cot A
(d) cot (90°- A) = tan A
(e) sec (90°- A) = cosec A
(f) cosec (90° - A) = sec A
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13min
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Trigonometrical Identities Part 5 - Lecture 29
Trigonometrical Identities : Here we will discuss about some Trigonometrical Identities and their uses to prove another identities like :
(i) sin² A+ cos² A = 1
(ii) 1+ tan² A = sec² A
(iii) 1+ cot2 A = cosec² A
Trigonometrical Ratios of Complementary Angles like:
For an acute angle A,
(a) sin (90° - A) = cos A
(b) cos (90°- A) = sin A
(c) tan (90°- A) = cot A
(d) cot (90°- A) = tan A
(e) sec (90°- A) = cosec A
(f) cosec (90° - A) = sec A
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21min
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Heights & Distances Part 1 - Lecture 30
Heights & Distances : Here we will use Trigonometrical Ratios with the help of angle of elevation and angle of depression for find height, distance , speed etc. according to given conditions or as per requirement of problems.
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37min
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Heights & Distances Part 2 - Lecture 31
Heights & Distances : Here we will use Trigonometrical Ratios with the help of angle of elevation and angle of depression for find height, distance , speed etc. according to given conditions or as per requirement of problems.
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28min
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Heights & Distance Part 3 - Lecture 32
Heights & Distances : Here we will use Trigonometrical Ratios with the help of angle of elevation and angle of depression for find height, distance , speed etc. according to given conditions or as per requirement of problems.
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35min
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Graphical Representation - Lecture 33
Here in Graphical Representation The statistical data can be represented by diagram, chart, etc.,
so that the significance attached to these data may immediately be grasped. But the diagrams should be neatly and accurately drawn.
Out of several types of diagrams, charts, etc., we shall be studying only the following three types of diagrams:
1. Histogram
2. Ogive (cumulative frequency curve)
3. Frequency polygon.
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42min
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Reflection Part 1 - Lecture 1
Here in this chapter we will learn how to do reflection of a point , more than two points, lines ,figures about co – ordinate axis , origin , invariant points with and without graph papers and finding their areas
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19min
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Measures of Central Tendency Part 1 - Lecture 34
The numerical expressions which represent the characteristics of a group are called Measures of Central Tendency (or, Averages). An average which is used to represent a whole series should neither have the lowest value nor the highest value in the group, but a value somewhere between two limits, possibly in the centre, where most of the items of the group cluster.
There are many types of statistical averages, out of them the following averages will be studied in this chapter.
1. Arithmetic Average or Mean :
The arithmetic mean of a set of numbers is obtained by dividing the sum of numbers of the set by the number of numbers.
Arithmetic Mean of Tabulated Data :
For a given discrete frequency distribution, the arithmetic mean can be using any one of the following three methods:
1. Direct method.
2. Short-cut method.
3. Step-deviation method.
2. Median: Median is the value of middle term of a set of variables the variables of the set are arranged in ascending or descending order.
1 Median for Raw Data
2 Median of Tabulated Data
3 Median for Grouped Data both Continuous and Discontinuous by using Ogive
4 Quartiles (Lower ,upper ,Inter)
3. Mode: Mode is the value which occurs most frequently in a set of observations. It is the point of maximum frequency.
1. Mode for raw data
2. Mode for tabulated data
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28min
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Reflection Part 2 - Lecture 2
Here in this chapter we will learn how to do reflection of a point , more than two points, lines ,figures about co – ordinate axis , origin , invariant points with and without graph papers and finding their areas
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23min
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Section & Mid-Point Formula Part 1 - Lecture 3
Here in this chapter we will discuss about Section Formula when on point will given in ratio then we can find the co – ordinates of other point
And also we will derive midpoint formula and some special cases like in case of points of Trisection , Centriod of Triangle and finding co-ordinates of vertices and point of intersection of their diagonals by using their properties
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19min
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Section & Mid-Point Formula Part 2 - Lecture 4
Here in this chapter we will discuss about Section Formula when on point will given in ratio then we can find the co – ordinates of other point
And also we will derive midpoint formula and some special cases like in case of points of Trisection , Centriod of Triangle and finding co-ordinates of vertices and point of intersection of their diagonals by using their properties
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17min
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Equation of a Line Part 1 - Lecture 5
Here in this chapter we will discuss about different concepts about equation of line like
How we can check given point will lie on line or not
How we can find inclination of line and finding slope when two lines are parallel, two lines are perpendicular, slope of a straight line passing through two given points etc.
Finding Equation of Line under different conditions:
- Slope intercept Form
- Point Slope Form
- Two point Form
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16min
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Equation of a Line Part 2 - Lecture 6
Here in this chapter we will discuss about different concepts about equation of line like
How we can check given point will lie on line or not
How we can find inclination of line and finding slope when two lines are parallel, two lines are perpendicular, slope of a straight line passing through two given points etc.
Finding Equation of Line under different conditions:
- Slope intercept Form
- Point Slope Form
- Two point Form
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20min
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Equation of a Line Part 3 - Lecture 7
Here in this chapter we will discuss about different concepts about equation of line like
How we can check given point will lie on line or not
How we can find inclination of line and finding slope when two lines are parallel, two lines are perpendicular, slope of a straight line passing through two given points etc.
Finding Equation of Line under different conditions:
- Slope intercept Form
- Point Slope Form
- Two point Form
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14min
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Equation of a Line Part 4 - Lecture 8
Here in this chapter we will discuss about different concepts about equation of line like
How we can check given point will lie on line or not
How we can find inclination of line and finding slope when two lines are parallel, two lines are perpendicular, slope of a straight line passing through two given points etc.
Finding Equation of Line under different conditions:
- Slope intercept Form
- Point Slope Form
- Two point Form
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19min
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Equation of a Line Part 5 - Lecture 9
Here in this chapter we will discuss about different concepts about equation of line like
How we can check given point will lie on line or not
How we can find inclination of line and finding slope when two lines are parallel, two lines are perpendicular, slope of a straight line passing through two given points etc.
Finding Equation of Line under different conditions:
- Slope intercept Form
- Point Slope Form
- Two point Form
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17min
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Equation of a Line Part 6 - Lecture 10
Here in this chapter we will discuss about different concepts about equation of line like
How we can check given point will lie on line or not
How we can find inclination of line and finding slope when two lines are parallel, two lines are perpendicular, slope of a straight line passing through two given points etc.
Finding Equation of Line under different conditions:
- Slope intercept Form
- Point Slope Form
- Two point Form
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15min
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Circles Part 1 - Lecture 11
Here in this chapter, we will discuss about different theorems and their applicability of Circles like:
- Equal chords subtends equal angles at centre;
- Chords of circle equidistant from centre are equal ;
- The angle which an arc subtends at the centre is double that which it subtends at any point on the remaining part of the circumference;
- Angle in same segment of a circle are equal etc.
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13min
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Circles Part 2 - Lecture 12
Here in this chapter, we will discuss about different theorems and their applicability of Circles like:
- Equal chords subtends equal angles at centre;
- Chords of circle equidistant from centre are equal ;
- The angle which an arc subtends at the centre is double that which it subtends at any point on the remaining part of the circumference;
- Angle in same segment of a circle are equal etc.
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20min
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Circles Part 3 - Lecture 13
Here in this chapter, we will discuss about different theorems and their applicability of Circles like:
- Equal chords subtends equal angles at centre;
- Chords of circle equidistant from centre are equal ;
- The angle which an arc subtends at the centre is double that which it subtends at any point on the remaining part of the circumference;
- Angle in same segment of a circle are equal etc.
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22min
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Circles Part 4 - Lecture 14
Here in this chapter, we will discuss about different theorems and their applicability of Circles like:
- Equal chords subtends equal angles at centre;
- Chords of circle equidistant from centre are equal ;
- The angle which an arc subtends at the centre is double that which it subtends at any point on the remaining part of the circumference;
- Angle in same segment of a circle are equal etc.
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26min
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Circles Part 5 - Lecture 15
Here in this chapter, we will discuss about different theorems and their applicability of Circles like:
- Equal chords subtends equal angles at centre;
- Chords of circle equidistant from centre are equal ;
- The angle which an arc subtends at the centre is double that which it subtends at any point on the remaining part of the circumference;
- Angle in same segment of a circle are equal etc.
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27min
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Circles Part 6 - Lecture 16
Here in this chapter, we will discuss about different theorems and their applicability of Circles like:
- Equal chords subtends equal angles at centre;
- Chords of circle equidistant from centre are equal ;
- The angle which an arc subtends at the centre is double that which it subtends at any point on the remaining part of the circumference;
- Angle in same segment of a circle are equal etc.
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23min
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Circles Part 7 - Lecture 17
Here in this chapter, we will discuss about different theorems and their applicability of Circles like:
- Equal chords subtends equal angles at centre;
- Chords of circle equidistant from centre are equal ;
- The angle which an arc subtends at the centre is double that which it subtends at any point on the remaining part of the circumference;
- Angle in same segment of a circle are equal etc.
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21min
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Circles Part 8 - Lecture 18
Here in this chapter, we will discuss about different theorems and their applicability of Circles like:
- Equal chords subtends equal angles at centre;
- Chords of circle equidistant from centre are equal ;
- The angle which an arc subtends at the centre is double that which it subtends at any point on the remaining part of the circumference;
- Angle in same segment of a circle are equal etc.
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18min
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Circles Part 9 - Lecture 19
Here in this chapter, we will discuss about different theorems and their applicability of Circles like:
- Equal chords subtends equal angles at centre;
- Chords of circle equidistant from centre are equal ;
- The angle which an arc subtends at the centre is double that which it subtends at any point on the remaining part of the circumference;
- Angle in same segment of a circle are equal etc.
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14min
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Circles Part 10 - Lecture 20
Here in this chapter, we will discuss about different theorems and their applicability of Circles like:
- Equal chords subtends equal angles at centre;
- Chords of circle equidistant from centre are equal ;
- The angle which an arc subtends at the centre is double that which it subtends at any point on the remaining part of the circumference;
- Angle in same segment of a circle are equal etc.
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18min
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Circles Part 11 - Lecture 21
Here in this chapter, we will discuss about different theorems and their applicability of Circles like:
- Equal chords subtends equal angles at centre;
- Chords of circle equidistant from centre are equal ;
- The angle which an arc subtends at the centre is double that which it subtends at any point on the remaining part of the circumference;
- Angle in same segment of a circle are equal etc.
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18min
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Tangent & Intersecting Chords Part 1 - Lecture 22
Tangent & Intersecting Chords : Here in this Chapter we will discuss about tangents and its different theorems like :
- The tangent at any point of a circle and the radius through this point perpendicular to each other.
- No tangent can be drawn to a circle through a point inside the circle.
- One and only one tangent can be drawn through a point on the circumference of the circle.
- Only two tangents can be drawn to a circle through a point outside the circle.
- Corollary: If two tangents are drawn to a circle from an exterior point (the point which lies outside the circle) :
(a) the tangents are equal in length
(b) the tangents subtend equal angles at the centre of the circle and
(c) the tangents are equally inclined to the line joining the point and the centre of the circle.
- If two chords of a circle intersect internally or externally then the product of the lengths of their segments is equal etc. These types of theorem and their applicability to find unknown values will also be discussed.
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16min
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Tangent & Intersecting Chords Part 2 - Lecture 23
Tangent & Intersecting Chords : Here in this Chapter we will discuss about tangents and its different theorems like :
- The tangent at any point of a circle and the radius through this point perpendicular to each other.
- No tangent can be drawn to a circle through a point inside the circle.
- One and only one tangent can be drawn through a point on the circumference of the circle.
- Only two tangents can be drawn to a circle through a point outside the circle.
- Corollary: If two tangents are drawn to a circle from an exterior point (the point which lies outside the circle) :
(a) the tangents are equal in length
(b) the tangents subtend equal angles at the centre of the circle and
(c) the tangents are equally inclined to the line joining the point and the centre of the circle.
- If two chords of a circle intersect internally or externally then the product of the lengths of their segments is equal etc. These types of theorem and their applicability to find unknown values will also be discussed.
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25min
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Tangent & Intersecting Chords Part 3 - Lecture 24
Tangent & Intersecting Chords : Here in this Chapter we will discuss about tangents and its different theorems like :
- The tangent at any point of a circle and the radius through this point perpendicular to each other.
- No tangent can be drawn to a circle through a point inside the circle.
- One and only one tangent can be drawn through a point on the circumference of the circle.
- Only two tangents can be drawn to a circle through a point outside the circle.
- Corollary: If two tangents are drawn to a circle from an exterior point (the point which lies outside the circle) :
(a) the tangents are equal in length
(b) the tangents subtend equal angles at the centre of the circle and
(c) the tangents are equally inclined to the line joining the point and the centre of the circle.
- If two chords of a circle intersect internally or externally then the product of the lengths of their segments is equal etc. These types of theorem and their applicability to find unknown values will also be discussed.
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24min
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Measures of Central Tendency Part 2 - Lecture 35
The numerical expressions which represent the characteristics of a group are called Measures of Central Tendency (or, Averages). An average which is used to represent a whole series should neither have the lowest value nor the highest value in the group, but a value somewhere between two limits, possibly in the centre, where most of the items of the group cluster.
There are many types of statistical averages, out of them the following averages will be studied in this chapter.
1. Arithmetic Average or Mean :
The arithmetic mean of a set of numbers is obtained by dividing the sum of numbers of the set by the number of numbers.
Arithmetic Mean of Tabulated Data :
For a given discrete frequency distribution, the arithmetic mean can be using any one of the following three methods:
1. Direct method.
2. Short-cut method.
3. Step-deviation method.
2. Median: Median is the value of middle term of a set of variables the variables of the set are arranged in ascending or descending order.
1 Median for Raw Data
2 Median of Tabulated Data
3 Median for Grouped Data both Continuous and Discontinuous by using Ogive
4 Quartiles (Lower ,upper ,Inter)
3. Mode: Mode is the value which occurs most frequently in a set of observations. It is the point of maximum frequency.
1. Mode for raw data
2. Mode for tabulated data
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30min
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Measures of Central Tendency Part 3 - Lecture 36
The numerical expressions which represent the characteristics of a group are called Measures of Central Tendency (or, Averages). An average which is used to represent a whole series should neither have the lowest value nor the highest value in the group, but a value somewhere between two limits, possibly in the centre, where most of the items of the group cluster.
There are many types of statistical averages, out of them the following averages will be studied in this chapter.
1. Arithmetic Average or Mean :
The arithmetic mean of a set of numbers is obtained by dividing the sum of numbers of the set by the number of numbers.
Arithmetic Mean of Tabulated Data :
For a given discrete frequency distribution, the arithmetic mean can be using any one of the following three methods:
1. Direct method.
2. Short-cut method.
3. Step-deviation method.
2. Median: Median is the value of middle term of a set of variables the variables of the set are arranged in ascending or descending order.
1 Median for Raw Data
2 Median of Tabulated Data
3 Median for Grouped Data both Continuous and Discontinuous by using Ogive
4 Quartiles (Lower ,upper ,Inter)
3. Mode: Mode is the value which occurs most frequently in a set of observations. It is the point of maximum frequency.
1. Mode for raw data
2. Mode for tabulated data
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34min
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Measures of Central Tendency Part 4 - Lecture 37
The numerical expressions which represent the characteristics of a group are called Measures of Central Tendency (or, Averages). An average which is used to represent a whole series should neither have the lowest value nor the highest value in the group, but a value somewhere between two limits, possibly in the centre, where most of the items of the group cluster.
There are many types of statistical averages, out of them the following averages will be studied in this chapter.
1. Arithmetic Average or Mean :
The arithmetic mean of a set of numbers is obtained by dividing the sum of numbers of the set by the number of numbers.
Arithmetic Mean of Tabulated Data :
For a given discrete frequency distribution, the arithmetic mean can be using any one of the following three methods:
1. Direct method.
2. Short-cut method.
3. Step-deviation method.
2. Median: Median is the value of middle term of a set of variables the variables of the set are arranged in ascending or descending order.
1 Median for Raw Data
2 Median of Tabulated Data
3 Median for Grouped Data both Continuous and Discontinuous by using Ogive
4 Quartiles (Lower ,upper ,Inter)
3. Mode: Mode is the value which occurs most frequently in a set of observations. It is the point of maximum frequency.
1. Mode for raw data
2. Mode for tabulated data
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13min
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Probability Part 1 - Lecture 38
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.
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18min
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Probability Part 2 - Lecture 39
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.
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19min
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Cylinder, Cone & Sphere Part 1 - Lecture 40
Cylinder, Cone & Sphere - Here we will study about Cylinder:
A solid which has uniform circular cross-section, is called a cylinder or a circular cylinder.
Let r be the radius of circular cross-section and h the height of the cylinder
(a) Area of cross-section = πr²
(b) Perimeter of cross-section = 2πr
(c ) Curved surface area = Perimeter of cross-section x height
= 2πrh
(d) Total surface area = Curved surface area + 2 (Area of cross-section)
= 2πrh + 2 πr²
(f) Volume = Area of cross-section x height
= πr²h
Hollow Cylinder :
Let R be the external radius of a hollow cylinder, r its internal radius and h height
(a) Thickness of its wall = R-r
(b) Area of cross-section = π (R² - r ²)
(c) External curved surface = 2πRh
(d) Internal curved surface = 2πrh
(e) Total surface area= External curved surface area + Internal curved surface area+ 2 (Area of cross-section)
=2лRh + 2лrh + 2π(R²- r ²)
(f) Volume of material= External volume - Internal volume
=π (R² - r ²)h
Cone:
The solid obtained on revolving a right-angled triangle about one of its sides (other than hypotenuse) is called a cone or a right circular cone.
Let the right-angled triangle ABC be revolved about its side AB to form a cone; then AB is the height (h) of the cone formed, BC is the radius (r) of its base and AC is its slant height (I).
l² = h² + r ² [with help of Pythagoras Theorem]
(a) Volume = πr²h/3
(b) Curved or lateral surface area = πrl
(c) Total surface area = curved surface area + base area = π r (l + r)
And there combination or melted from one form to another
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51min
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Cylinder, Cone & Sphere Part 2 - Lecture 41
Cylinder, Cone & Sphere - Here we will study about Cylinder:
A solid which has uniform circular cross-section, is called a cylinder or a circular cylinder.
Let r be the radius of circular cross-section and h the height of the cylinder
(a) Area of cross-section = πr²
(b) Perimeter of cross-section = 2πr
(c ) Curved surface area = Perimeter of cross-section x height
= 2πrh
(d) Total surface area = Curved surface area + 2 (Area of cross-section)
= 2πrh + 2 πr²
(f) Volume = Area of cross-section x height
= πr²h
Hollow Cylinder :
Let R be the external radius of a hollow cylinder, r its internal radius and h height
(a) Thickness of its wall = R-r
(b) Area of cross-section = π (R² - r ²)
(c) External curved surface = 2πRh
(d) Internal curved surface = 2πrh
(e) Total surface area= External curved surface area + Internal curved surface area+ 2 (Area of cross-section)
=2лRh + 2лrh + 2π(R²- r ²)
(f) Volume of material= External volume - Internal volume
=π (R² - r ²)h
Cone:
The solid obtained on revolving a right-angled triangle about one of its sides (other than hypotenuse) is called a cone or a right circular cone.
Let the right-angled triangle ABC be revolved about its side AB to form a cone; then AB is the height (h) of the cone formed, BC is the radius (r) of its base and AC is its slant height (I).
l² = h² + r ² [with help of Pythagoras Theorem]
(a) Volume = πr²h/3
(b) Curved or lateral surface area = πrl
(c) Total surface area = curved surface area + base area = π r (l + r)
And there combination or melted from one form to another
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28min
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Cylinder, Cone & Sphere Part 3 - Lecture 42
Cylinder, Cone & Sphere - Here we will study about Cylinder:
A solid which has uniform circular cross-section, is called a cylinder or a circular cylinder.
Let r be the radius of circular cross-section and h the height of the cylinder
(a) Area of cross-section = πr²
(b) Perimeter of cross-section = 2πr
(c ) Curved surface area = Perimeter of cross-section x height
= 2πrh
(d) Total surface area = Curved surface area + 2 (Area of cross-section)
= 2πrh + 2 πr²
(f) Volume = Area of cross-section x height
= πr²h
Hollow Cylinder :
Let R be the external radius of a hollow cylinder, r its internal radius and h height
(a) Thickness of its wall = R-r
(b) Area of cross-section = π (R² - r ²)
(c) External curved surface = 2πRh
(d) Internal curved surface = 2πrh
(e) Total surface area= External curved surface area + Internal curved surface area+ 2 (Area of cross-section)
=2лRh + 2лrh + 2π(R²- r ²)
(f) Volume of material= External volume - Internal volume
=π (R² - r ²)h
Cone:
The solid obtained on revolving a right-angled triangle about one of its sides (other than hypotenuse) is called a cone or a right circular cone.
Let the right-angled triangle ABC be revolved about its side AB to form a cone; then AB is the height (h) of the cone formed, BC is the radius (r) of its base and AC is its slant height (I).
l² = h² + r ² [with help of Pythagoras Theorem]
(a) Volume = πr²h/3
(b) Curved or lateral surface area = πrl
(c) Total surface area = curved surface area + base area = π r (l + r)
And there combination or melted from one form to another
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20min
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Cylinder, Cone & Sphere Part 4 - Lecture 43
Cylinder, Cone & Sphere - Here we will study about Cylinder:
A solid which has uniform circular cross-section, is called a cylinder or a circular cylinder.
Let r be the radius of circular cross-section and h the height of the cylinder
(a) Area of cross-section = πr²
(b) Perimeter of cross-section = 2πr
(c ) Curved surface area = Perimeter of cross-section x height
= 2πrh
(d) Total surface area = Curved surface area + 2 (Area of cross-section)
= 2πrh + 2 πr²
(f) Volume = Area of cross-section x height
= πr²h
Hollow Cylinder :
Let R be the external radius of a hollow cylinder, r its internal radius and h height
(a) Thickness of its wall = R-r
(b) Area of cross-section = π (R² - r ²)
(c) External curved surface = 2πRh
(d) Internal curved surface = 2πrh
(e) Total surface area= External curved surface area + Internal curved surface area+ 2 (Area of cross-section)
=2лRh + 2лrh + 2π(R²- r ²)
(f) Volume of material= External volume - Internal volume
=π (R² - r ²)h
Cone:
The solid obtained on revolving a right-angled triangle about one of its sides (other than hypotenuse) is called a cone or a right circular cone.
Let the right-angled triangle ABC be revolved about its side AB to form a cone; then AB is the height (h) of the cone formed, BC is the radius (r) of its base and AC is its slant height (I).
l² = h² + r ² [with help of Pythagoras Theorem]
(a) Volume = πr²h/3
(b) Curved or lateral surface area = πrl
(c) Total surface area = curved surface area + base area = π r (l + r)
And there combination or melted from one form to another
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18min
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Cylinder, Cone & Sphere Part 5 - Lecture 44
Cylinder, Cone & Sphere - Here we will study about Cylinder:
A solid which has uniform circular cross-section, is called a cylinder or a circular cylinder.
Let r be the radius of circular cross-section and h the height of the cylinder
(a) Area of cross-section = πr²
(b) Perimeter of cross-section = 2πr
(c ) Curved surface area = Perimeter of cross-section x height
= 2πrh
(d) Total surface area = Curved surface area + 2 (Area of cross-section)
= 2πrh + 2 πr²
(f) Volume = Area of cross-section x height
= πr²h
Hollow Cylinder :
Let R be the external radius of a hollow cylinder, r its internal radius and h height
(a) Thickness of its wall = R-r
(b) Area of cross-section = π (R² - r ²)
(c) External curved surface = 2πRh
(d) Internal curved surface = 2πrh
(e) Total surface area= External curved surface area + Internal curved surface area+ 2 (Area of cross-section)
=2лRh + 2лrh + 2π(R²- r ²)
(f) Volume of material= External volume - Internal volume
=π (R² - r ²)h
Cone:
The solid obtained on revolving a right-angled triangle about one of its sides (other than hypotenuse) is called a cone or a right circular cone.
Let the right-angled triangle ABC be revolved about its side AB to form a cone; then AB is the height (h) of the cone formed, BC is the radius (r) of its base and AC is its slant height (I).
l² = h² + r ² [with help of Pythagoras Theorem]
(a) Volume = πr²h/3
(b) Curved or lateral surface area = πrl
(c) Total surface area = curved surface area + base area = π r (l + r)
And there combination or melted from one form to another
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26min
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Cylinder, Cone & Sphere Part 6 - Lecture 45
Cylinder, Cone & Sphere - Here we will study about Cylinder:
A solid which has uniform circular cross-section, is called a cylinder or a circular cylinder.
Let r be the radius of circular cross-section and h the height of the cylinder
(a) Area of cross-section = πr²
(b) Perimeter of cross-section = 2πr
(c ) Curved surface area = Perimeter of cross-section x height
= 2πrh
(d) Total surface area = Curved surface area + 2 (Area of cross-section)
= 2πrh + 2 πr²
(f) Volume = Area of cross-section x height
= πr²h
Hollow Cylinder :
Let R be the external radius of a hollow cylinder, r its internal radius and h height
(a) Thickness of its wall = R-r
(b) Area of cross-section = π (R² - r ²)
(c) External curved surface = 2πRh
(d) Internal curved surface = 2πrh
(e) Total surface area= External curved surface area + Internal curved surface area+ 2 (Area of cross-section)
=2лRh + 2лrh + 2π(R²- r ²)
(f) Volume of material= External volume - Internal volume
=π (R² - r ²)h
Cone:
The solid obtained on revolving a right-angled triangle about one of its sides (other than hypotenuse) is called a cone or a right circular cone.
Let the right-angled triangle ABC be revolved about its side AB to form a cone; then AB is the height (h) of the cone formed, BC is the radius (r) of its base and AC is its slant height (I).
l² = h² + r ² [with help of Pythagoras Theorem]
(a) Volume = πr²h/3
(b) Curved or lateral surface area = πrl
(c) Total surface area = curved surface area + base area = π r (l + r)
And there combination or melted from one form to another
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32min
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Cylinder, Cone & Sphere Part 7 - Lecture 46
Cylinder, Cone & Sphere - Here we will study about Cylinder:
A solid which has uniform circular cross-section, is called a cylinder or a circular cylinder.
Let r be the radius of circular cross-section and h the height of the cylinder
(a) Area of cross-section = πr²
(b) Perimeter of cross-section = 2πr
(c ) Curved surface area = Perimeter of cross-section x height
= 2πrh
(d) Total surface area = Curved surface area + 2 (Area of cross-section)
= 2πrh + 2 πr²
(f) Volume = Area of cross-section x height
= πr²h
Hollow Cylinder :
Let R be the external radius of a hollow cylinder, r its internal radius and h height
(a) Thickness of its wall = R-r
(b) Area of cross-section = π (R² - r ²)
(c) External curved surface = 2πRh
(d) Internal curved surface = 2πrh
(e) Total surface area= External curved surface area + Internal curved surface area+ 2 (Area of cross-section)
=2лRh + 2лrh + 2π(R²- r ²)
(f) Volume of material= External volume - Internal volume
=π (R² - r ²)h
Cone:
The solid obtained on revolving a right-angled triangle about one of its sides (other than hypotenuse) is called a cone or a right circular cone.
Let the right-angled triangle ABC be revolved about its side AB to form a cone; then AB is the height (h) of the cone formed, BC is the radius (r) of its base and AC is its slant height (I).
l² = h² + r ² [with help of Pythagoras Theorem]
(a) Volume = πr²h/3
(b) Curved or lateral surface area = πrl
(c) Total surface area = curved surface area + base area = π r (l + r)
And there combination or melted from one form to another
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25min
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