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      Class 10 Maths

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      • Class 10 Maths
      CoursesClass 10MathsClass 10 Maths
      • 01. Real Numbers
        9
        • Lecture1.1
          Real Numbers and Fundamental Theorem of Arithmetic 59 min
        • Lecture1.2
          Divisibility and Euclid’s Division Lemma 49 min
        • Lecture1.3
          Finding HCF and LCM Using Fundamental Theorem of Arithmetic 02 hour
        • Lecture1.4
          Miscellaneous Questions 31 min
        • Lecture1.5
          Chapter Notes – Real Numbers
        • Lecture1.6
          NCERT Solutions – Real Numbers Exercise 1.1 – 1.4
        • Lecture1.7
          Revision Notes Real Numbers
        • Lecture1.8
          R S Aggarwal Real Numbers
        • Lecture1.9
          R D Sharma Real Numbers
      • 02. Polynomials
        11
        • Lecture2.1
          Introduction to Polynomials and Its Zeroes 44 min
        • Lecture2.2
          Finding Zeroes of Quadratic Polynomial 01 hour
        • Lecture2.3
          Relationship b/w the Zeroes and coefficients of a Polynomial 01 hour
        • Lecture2.4
          Cubic Polynomial 35 min
        • Lecture2.5
          Division and Division Algorithm for Polynomials 01 hour
        • Lecture2.6
          Geometrical Meaning of Zeroes of Polynomial 15 min
        • Lecture2.7
          Chapter Notes – Polynomials
        • Lecture2.8
          NCERT Solutions – Polynomials Exercise 2.1 – 2.4
        • Lecture2.9
          Revision Notes Polynomials
        • Lecture2.10
          R S Aggarwal Polynomials
        • Lecture2.11
          R D Sharma Polynomials
      • 03. Linear Equation
        9
        • Lecture3.1
          Solution of linear Equation in Two Variable by Graphical and Algebraic Methods 01 hour
        • Lecture3.2
          Some Basic Questions on Solving Pair of Linear Equations 01 hour
        • Lecture3.3
          Some Basics Problems on Numbers and Ages 40 min
        • Lecture3.4
          Problems on Money Matters, Time, Distance, Speed, Time and Work 01 hour
        • Lecture3.5
          Chapter Notes – Linear Equation
        • Lecture3.6
          NCERT Solutions – Linear Equation Exercise 3.1 – 3.7
        • Lecture3.7
          Revision Notes Linear Equation
        • Lecture3.8
          R S Aggarwal Linear Equation
        • Lecture3.9
          R D Sharma Linear Equation
      • 04. Quadratic Equation
        8
        • Lecture4.1
          Introduction and Finding The Roots of a Quadratic Equation 37 min
        • Lecture4.2
          Miscellaneous Questions 1 02 hour
        • Lecture4.3
          Miscellaneous Questions 2 02 hour
        • Lecture4.4
          Chapter Notes – Quadratic Equation
        • Lecture4.5
          NCERT Solutions – Quadratic Equation Exercise 4.1 – 4.4
        • Lecture4.6
          Revision Notes Quadratic Equation
        • Lecture4.7
          R S Aggarwal Quadratic Equation
        • Lecture4.8
          R D Sharma Quadratic Equation
      • 05. Arithmetic Progressions
        11
        • Lecture5.1
          Introduction to Arithmetic Progression 59 min
        • Lecture5.2
          Miscellaneous Questions Based on nth Term Formula of A.P. 55 min
        • Lecture5.3
          Middle term (s) of Finite A.P. and Arithmetic Mean 01 hour
        • Lecture5.4
          Selection of the Terms and Sum of nth Terms of A.P. 01 hour
        • Lecture5.5
          Miscellaneous Questions Based on Sum of nth Term of A.P. 01 hour
        • Lecture5.6
          Word Problems related to nth term and sum of nth terms of A.P. 01 hour
        • Lecture5.7
          Chapter Notes – Arithmetic Progressions
        • Lecture5.8
          NCERT Solutions – Arithmetic Progressions Exercise 5.1 – 5.4
        • Lecture5.9
          Revision Notes Arithmetic Progressions
        • Lecture5.10
          R S Aggarwal Arithmetic Progressions
        • Lecture5.11
          R D Sharma Arithmetic Progressions
      • 06. Some Applications of Trigonometry
        7
        • Lecture6.1
          Angle of Elevation and Depression; Problems involving Elevation and Double Elevation 01 hour
        • Lecture6.2
          Miscellaneous Problems Involving Double Elevation, Depression and Elevation 01 hour
        • Lecture6.3
          Miscellaneous Questions (Level-1, 2, 3, 4) 49 min
        • Lecture6.4
          Chapter Notes – Some Applications of Trigonometry
        • Lecture6.5
          NCERT Solutions – Some Applications of Trigonometry
        • Lecture6.6
          Revision Notes Some Applications of Trigonometry
        • Lecture6.7
          R D Sharma Some Applications of Trigonometry
      • 07. Coordinate Geometry
        17
        • Lecture7.1
          Introduction to Terms related to Coordinate Geometry 49 min
        • Lecture7.2
          Locating Coordinates of Point on the Axes 37 min
        • Lecture7.3
          Finding vertices of a Geometrical Fig. and Distance b/w Two Points 58 min
        • Lecture7.4
          Distance b/w Two Points Formula Based Examples 44 min
        • Lecture7.5
          Finding the type of Triangle and Quadrilateral 01 hour
        • Lecture7.6
          Find the Collinear or Non-collinear points and Missing Vertex of a Geometrical Figure 42 min
        • Lecture7.7
          Section Formula and Corollary 01 hour
        • Lecture7.8
          Finding the Section Ratio and Involving Equation of Line 53 min
        • Lecture7.9
          Proof Related to Mid-points and Centroid of a Triangle 59 min
        • Lecture7.10
          Finding Area of Triangle and Quadrilateral 53 min
        • Lecture7.11
          Collinearity 34 min
        • Lecture7.12
          Examples Based on If Areas are Given 34 min
        • Lecture7.13
          Chapter Notes – Coordinate Geometry
        • Lecture7.14
          NCERT Solutions – Coordinate Geometry Exercise 7.1 – 7.4
        • Lecture7.15
          Revision Notes Coordinate Geometry
        • Lecture7.16
          R S Aggarwal Coordinate Geometry
        • Lecture7.17
          R D Sharma Coordinate Geometry
      • 08. Triangles
        15
        • Lecture8.1
          Introduction, Similarity of Triangles, Properties of Triangles, Thales’s Theorem 52 min
        • Lecture8.2
          Questions Based on Thales’s Theorem, Converse Thales’s Theorem 01 hour
        • Lecture8.3
          Questions Based on Converse Thales’s Theorem, Questions Based On Mid-points and its Converse 59 min
        • Lecture8.4
          Questions Based on Internal Bisectors of an Angle, Similar Triangles, AAA criterion for Similarity 52 min
        • Lecture8.5
          SSS & SAS Criterion of Similarity, Question Based on Criteria for Similarity 02 hour
        • Lecture8.6
          Questions Based on Criteria for Similarity Conti. 01 hour
        • Lecture8.7
          Questions Based On Area of Similar Triangles 02 hour
        • Lecture8.8
          Questions Based On Area of Similar Triangles cont., Pythagoras Theorem Level-1 01 hour
        • Lecture8.9
          Pythagoras Theorem Level-1 cont. 01 hour
        • Lecture8.10
          Miscellaneous Questions 01 hour
        • Lecture8.11
          Chapter Notes – Triangles
        • Lecture8.12
          NCERT Solutions – Triangles Exercise 8.1 – 8.6
        • Lecture8.13
          Revision Notes Triangles
        • Lecture8.14
          R S Aggarwal Triangles
        • Lecture8.15
          R D Sharma Triangles
      • 09. Circles
        8
        • Lecture9.1
          Introduction to Circle and Tangent and Theorems-1, 2 01 hour
        • Lecture9.2
          Property of Chord of Circle and Theorem-3 52 min
        • Lecture9.3
          Theorem 4 and Angle in Semicircle 01 hour
        • Lecture9.4
          Chapter Notes – Circles
        • Lecture9.5
          NCERT Solutions – Circles Exercise
        • Lecture9.6
          Revision Notes Circles
        • Lecture9.7
          R S Aggarwal Circles
        • Lecture9.8
          R D Sharma Circles
      • 10. Areas Related to Circles
        10
        • Lecture10.1
          Area and Perimeter of Circle, Semicircle and Quarter circle 56 min
        • Lecture10.2
          Touching Circles and Example on Bending Wire, Wheel Rotation 58 min
        • Lecture10.3
          Sector of A Circle 51 min
        • Lecture10.4
          Segment of Circle and Area of Combination of Plane Figures 01 hour
        • Lecture10.5
          Questions Based on Area of Combination of Plane Figures 01 hour
        • Lecture10.6
          Chapter Notes – Areas Related to Circles
        • Lecture10.7
          NCERT Solutions – Areas Related to Circles
        • Lecture10.8
          Revision Notes Areas Related to Circles
        • Lecture10.9
          R S Aggarwal Areas Related to Circles
        • Lecture10.10
          R D Sharma Areas Related to Circles
      • 11. Introduction to Trigonometry
        7
        • Lecture11.1
          Introduction, Trigonometric Ratios, Sums when Sides of Triangle are given, Miscellaneous Questions 01 hour
        • Lecture11.2
          Trigonometric Ratios for Some Specific Angles, Trigonometric Ratio for 30 & 60, Value Table, Word Problems 48 min
        • Lecture11.3
          Complimentary angles in Inverse Multiplication, Miscellaneous Problems 01 hour
        • Lecture11.4
          Miscellaneous Questions 01 hour
        • Lecture11.5
          Chapter Notes – Introduction to Trigonometry
        • Lecture11.6
          NCERT Solutions – Introduction to Trigonometry
        • Lecture11.7
          Revision Notes Introduction to Trigonometry
      • 12. Surface Areas and Volumes
        9
        • Lecture12.1
          Introduction, Surface Area of Cube, Cuboid, Cylinder, Hollow cylinder, Cone, Sphere, Type-1 : Surface Area and Volume of A Solid 01 hour
        • Lecture12.2
          Volume Related Questions, Based On Embarkment 48 min
        • Lecture12.3
          Based on the Rate of Flowing, Frustum of Cone (A) Surface Area (B) Volume 52 min
        • Lecture12.4
          Quantity, Percentage, Very Short Answer Types Questions 44 min
        • Lecture12.5
          Chapter Notes – Surface Areas and Volumes
        • Lecture12.6
          NCERT Solutions – Surface Areas and Volumes
        • Lecture12.7
          Revision Notes Surface Areas and Volumes
        • Lecture12.8
          R S Aggarwal Surface Areas and Volumes
        • Lecture12.9
          R D Sharma Surface Areas and Volumes
      • 13. Statistics
        12
        • Lecture13.1
          Introduction and Mean of Ungrouped Data 46 min
        • Lecture13.2
          Mean of Grouped Data 58 min
        • Lecture13.3
          Median of Ungrouped and grouped Data 01 hour
        • Lecture13.4
          Mode of Ungrouped and Grouped Data 49 min
        • Lecture13.5
          Mean, Median and Mode & Cumulative Frequency Curve-Less Than Type 53 min
        • Lecture13.6
          Cumulative Frequency Curve (Ogive)-More Than Type 52 min
        • Lecture13.7
          Miscellaneous Questions 38 min
        • Lecture13.8
          Chapter Notes – Statistics
        • Lecture13.9
          NCERT Solutions – Statistics
        • Lecture13.10
          Revision Notes Statistics
        • Lecture13.11
          R S Aggarwal Statistics
        • Lecture13.12
          R D Sharma Statistics
      • 14. Probability
        9
        • Lecture14.1
          Activities, Understanding term Probability, Experiments 54 min
        • Lecture14.2
          Calculations 43 min
        • Lecture14.3
          Event, Favorable Outcomes, Probability, Some important experiments- Tossing a coin, Rolling dice, Drawing a card 01 hour
        • Lecture14.4
          Complement of an event, Elementary Events, Equally Likely events, Some problems of Probability 58 min
        • Lecture14.5
          Chapter Notes – Probability
        • Lecture14.6
          NCERT Solutions – Probability
        • Lecture14.7
          Revision Notes Probability
        • Lecture14.8
          R S Aggarwal Probability
        • Lecture14.9
          R D Sharma Probability
      • 15. Construction
        7
        • Lecture15.1
          Introduction, Construction to Divide a Line Segment in Certain Ratio, Construction of Similar Triangles 44 min
        • Lecture15.2
          Construction of Different Angles, Construction of Angle Bisector 41 min
        • Lecture15.3
          Construction of Tangent of Circle at a Given Point 35 min
        • Lecture15.4
          Chapter Notes – Construction
        • Lecture15.5
          NCERT Solutions – Construction
        • Lecture15.6
          R S Aggarwal Construction
        • Lecture15.7
          R D Sharma Construction

        Chapter Notes – Statistics

        (1) Data : It is a collection of facts such as numbers, words, measurements, alphabets, symbols, observations or even just description of things.
        For Example: Data include marks of students, present-absent report of students, name of students, runs made by batsman, etc.

        (2) Data Organization : The data available in an unorganized form is called as raw data. The extraction of the information from these raw data to give meaning to these data is known as data organization.

        (3) Frequency of data : The number of times a particular quantity repeats itself in the given data is known as its frequency.
        For Example: Table below represents number of cars possessed by different families in a society.

        Number of cars No of families
        0 4
        1 8
        2 2

        Here, the frequency of families who have one car is 8.

        (4) Frequency Distribution Table : The table which represents the number of times a particular quantity is repeated is known as the frequency distribution table.
        For Example: Table below represents number of cars possessed by different families in a society.

        Number of cars Frequency
        0 4
        1 8
        2 2
        3 3
        4 2
        5 1

         

        (5) Mean of Grouped Data : the mean value of a variable is defined as the sum of all the values of the variable divided by the number of values. Suppose, if x1 , x2 ,. . ., xn are observations with respective frequencies f1 , f2 , . . ., fn , then this means observation x1 occurs f1 times, x2 occurs f2 times, and so on. Now, the sum of the values of all the observations = f1x1 + f2x2 + . . . + fnxn , and the number of observations = f1 + f2 + . . . + fn.
        Hence, the mean of the data is given by
         or 

        (6) Data Grouping : When the amount of data is huge, then the frequency distribution table for individual observation will result into a large table. In such case, we form group of data and then prepare a table. This type of table is called as grouped frequency distribution.
        For Example: Suppose, we need to prepare a table for Science marks obtained by 60 students in a class. Then preparing table for individual marks will result into a big table, so we will group the data as shown in the table below:

        Range of Marks No of students
        0 – 10 2
        10-20 9
        20-30 22
        30-40 20
        40-50 6
        50-60 1
        Total 60

         (i) Class Interval or Class: It represents the range in which the data are grouped. For the above example, groups 0-10, 10-20, 20-30, etc. represents class interval.
        (ii) Lower class limit: The lowest number occurring in a particular class interval is known as its lower class limit. For the above example, if we consider the class interval 10-20 then 10 is called the lower class limit of that interval.
        (iii) Upper class limit: The highest number occurring in a particular class interval is known as its upper class limit. For the above example, if we consider the class interval 10-20 then 20 is called the upper class limit of that interval.
        (iv) Width or size of class interval: The difference between the upper class limit and the lower class limit is called as the width or size of class interval. For the above example, if we consider the class interval 10-20, then width or size of this class interval will be 10.
        (v) Class mark: The frequency of each class interval is centred around its mid-point. Class mark = (Upper class limit + lower class limit)/2. For the above example, if we consider the class interval 10-20, then class mark will be 15.

         

        (7) Methods to find mean:
        (i) Direct Method:
        For Example: A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

        No of plants 0 – 2 2 – 4 4 – 6 6 – 8 8 – 10 10- 12 12 – 14
        No of houses 1 2 1 5 6 2 3

        We know that, Class mark (xi) = (Upper class limit + lower class limit)/2.

        No of plants No of houses xi fixi
        0 – 2 1 1 1
        2 – 4 2 3 6
        4 – 6 1 5 5
        6 – 8 5 7 35
        8 – 10 6 9 54
        10 – 12 2 11 22
        12 – 14 3 13 39
        Total 20 162

        = 20
        = 162
         = 162/20 = 8.1
        Therefore, mean number of plants per house is 8.1

        (ii) Assumed Mean Method:
        For Example: The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency f.

        Daily pocket allowance

        (in Rs)

        11 – 13 13 – 15 15 – 17 17 – 19 19 – 21 21- 23 23 – 25
        No of children 7 6 9 13 f 5 4

        We know that, Class mark (xi) = (Upper class limit + lower class limit)/2.
        Given, mean pocket allowance, = 18 Rs.

        Daily pocket allowance

        (in Rs)

        No of children

        fi

        Class mark

        xi

        di = xi – 18 fidi
        11 – 13 7 12 -6 -42
        13 – 15 6 14 -4 -24
        15 – 17 9 16 -2 -18
        17 – 19 13 18 0 0
        19 – 21 f 20 2 2f
        21 – 23 5 22 4 20
        23 – 25 4 24 6 24
        Total = 44 + f 2f – 40

        From the table, we get,
        = 44 + f
        = 2f – 40
        = a +  /
        18 = 18 + (2f – 40)/(44 + f)
        0 = (2f – 40)/(44 + f)
        2f – 40 = 0
        f = 20.
        Therefore, the missing frequency is 20.

         

        (iii) Step-deviation method:
        For Example: Consider the following distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory.

        Daily wages (in Rs) 100 – 120 120 – 140 140 – 160 160 – 180 180 – 200
        No of workers 12 14 8 6 10

        We know that, Class mark (xi) = (Upper class limit + lower class limit)/2.
        Here, Class size(h) = 20.
        Taking 150 as assured mean(a), di, ui and fiui can be calculated as follows:

        Daily wages

        (in Rs)

        No of workers

        fi

        xi di = xi – 150 ui = di/20 fiui
        100 – 120 12 110 -40 -2 -24
        120 – 140 14 130 -20 -1 -14
        140 – 160 8 150 0 0 0
        160 – 180 6 170 20 1 6
        180 – 200 10 190 40 2 20
        Total -12

        From the table, we get,
        = 50
        = – 12
        Mean  = a + /
        = 150 + (-12/50) 20
        = 150 – 24/5
        = 145.2
        Therefore, the mean daily wage of the workers of the factory is 145.20 Rs.

         

        (8) Mode of Grouped Data:
        Modal class: The class interval having highest frequency is called the modal class and Mode is obtained using the modal class.http://physicscatalyst.com/Class10/mode_group.PNGWhere
        l = lower limit of the modal class,
        h = size of the class interval (assuming all class sizes to be equal),
        f1 = frequency of the modal class,
        f0 = frequency of the class preceding the modal class,
        f2 = frequency of the class succeeding the modal class.

        For Example: The following data gives the information on the observed lifetimes (in hours) of 225 electrical components. Determine the modal lifetimes of the components.

        Lifetimes (in hours) 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120
        Frequency 10 35 52 61 38 29

        For the given data, it can be observed that the maximum class frequency is 61 which belong to class interval 60 – 80.
        Therefore, modal class = 60 – 80.
        Lower class limit (l) of modal class = 60
        Frequency (f1) of modal class = 61
        Frequency (f0) of class preceding the modal class = 52
        Frequency (f2) of class succeeding the modal class = 38
        Class size (h) = 20http://physicscatalyst.com/Class10/mode_group.PNG= 60 + ((61 – 52)/(2 x 61 – 52 – 38) (20)
        = 60 + (9/(122 – 90)) (20)
        = 60 + 90/16
        =65.625
        Therefore, modal lifetime of electrical components is 65.625 hours.

        (9) Median of Grouped Data: For the given data, we need to have class interval, frequency distribution and cumulative frequency distribution. Then, median is calculated as
        Where
        l = lower limit of median class,
        n = number of observations,
        cf = cumulative frequency of class preceding the median class,
        f = frequency of median class,
        h = class size (assuming class size to be equal)

        For Example: The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median of the data.

        Monthly consumption

        (in units)

        No of consumers
        65 – 85 4
        85 – 105 5
        105 – 125 13
        125 – 145 20
        145 – 165 14
        165 – 185 8
        185 – 205 4

         

        To find the median of the given data, cumulative frequency is calculated as follows:

        Monthly consumption

        (in units)

        No of consumers Cumulative frequency
        65 – 85 4 4
        85 – 105 5 4 + 5 = 9
        105 – 125 13 9 + 13 = 22
        125 – 145 20 22 + 20 = 42
        145 – 165 14 42 + 14 = 56
        165 – 185 8 56 + 8 = 64
        185 – 205 4 64 + 4 = 68

        From the table, we get n = 68.
        The cumulative frequency (cf) is just greater than n/2 (i.e. 68/2 = 34) is 42, belonging to interval 125 – 145.
        Therefore, median class = 125 – 145
        Lower limit (l) of median class = 125
        Class size (h) = 20
        Frequency (f) of median class = 20
        Cumulative frequency (cf) of class preceding median class = 22.= 125 + ((34 – 22)/20) (20)
        = 125 + 12 = 137.
        Therefore, median of the given data is 137.

        (10) Graphical Representation of Cumulative Frequency Distribution:
        For Example: The following distribution gives the daily income of 50 workers of a factory. Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

        Daily income

        (in Rs)

        No of workers
        100 – 120 12
        120 – 140 14
        140 – 160 8
        160 – 180 6
        180 – 200 10

        The less than type cumulative frequency distribution is given as follows:

        Daily income

        (in Rs)

        No of workers Cumulative frequency
        100 – 120 12 12
        120 – 140 14 12 + 14 = 26
        140 – 160 8 26 + 8 = 34
        160 – 180 6 34 + 6 = 40
        180 – 200 10 40 + 10 = 50

         

        Now, we will draw the ogive curve by plotting points (120, 12), (140, 26), (160, 34), (180, 40), (200, 50).

        Prev Miscellaneous Questions
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          6 Comments

        1. Priyanshu Kumar
          May 28, 2021

          How we access live tutorial classes please tell me

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            May 31, 2021

            For any information regarding live class please call us at 8287971571

        2. Rohan Yedla
          September 15, 2021

          I am not able to access any test of coordinate geometry, can you pls resolve the issue?

          • Dronstudy
            September 20, 2021

            We have fixed the issue. Please feel free to call us at 8287971571 if you face such type of issues.

        3. Ananyaa
          November 12, 2021

          Hi!
          I am a student in class 10th and ive noticed that you dont give full courses on your youtube channel. I mean, its understandable. But we request you to at least put full course of only one chapter on youtube so that we can refer to that. Only one from the book Because your videos are very good and they enrich our learning.
          Please give this feedback a chance and consider our request.

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          Ananyaa

        4. Nucleon IIT JEE KOTA
          December 17, 2022

          Great article, the information provided to us. Thank you

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