• CBSE Sample Papers(2021)
    • CBSE Sample Papers(2021)
      • CBSE sample paper 2020
        • 12
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            • Sample Paper - 1
          • Biology
            • Sample Paper - 1
        • 10
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            • Sample Paper - 1
            • Sample Paper - 2
  • Student Useful Links
    • Important book solutions
      • RD Sharma
        • class-6
          • Mathematics
            • Chapter 1 Knowing Our Numbers
              • Exercise 1.1
              • Exercise 1.2
              • Exercise 1.3
              • Exercise 1.4
              • Exercise 1.5
              • Exercise 1.6
              • Exercise 1.7
            • Chapter 2 Playing With Numbers
              • Exercise 2.1
              • Exercise 2.2
              • Exercise 2.3
              • Exercise 2.4
              • Exercise 2.5
              • Exercise 2.6
              • Exercise 2.7
              • Exercise 2.8
              • Exercise 2.9
              • Exercise 2.10
              • Exercise 2.11
            • Chapter 3 Whole Numbers
              • Exercise 3.1
            • Chapter 4 Operations On Whole Numbers
              • Exercise 4.1
              • Exercise 4.2
              • Exercise 4.3
              • Exercise 4.4
              • Exercise 4.5
            • Chapter 5 Negative Numbers and Integers
              • Exercise 5.1
              • Exercise 5.2
              • Exercise 5.3
              • Exercise 5.4
            • Chapter 6 Fractions
              • Exercise 6.1
              • Exercise 6.2
              • Exercise 6.3
              • Exercise 6.4
              • Exercise 6.5
              • Exercise 6.6
              • Exercise 6.7
              • Exercise 6.8
              • Exercise 6.9
            • Chapter 7 Decimals
              • Exercise 7.1
              • Exercise 7.2
              • Exercise 7.3
              • Exercise 7.4
              • Exercise 7.5
              • Exercise 7.6
              • Exercise 7.7
              • Exercise 7.8
              • Exercise 7.9
              • Exercise 7.10
            • Chapter 8 Introduction To Algebra
              • Exercise 8.1
              • Exercise 8.2
              • Exercise 8.3
            • Chapter 9 Ratio, Proportion and Unitary Method
              • Exercise 9.1
              • Exercise 9.2
              • Exercise 9.3
              • Exercise 9.4
            • Chapter 10 Basic Geometrical Concepts
              • Exercise 10.1
              • Exercise 10.2
              • Exercise 10.3
            • Chapter 11 Angles
              • Exercise 11.1
              • Exercise 11.2
            • Chapter 12 Triangles
              • Exercise 12.1
              • Exercise 12.2
            • Chapter 13 Quadrilaterals
              • Exercise 13.1
            • Chapter 14 Circles
              • Exercise 14.1
            • Chapter 15 Pair Of Lines and Transversal
              • Exercise 15.1
              • Exercise 15.2
            • Chapter 16 Understanding Three Dimensional Shapes
              • Exercise 16.1
              • Exercise 16.2
            • Chapter 17 Symmetry
              • Exercise 17.1
              • Exercise 17.2
              • Exercise 17.3
              • Exercise 17.4
            • Chapter 18 Basic Geometrical Tools
              • Exercise 18.1
              • Exercise 18.2
            • Chapter 19 Geometrical Constructions
              • Exercise 19.1
              • Exercise 19.2
              • Exercise 19.3
              • Exercise 19.4
              • Exercise 19.5
              • Exercise 19.6
            • Chapter 20 Mensuration
              • Exercise 20.1
              • Exercise 20.2
              • Exercise 20.3
              • Exercise 20.4
            • Chapter 21 Data Handling I (Presentation of Data)
              • Exercise 21.1
            • Chapter 22 Data Handling II (Pictographs)
              • Exercise 22.1
              • Exercise 22.2
          • Science
            • Chapter 20 Mensuration
              • Exercise 20.5
          • Social Studies
        • class-7
          • Mathematics
            • Chapter 1 Integers
              • Exercise 1.1
              • Exercise 1.2
              • Exercise 1.3
              • Exercise 1.4
            • Chapter 2 Fractions
              • Exercise 2.1
              • Exercise 2.2
              • Exercise 2.3
            • Chapter 3 Decimals
              • Exercise 3.1
              • Exercise 3.2
              • Exercise 3.3
            • Chapter 4 Rational Numbers
              • Exercise 4.1
              • Exercise 4.2
              • Exercise 4.3
              • Exercise 4.4
              • Exercise 4.4
              • Exercise 4.5
              • Exercise 4.6
            • Chapter 5 Operations on Rational Numbers
              • Exercise 5.1
              • Exercise 5.2
              • Exercise 5.3
              • Exercise 5.4
              • Exercise 5.5
            • Chapter 6 Exponents
              • Exercise 6.1
              • Exercise 6.2
              • Exercise 6.3
            • Chapter 7 Algebraic Expressions
              • Exercise 7.1
              • Exercise 7.2
              • Exercise 7.3
              • Exercise 7.4
            • Chapter 8 Linear Equations in One Variable
              • Exercise 8.1
              • Exercise 8.2
              • Exercise 8.3
              • Exercise 8.4
            • Chapter 9 Ratio and Proportion
              • Exercise 9.1
              • Exercise 9.2
              • Exercise 9.3
            • Chapter 10 Unitary Method
              • Exercise 10.1
            • Chapter 11 Percentage
              • Exercise 11.1
              • Exercise 11.2
              • Exercise 11.3
              • Exercise 11.4
              • Exercise 11.5
              • Exercise 11.6
            • Chapter 12 Profit and Loss
              • Exercise 12.1
            • Chapter 13 Simple Interest
              • Exercise 13.1
            • Chapter 14 Lines and Angles
              • Exercise 14.1
              • Exercise 14.2
            • Chapter 15 Properties of Triangles
              • Exercise 15.1
              • Exercise 15.2
              • Exercise 15.3
              • Exercise 15.4
              • Exercise 15.5
            • Chapter 16 Congruence
              • Exercise 16.1
              • Exercise 16.2
              • Exercise 16.3
              • Exercise 16.4
              • Exercise 16.5
            • Chapter 17 Constructions
              • Exercise 17.1
              • Exercise 17.2
              • Exercise 17.3
              • Exercise 17.4
              • Exercise 17.5
            • Chapter 18 Symmetry
              • Exercise 18.1
              • Exercise 18.2
              • Exercise 18.3
            • Chapter 19 Visualising Solid Shapes
              • Exercise 19.1
              • Exercise 19.2
            • Chapter 20 Mensuration I
              • Exercise 20.1
              • Exercise 20.2
              • Exercise 20.3
              • Exercise 20.4
            • Chapter 21 Mensuration II Area of Circle
              • Exercise 21.1
              • Exercise 21.2
            • Chapter 22 Data Handling I Collection Organisation Data
              • Exercise 22.1
            • Chapter 23 Data Handling II Central Values
              • Exercise 23.1
              • Exercise 23.2
              • Exercise 23.3
              • Exercise 23.4
            • Chapter 24 Data Handling III Construction of Bar Graphs
              • Exercise 24.1
            • Chapter 25 Data Handling IV Probability
              • Exercise 25.1
          • Science
          • Social Studies
        • class-8
          • Mathematics
            • Chapter 1 Rational Numbers
              • Exercise 1.1
              • Exercise 1.2
              • Exercise 1.3
              • Exercise 1.4
              • Exercise 1.5
              • Exercise 1.6
              • Exercise 1.7
              • Exercise 1.8
            • Chapter 2 Powers
              • Exercise 2.1
              • Exercise 2.2
              • Exercise 2.3
            • Chapter 3 Squares and Square Roots
              • Exercise 3.1
              • Exercise 3.2
              • Exercise 3.3
              • Exercise 3.4
              • Exercise 3.5
              • Exercise 3.6
              • Exercise 3.7
              • Exercise 3.8
              • Exercise 3.9
            • Chapter 4 Cubes and Cube Roots
              • Exercise 4.1
              • Exercise 4.2
              • Exercise 4.3
              • Exercise 4.4
              • Exercise 4.5
            • Chapter 5 Playing With Numbers
              • Exercise 5.1
              • Exercise 5.2
              • Exercise 5.3
            • Chapter 6 Algebraic Expressions And Identities
              • Exercise 6.1
              • Exercise 6.2
              • Exercise 6.3
              • Exercise 6.4
              • Exercise 6.5
              • Exercise 6.6
              • Exercise 6.7
            • Chapter 7 Factorization
              • Exercise 7.1
              • Exercise 7.2
              • Exercise 7.3
              • Exercise 7.4
              • Exercise 7.5
              • Exercise 7.6
              • Exercise 7.7
              • Exercise 7.8
              • Exercise 7.9
            • Chapter 8 Division Of Algebraic Expressions
              • Exercise 8.1
              • Exercise 8.2
              • Exercise 8.3
              • Exercise 8.4
              • Exercise 8.5
              • Exercise 8.6
            • Chapter 9 Linear Equation In One Variable
              • Exercise 9.1
              • Exercise 9.2
              • Exercise 9.3
              • Exercise 9.4
            • Chapter 10 Direct And Inverse Variations
              • Exercise 10.1
              • Exercise 10.2
            • Chapter 11 Time And Work
              • Exercise 11.1
            • Chapter 12 Percentage
              • Exercise 12.1
              • Exercise 12.2
            • Chapter 13 Profit Loss Discount And Value Added Tax
              • Exercise 13.1
              • Exercise 13.2
              • Exercise 13.3
            • Chapter 14 Compound Interest
              • Exercise 14.1
              • Exercise 14.2
              • Exercise 14.3
              • Exercise 14.4
              • Exercise 14.5
            • Chapter 15 Understanding Shapes Polygons
              • Exercise 15.1
            • Chapter 16 Understanding Shapes Quadrilaterals
              • Exercise 16.1
            • Chapter 17 Understanding Shapes Special Types Quadrilaterals
              • Exercise 17.1
              • Exercise 17.2
              • Exercise 17.3
            • Chapter 18 Practical Geometry
              • Exercise 18.1
              • Exercise 18.2
              • Exercise 18.3
              • Exercise 18.4
              • Exercise 18.5
            • Chapter 19 Visualising Shapes
              • Exercise 19.1
              • Exercise 19.2
            • Chapter 20 Area Of Trapezium And Polygon
              • Exercise 20.1
              • Exercise 20.2
              • Exercise 20.3
            • Chapter 21 Mensuration II Volumes Surface Area Cuboid Cube
              • Exercise 21.1
              • Exercise 21.2
              • Exercise 21.3
              • Exercise 21.4
            • Chapter 22 Mensuration III Surface Area And Volume Of Right Circular Cylinder
              • Exercise 22.1
              • Exercise 22.2
            • Chapter 23 Data Handling I Classification And Tabulation Of Data
              • Exercise 23.1
              • Exercise 23.2
            • Chapter 24 Data Handling II Graphical Representation Of Data As Histograms
              • Exercise 24.1
            • Chapter 25 Data Handling III Pictorial Representation Of Data As Pie Charts Or Circle Graphs
              • Exercise 25.1
            • Chapter 26 Data Handling Iv Probability
              • Exercise 26.1
            • Chapter 27 Introduction to Graphs
              • Exercise 27.1
              • Exercise 27.2
          • Science
          • Social Studies
        • class-9
          • Mathematics
            • Chapter 1 Number System
              • Exercise 1.1
              • Exercise 1.2
              • Exercise 1.3
              • Exercise 1.4
            • Chapter 2 Exponents of Real Numbers
              • Exercise 2.1
              • Exercise 2.2
            • Chapter 3 Rationalisation
              • Exercise 3.1
              • Exercise 3.2
            • Chapter 4 Algebraic Identities
              • Exercise 4.1
              • Exercise 4.2
              • Exercise 4.3
              • Exercise 4.4
            • Chapter 5 Factorisation of Algebraic Expressions
              • Exercise 5.1
              • Exercise 5.2
              • Exercise 5.3
              • Exercise 5.4
            • Chapter 6 Factorisation of Polynomials
              • Exercise 6.1
              • Exercise 6.2
              • Exercise 6.3
              • Exercise 6.4
              • Exercise 6.5
            • Chapter 7 Introduction to Euclid’s Geometry
              • Exercise 7.1
            • Chapter 8 Lines and And Angles
              • Exercise 8.1
              • Exercise 8.2
              • Exercise 8.3
              • Exercise 8.4
            • Chapter 9 Triangles and its Angles
              • Exercise 9.1
              • Exercise 9.2
            • Chapter 10 Congruent Triangles
              • Exercise 10.1
              • Exercise 10.2
              • Exercise 10.3
              • Exercise 10.4
              • Exercise 10.5
              • Exercise 10.6
            • Chapter 11 Coordinate Geometry
              • Exercise 11.1
            • Chapter 12 Heron’s Formula
              • Exercise 12.1
              • Exercise 12.2
            • Chapter 13 Linear Equations in Two Variables
              • Exercise 13.1
              • Exercise 13.2
              • Exercise 13.3
              • Exercise 13.4
            • Chapter 14 Quadrilaterals
              • Exercise 14.1
              • Exercise 14.2
              • Exercise 14.3
              • Exercise 14.4
            • Chapter 15 Area of Parallelograms and Triangles
              • Exercise 15.1
              • Exercise 15.2
              • Exercise 15.3
            • Chapter 16 Circles
              • Exercise 16.1
              • Exercise 16.2
              • Exercise 16.3
              • Exercise 16.4
            • Chapter 17 Constructions
              • Exercise 17.1
            • Chapter 18 Surface Area and Volume of a Cuboid and Cube
              • Exercise 18.1
            • Chapter 18 Surface Area and Volume of a Cuboid and Cube
              • Exercise 18.2
              • Exercise 19.1
              • Exercise 19.2
            • Chapter 20 Surface Area And Volume of A Right Circular Cone
              • Exercise 20.1
              • Exercise 20.2
            • Chapter 21 Surface Area and Volume of a Sphere
              • Exercise 21.1
              • Exercise 21.2
            • Chapter 22 Tabular Representation of Statistical Data
              • Exercise 22.1
              • Exercise 22.2
            • Chapter 23 Graphical Representation of Statistical Data
              • Exercise 23.1
              • Exercise 23.2
            • Chapter 24 Measures of Central Tendency
              • Exercise 24.1
              • Exercise 24.2
              • Exercise 24.3
              • Exercise 24.4
            • Chapter 25 Probability
              • Exercise 25.1
          • Science
          • Social Studies
        • class-10
          • Mathematics
            • Chapter 1 Real Numbers
              • Exercise 1.1
              • Exercise 1.2
              • Exercise 1.3
              • Exercise 1.4
              • Exercise 1.5
            • Chapter 2 Polynomials
              • Exercise 2.1
              • Exercise 2.2
              • Exercise 2.3
            • Chapter 3 Pair of Linear Equations in Two Variables
              • Exercise 3.1
              • Exercise 3.2
              • Exercise 3.3
              • Exercise 3.4
              • Exercise 3.5
              • Exercise 3.6
              • Exercise 3.7
              • Exercise 3.8
              • Exercise 3.9
              • Exercise 3.10
              • Exercise 3.11
            • Chapter 4 Triangles
              • Exercise 4.1
              • Exercise 4.2
              • Exercise 4.3
              • Exercise 4.4
              • Exercise 4.5
              • Exercise 4.6
              • Exercise 4.7
            • Chapter 5 Trigonometric Ratios
              • Exercise 5.1
              • Exercise 5.2
              • Exercise 5.3
            • Chapter 6 Trigonometric Identities
              • Exercise 6.1
              • Exercise 6.2
            • Chapter 7 Statistics
              • Exercise 7.1
              • Exercise 7.2
              • Exercise 7.3
              • Exercise 7.4
              • Exercise 7.5
              • Exercise 7.6
            • Chapter 8 Quadratic Equations
              • Exercise 8.1
              • Exercise 8.2
              • Exercise 8.3
              • Exercise 8.4
              • Exercise 8.5
              • Exercise 8.6
              • Exercise 8.7
              • Exercise 8.8
              • Exercise 8.9
              • Exercise 8.11
              • Exercise 8.12
              • Exercise 8.13
            • Chapter 9 Arithmetic Progressions
              • Exercise 9.1
              • Exercise 9.2
              • Exercise 9.3
              • Exercise 9.4
              • Exercise 9.5
              • Exercise 9.6
            • Chapter 10 Circles
              • Exercise 10.1
              • Exercise 10.2
            • Chapter 11 Constructions
              • Exercise 11.1
              • Exercise 11.2
              • Exercise 11.3
            • Chapter 12 Some Applications of Trigonometry
              • Exercise 12.1
            • Chapter 13 Probability
              • Exercise 13.1
              • Exercise 13.2
            • Chapter 14 Coordinate Geometry
              • Exercise 14.1
              • Exercise 14.2
              • Exercise 14.3
              • Exercise 14.4
              • Exercise 14.5
            • Chapter 15 Areas Related to Circles
              • Exercise 15.1
              • Exercise 15.2
              • Exercise 15.3
              • Exercise 15.4
            • Chapter 16 Surface Areas and Volumes
              • Exercise 16.1
              • Exercise 16.2
              • Exercise 16.3
          • Science
          • Social Studies
        • class-11
          • Mathematics
            • Chapter 1 Sets
              • Exercise 1.1
              • Exercise 1.2
              • Exercise 1.3
              • Exercise 1.4
              • Exercise 1.5
              • Exercise 1.6
              • Exercise 1.7
              • Exercise 1.8
            • Chapter 2 Relations
              • Exercise 2.1
              • Exercise 2.2
              • Exercise 2.3
            • Chapter 3 Functions
              • Exercise 3.1
              • Exercise 3.2
              • Exercise 3.3
              • Exercise 3.4
            • Chapter 4 Measurement of Angles
              • Exercise 4.1
            • Chapter 5 Trigonometric Functions
              • Exercise 5.1
              • Exercise 5.2
              • Exercise 5.3
            • Chapter 6 Graphs of Trigonometric Functions
              • Exercise 6.1
              • Exercise 6.2
              • Exercise 6.3
            • Chapter 7 Trigonometric Ratios of Compound Angles
              • Exercise 7.1
              • Exercise 7.2
            • Chapter 8 Transformation Formulae
              • Exercise 8.1
              • Exercise 8.2
            • Chapter 9 Trigonometric Ratios of Multiple and Submultiple Angles
              • Exercise 9.1
              • Exercise 9.2
              • Exercise 9.3
            • Chapter 10 Sine and Cosine Formulae and Their Applications
              • Exercise 10.1
              • Exercise 10.2
            • Chapter 11 Trigonometric Equations
              • Exercise 11.1
            • Chapter 12 Mathematical Induction
              • Exercise 12.1
              • Exercise 12.2
            • Chapter 13 Complex Numbers
              • Exercise 13.1
              • Exercise 13.2
              • Exercise 13.3
              • Exercise 13.4
            • Chapter 14 Quadratic Equations
              • Exercise 14.1
              • Exercise 14.2
            • Chapter 15 Linear Inequations
              • Exercise 15.1
              • Exercise 15.2
              • Exercise 15.3
              • Exercise 15.4
              • Exercise 15.5
              • Exercise 15.6
            • Chapter 16 Permutations
              • Exercise 16.1
              • Exercise 16.2
              • Exercise 16.3
              • Exercise 16.4
              • Exercise 16.5
            • Chapter 17 Combinations
              • Exercise 17.1
              • Exercise 17.2
              • Exercise 17.3
            • Chapter 18 Binomial Theorem
              • Exercise 18.1
              • Exercise 18.2
            • Chapter 19 Arithmetic Progressions
              • Exercise 19.1
              • Exercise 19.2
              • Exercise 19.3
              • Exercise 19.4
              • Exercise 19.5
              • Exercise 19.6
              • Exercise 19.7
            • Chapter 20 Geometric Progressions
              • Exercise 20.1
              • Exercise 20.2
              • Exercise 20.3
              • Exercise 20.4
              • Exercise 20.5
              • Exercise 20.6
            • Chapter 21 Some Special Series
              • Exercise 21.1
              • Exercise 21.2
            • Chapter 22 Brief Review of Cartesian System of Rectangular Coordinates
              • Exercise 22.1
              • Exercise 22.2
              • Exercise 22.3
            • Chapter 23 The Straight Lines
              • Exercise 23.1
              • Exercise 23.2
              • Exercise 23.3
              • Exercise 23.4
              • Exercise 23.5
              • Exercise 23.6
              • Exercise 23.7
              • Exercise 23.8
              • Exercise 23.9
              • Exercise 23.11
              • Exercise 23.12
              • Exercise 23.13
              • Exercise 23.14
              • Exercise 23.15
              • Exercise 23.16
              • Exercise 23.17
              • Exercise 23.18
              • Exercise 23.19
            • Chapter 24 The Circle
              • Exercise 24.1
              • Exercise 24.2
              • Exercise 24.3
            • Chapter 25 Parabola
              • Exercise 25.1
            • Chapter 26 Ellipse
              • Exercise 26.1
            • Chapter 27 Hyperbola
              • Exercise 27.1
            • Chapter 28 Introduction to 3D Coordinate Geometry
              • Exercise 28.1
              • Exercise 28.2
              • Exercise 28.3
            • Chapter 29 Limits
              • Exercise 29.1
              • Exercise 29.2
              • Exercise 29.3
              • Exercise 29.4
              • Exercise 29.5
              • Exercise 29.6
              • Exercise 29.7
              • Exercise 29.8
              • Exercise 29.9
              • Exercise 29.11
            • Chapter 30 Derivatives
              • Exercise 30.1
              • Exercise 30.2
              • Exercise 30.3
              • Exercise 30.4
              • Exercise 30.5
            • Chapter 31 Mathematical Reasoning
              • Exercise 31.1
              • Exercise 31.2
              • Exercise 31.3
              • Exercise 31.4
              • Exercise 31.5
              • Exercise 31.6
              • Exercise 32.2
              • Exercise 32.3
              • Exercise 32.4
            • Chapter 32 Statistics
              • Exercise 32.1
              • Exercise 32.5
              • Exercise 32.6
              • Exercise 32.7
              • Exercise 33.3
            • Chapter 33 Probability
              • Exercise 33.1
              • Exercise 33.2
              • Exercise 33.4
          • Science
          • Social Studies
        • class-12
          • Mathematics
            • Chapter 1 Relations
              • Exercise 1.1
              • Exercise 1.2
            • Chapter 2 Functions
              • Exercise 2.1
              • Exercise 2.2
              • Exercise 2.3
            • Chapter 3 Binary Operations
              • Exercise 3.1
              • Exercise 3.2
              • Exercise 3.3
              • Exercise 3.4
              • Exercise 3.5
            • Chapter 4 Inverse Trigonometric Functions
              • Exercise 4.1
            • Chapter 5 Algebra of Matrices
              • Exercise 5.1
              • Exercise 5.2
              • Exercise 5.3
              • Exercise 5.4
              • Exercise 5.5
            • Chapter 6 Determinants
              • Exercise 6.1
              • Exercise 6.2
              • Exercise 6.3
              • Exercise 6.4
              • Exercise 6.5
            • Chapter 7 Adjoint and Inverse of a Matrix
              • Exercise 7.1
              • Exercise 7.2
            • Chapter 8 Solution of Simultaneous Linear Equations
              • Exercise 8.1
              • Exercise 8.2
            • Chapter 9 Continuity
              • Exercise 9.1
              • Exercise 9.2
            • Chapter 10 Differentiability
              • Exercise 10.1
              • Exercise 10.2
            • Chapter 11 Differentiation
              • Exercise 11.1
              • Exercise 11.2
              • Exercise 11.3
              • Exercise 11.4
              • Exercise 11.5
              • Exercise 11.6
              • Exercise 11.7
              • Exercise 11.8
            • Chapter 12 Higher Order Derivatives
              • Exercise 12.1
            • Chapter 13 Derivative as a Rate Measurer
              • Exercise 13.1
              • Exercise 13.2
            • Chapter 14 Differentials, Errors and Approximations
              • Exercise 14.1
            • Chapter 15 Mean Value Theorems
              • Exercise 15.1
              • Exercise 15.2
            • Chapter 16 Tangents and Normals
              • Exercise 16.1
              • Exercise 16.2
              • Exercise 16.3
            • Chapter 17 Increasing and Decreasing Functions
              • Exercise 17.1
              • Exercise 17.2
            • Chapter 18 Maxima and Minima
              • Exercise 18.1
              • Exercise 18.2
              • Exercise 18.3
              • Exercise 18.4
              • Exercise 18.5
            • Chapter 19 Indefinite Integrals
              • Exercise 19.1
              • Exercise 19.1(1)
              • Exercise 19.2
              • Exercise 19.2(1)
              • Exercise 19.3
              • Exercise 19.3(1)
              • Exercise 19.4
              • Exercise 19.5
              • Exercise 19.6
              • Exercise 19.7
              • Exercise 19.8
              • Exercise 19.9
              • Exercise 19.11
              • Exercise 19.12
              • Exercise 19.13
              • Exercise 19.14
              • Exercise 19.15
              • Exercise 19.16
              • Exercise 19.17
              • Exercise 19.18
              • Exercise 19.19
              • Exercise 19.21
              • Exercise 19.22
              • Exercise 19.23
              • Exercise 19.24
              • Exercise 19.25
              • Exercise 19.26
              • Exercise 19.27
              • Exercise 19.28
              • Exercise 19.29
              • Exercise.19.31
              • Exercise 19.32
            • Chapter 20 Definite Integrals
              • Exercise 20.1
              • Exercise 20.2
              • Exercise 20.3
              • Exercise 20.4
              • Exercise 20.5
            • Chapter 21 Areas of Bounded Regions
              • Exercise 21.1
              • Exercise 21.2
              • Exercise 21.3
              • Exercise 21.4
            • Chapter 22 Differential Equations
              • Exercise 22.1
              • Exercise 22.1(1)
              • Exercise 22.2
              • Exercise 22.3
              • Exercise 22.4
              • Exercise 22.5
              • Exercise 22.6
              • Exercise 22.7
              • Exercise 22.8
              • Exercise 22.9
              • Exercise 22.11
            • Chapter 23 Algebra of Vectors
              • Exercise 23.1
              • Exercise 23.2
              • Exercise 23.3
              • Exercise 23.4
              • Exercise 23.5
              • Exercise 23.6
              • Exercise 23.7
              • Exercise 23.8
              • Exercise 23.9
            • Chapter 24 Scalar or Dot Product
              • Exercise 24.1
              • Exercise 24.2
            • Chapter 25 Vector or Cross Product
              • Exercise 25.1
            • Chapter 26 Scalar Triple Product
              • Exercise 26.1
            • Chapter 27 Direction Cosines and Direction Ratios
              • Exercise 27.1
            • Chapter 28 The Straight Line in Space
              • Exercise 28.1
              • Exercise 28.2
              • Exercise 28.3
              • Exercise 28.4
              • Exercise 28.5
            • Chapter 29 The Plane
              • Exercise 29.1
              • Exercise 29.1(1)
              • Exercise 29.2
              • Exercise 29.3
              • Exercise 29.4
              • Exercise 29.5
              • Exercise 29.6
              • Exercise 29.7
              • Exercise 29.8
              • Exercise 29.9
              • Exercise 29.11
              • Exercise 29.12
              • Exercise 29.13
              • Exercise 29.14
              • Exercise 29.15
            • Chapter 30 Linear Programming
              • Exercise 30.1
              • Exercise 30.2
              • Exercise 30.3
              • Exercise 30.4
              • Exercise 30.5
            • Chapter 31 Probability
              • Exercise 31.1
              • Exercise 31.2
              • Exercise 31.3
              • Exercise 31.4
              • Exercise 31.5
              • Exercise 31.6
              • Exercise 31.7
            • Chapter 32 Mean and Variance of a Random Variable
              • Exercise 32.1
              • Exercise 32.2
            • Chapter 33 Binomial Distribution
              • Exercise 33.1
              • Exercise 33.2
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          • Part A - Statistics for Economics
          • Part B - Introductory Micro Economics
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          • Section C - Changing Traditions
          • Section D - Paths to Modernisation
        • Class-12
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          • Accounts Part I
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          • History Part I
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          • Geography I (Fundamentals of Human Geography)
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          • CCT Part-I
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          • General Basic English
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          • Part A - Statistics for Economics
          • Part B - Introductory Micro Economics
          • Section A - Early Societies
          • Section B - Empires
          • Section C - Changing Traditions
          • Section D - Paths to Modernisation
        • Class-12
          • Mathematics
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          • Accounts Part I
          • Accounts Part II
          • Business Studies
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          • Macro Economics
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          • History Part I
          • History Part II
          • History Part III
          • Geography I (Fundamentals of Human Geography)
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          • Geography III (India- People and Economy)
          • General Basic English
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      • Goa
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        • Class-3
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        • Class-4
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        • Class-5
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        • Class-6
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        • Class-9
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        • Class-11
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          • Geography Part I
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          • CCT Part-I
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          • General Basic English
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          • General Advanced English
          • Part A - Statistics for Economics
          • Part B - Introductory Micro Economics
          • Section A - Early Societies
          • Section B - Empires
          • Section C - Changing Traditions
          • Section D - Paths to Modernisation
        • Class-12
          • Mathematics
          • Biology
          • Chemistry
          • Physics
          • Accounts Part I
          • Accounts Part II
          • Business Studies
          • Indian Economic Development
          • Macro Economics
          • Political Science I
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          • History Part I
          • History Part II
          • History Part III
          • Geography I (Fundamentals of Human Geography)
          • Geography II (Practical Work in Geography II)
          • Geography III (India- People and Economy)
          • General Basic English
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          • General Advanced English
      • Chhattisgarh
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        • Class-1
          • Mathematics
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        • Class-2
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        • Class-3
          • Mathematics
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          • General Basic English
        • Class-4
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          • General Basic English
        • Class-5
          • Mathematics
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        • Class-6
          • Mathematics
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        • Class-7
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        • Class-8
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        • Class-9
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          • Geography Part I
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          • CCT Part-I
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          • General Basic English
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          • Part A - Statistics for Economics
          • Part B - Introductory Micro Economics
          • Section A - Early Societies
          • Section B - Empires
          • Section C - Changing Traditions
          • Section D - Paths to Modernisation
        • Class-12
          • Mathematics
          • Biology
          • Chemistry
          • Physics
          • Accounts Part I
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          • Business Studies
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          • Macro Economics
          • Political Science I
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          • History Part I
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          • History Part III
          • Geography I (Fundamentals of Human Geography)
          • Geography II (Practical Work in Geography II)
          • Geography III (India- People and Economy)
          • General Basic English
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          • General Advanced English
      • Gujarat
        • Class-KG
          • KG (English)
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        • Class-1
          • Mathematics
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        • Class-2
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        • Class-3
          • Mathematics
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          • General Basic English
        • Class-4
          • Mathematics
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          • General Basic English
        • Class-5
          • Mathematics
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        • Class-6
          • Mathematics
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        • Class-7
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          • History
          • General Computer
          • General Basic English
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        • Class-8
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          • Geography
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          • History Part I
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          • General Computer
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        • Class-9
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        • Class-10
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          • Geography
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          • History
          • General Computer
          • General Basic English
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        • Class-11
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          • Financial Accounting I
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          • Geography Part I
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          • Accountancy II
          • Geography Part III
          • CCT Part-I
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          • General Basic English
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          • General Advanced English
          • Part A - Statistics for Economics
          • Part B - Introductory Micro Economics
          • Section A - Early Societies
          • Section B - Empires
          • Section C - Changing Traditions
          • Section D - Paths to Modernisation
        • Class-12
          • Mathematics
          • Biology
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          • Accounts Part I
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          • Business Studies
          • Indian Economic Development
          • Macro Economics
          • Political Science I
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          • History Part I
          • History Part II
          • History Part III
          • Geography I (Fundamentals of Human Geography)
          • Geography II (Practical Work in Geography II)
          • Geography III (India- People and Economy)
          • General Basic English
          • General Intermediate English
          • General Advanced English
      • Karnataka
        • Class-KG
          • KG (English)
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        • Class-1
          • Mathematics
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        • Class-2
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        • Class-3
          • Mathematics
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          • General Basic English
        • Class-4
          • Mathematics
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          • General Basic English
        • Class-5
          • Mathematics
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          • General Basic English
        • Class-6
          • Mathematics
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          • History
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        • Class-7
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          • History
          • General Computer
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        • Class-8
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          • Geography
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          • History Part I
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          • General Computer
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        • Class-9
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          • Physics
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          • History
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          • General Computer
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        • Class-10
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          • Physics
          • Geography
          • Economics
          • Political Science
          • History
          • General Computer
          • General Basic English
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          • General Advanced English
        • Class-11
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          • Financial Accounting I
          • Business Studies
          • Political Science I
          • Political Science II
          • Geography Part I
          • Geography Part II
          • Accountancy II
          • Geography Part III
          • CCT Part-I
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          • General Basic English
          • General Intermediate English
          • General Advanced English
          • Part A - Statistics for Economics
          • Part B - Introductory Micro Economics
          • Section A - Early Societies
          • Section B - Empires
          • Section C - Changing Traditions
          • Section D - Paths to Modernisation
        • Class-12
          • Mathematics
          • Biology
          • Chemistry
          • Physics
          • Accounts Part I
          • Accounts Part II
          • Business Studies
          • Indian Economic Development
          • Macro Economics
          • Political Science I
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          • History Part I
          • History Part II
          • History Part III
          • Geography I (Fundamentals of Human Geography)
          • Geography II (Practical Work in Geography II)
          • Geography III (India- People and Economy)
          • General Basic English
          • General Intermediate English
          • General Advanced English
      • Jammu & Kashmir
        • Class-KG
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          • KG (Hindi)
        • Class-1
          • Mathematics
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          • General Basic English
        • Class-2
          • Mathematics
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          • General Basic English
        • Class-3
          • Mathematics
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          • General Basic English
        • Class-4
          • Mathematics
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          • General Basic English
        • Class-5
          • Mathematics
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          • General Basic English
        • Class-6
          • Mathematics
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          • Civics
          • History
          • General Computer
          • General Basic English
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        • Class-7
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          • Civics
          • History
          • General Computer
          • General Basic English
          • General Intermediate English
        • Class-8
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          • Geography
          • Civics
          • History Part I
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          • General Computer
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        • Class-9
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          • Physics
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          • History
          • General Computer
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        • Class-11
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          • Financial Accounting I
          • Business Studies
          • Political Science I
          • Political Science II
          • Geography Part I
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          • Accountancy II
          • Geography Part III
          • CCT Part-I
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          • General Basic English
          • General Intermediate English
          • General Advanced English
          • Part A - Statistics for Economics
          • Part B - Introductory Micro Economics
          • Section A - Early Societies
          • Section B - Empires
          • Section C - Changing Traditions
          • Section D - Paths to Modernisation
        • Class-12
          • Mathematics
          • Biology
          • Chemistry
          • Physics
          • Accounts Part I
          • Accounts Part II
          • Business Studies
          • Indian Economic Development
          • Macro Economics
          • Political Science I
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          • History Part I
          • History Part II
          • History Part III
          • Geography I (Fundamentals of Human Geography)
          • Geography II (Practical Work in Geography II)
          • Geography III (India- People and Economy)
          • General Basic English
          • General Intermediate English
          • General Advanced English
      • Uttar Pradesh
        • Class-KG
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        • Class-1
          • Mathematics
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          • General Basic English
        • Class-2
          • Mathematics
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          • General Basic English
        • Class-3
          • Mathematics
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          • General Basic English
        • Class-4
          • Mathematics
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          • General Basic English
        • Class-5
          • Mathematics
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          • General Basic English
        • Class-6
          • Mathematics
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          • History
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          • General Basic English
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        • Class-7
          • Mathematics
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          • Civics
          • History
          • General Computer
          • General Basic English
          • General Intermediate English
        • Class-8
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          • Geography
          • Civics
          • History Part I
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          • General Computer
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        • Class-9
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          • Physics
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        • Class-11
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          • Financial Accounting I
          • Business Studies
          • Political Science I
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          • Geography Part I
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          • Accountancy II
          • Geography Part III
          • CCT Part-I
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          • General Basic English
          • General Intermediate English
          • General Advanced English
          • Part A - Statistics for Economics
          • Part B - Introductory Micro Economics
          • Section A - Early Societies
          • Section B - Empires
          • Section C - Changing Traditions
          • Section D - Paths to Modernisation
        • Class-12
          • Mathematics
          • Biology
          • Chemistry
          • Physics
          • Accounts Part I
          • Accounts Part II
          • Business Studies
          • Indian Economic Development
          • Macro Economics
          • Political Science I
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          • History Part I
          • History Part II
          • History Part III
          • Geography I (Fundamentals of Human Geography)
          • Geography II (Practical Work in Geography II)
          • Geography III (India- People and Economy)
          • General Basic English
          • General Intermediate English
          • General Advanced English
      • Rajasthan
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        • Class-1
          • Mathematics
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          • General Basic English
        • Class-2
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        • Class-3
          • Mathematics
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          • General Basic English
        • Class-4
          • Mathematics
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          • General Basic English
        • Class-5
          • Mathematics
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          • General Basic English
        • Class-6
          • Mathematics
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          • Civics
          • History
          • General Computer
          • General Basic English
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        • Class-7
          • Mathematics
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          • Civics
          • History
          • General Computer
          • General Basic English
          • General Intermediate English
        • Class-8
          • Mathematics
          • Science
          • Geography
          • Civics
          • History Part I
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          • General Computer
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          • General Intermediate English
        • Class-9
          • Mathematics
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          • Biology
          • Physics
          • Economics
          • Geography
          • History
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          • General Computer
          • General Basic English
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          • General Advanced English
        • Class-10
          • Mathematics
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          • Physics
          • Geography
          • Economics
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          • History
          • General Computer
          • General Basic English
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          • General Advanced English
        • Class-11
          • Mathematics
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          • Physics
          • Financial Accounting I
          • Business Studies
          • Political Science I
          • Political Science II
          • Geography Part I
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          • Accountancy II
          • Geography Part III
          • CCT Part-I
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          • General Basic English
          • General Intermediate English
          • General Advanced English
          • Part A - Statistics for Economics
          • Part B - Introductory Micro Economics
          • Section A - Early Societies
          • Section B - Empires
          • Section C - Changing Traditions
          • Section D - Paths to Modernisation
        • Class-12
          • Mathematics
          • Biology
          • Chemistry
          • Physics
          • Accounts Part I
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          • Business Studies
          • Indian Economic Development
          • Macro Economics
          • Political Science I
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          • History Part I
          • History Part II
          • History Part III
          • Geography I (Fundamentals of Human Geography)
          • Geography II (Practical Work in Geography II)
          • Geography III (India- People and Economy)
          • General Basic English
          • General Intermediate English
          • General Advanced English
      • Maharashtra
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        • Class-1
          • Mathematics
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        • Class-2
          • Mathematics
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        • Class-3
          • Mathematics
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          • General Basic English
        • Class-4
          • Mathematics
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          • General Basic English
        • Class-5
          • Mathematics
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          • General Basic English
        • Class-6
          • Mathematics
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          • History
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        • Class-7
          • Mathematics
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          • Civics
          • History
          • General Computer
          • General Basic English
          • General Intermediate English
        • Class-8
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          • Geography
          • Civics
          • History Part I
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          • General Computer
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          • Mathematics
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          • Financial Accounting I
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          • Geography Part I
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          • Accountancy II
          • Geography Part III
          • CCT Part-I
          • CCT Part-II
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          • General Intermediate English
          • General Advanced English
          • Part A - Statistics for Economics
          • Part B - Introductory Micro Economics
          • Section A - Early Societies
          • Section B - Empires
          • Section C - Changing Traditions
          • Section D - Paths to Modernisation
        • Class-12
          • Mathematics
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          • Accounts Part I
          • Accounts Part II
          • Business Studies
          • Indian Economic Development
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          • Political Science I
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          • History Part I
          • History Part II
          • History Part III
          • Geography I (Fundamentals of Human Geography)
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          • Geography III (India- People and Economy)
          • General Basic English
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        • Class-4
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        • Class-11
          • Mathematics
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          • Financial Accounting I
          • Business Studies
          • Political Science I
          • Political Science II
          • Geography Part I
          • Geography Part II
          • Accountancy II
          • Geography Part III
          • CCT Part-I
          • CCT Part-II
          • General Basic English
          • General Intermediate English
          • General Advanced English
          • Part A - Statistics for Economics
          • Part B - Introductory Micro Economics
          • Section A - Early Societies
          • Section B - Empires
          • Section C - Changing Traditions
          • Section D - Paths to Modernisation
        • Class-12
          • Mathematics
          • Biology
          • Chemistry
          • Physics
          • Accounts Part I
          • Accounts Part II
          • Business Studies
          • Indian Economic Development
          • Macro Economics
          • Political Science I
          • Political Science II
          • History Part I
          • History Part II
          • History Part III
          • Geography I (Fundamentals of Human Geography)
          • Geography II (Practical Work in Geography II)
          • Geography III (India- People and Economy)
          • General Basic English
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        • Class-4
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        • Class-5
          • Mathematics
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        • Class-6
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        • Class-7
          • Mathematics
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        • Class-8
          • Mathematics
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          • Geography
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          • History Part I
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          • General Computer
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        • Class-9
          • Mathematics
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        • Class-10
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        • Class-11
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          • Geography Part I
          • Geography Part II
          • Accountancy II
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          • CCT Part-I
          • CCT Part-II
          • General Basic English
          • General Intermediate English
          • General Advanced English
          • Part A - Statistics for Economics
          • Part B - Introductory Micro Economics
          • Section A - Early Societies
          • Section B - Empires
          • Section C - Changing Traditions
          • Section D - Paths to Modernisation
        • Class-12
          • Mathematics
          • Biology
          • Chemistry
          • Physics
          • Accounts Part I
          • Accounts Part II
          • Business Studies
          • Indian Economic Development
          • Macro Economics
          • Political Science I
          • Political Science II
          • History Part I
          • History Part II
          • History Part III
          • Geography I (Fundamentals of Human Geography)
          • Geography II (Practical Work in Geography II)
          • Geography III (India- People and Economy)
          • General Basic English
          • General Intermediate English
          • General Advanced English
      • Tripura
        • Class-KG
          • KG (English)
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        • Class-1
          • Mathematics
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          • General Basic English
        • Class-2
          • Mathematics
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        • Class-3
          • Mathematics
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        • Class-4
          • Mathematics
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        • Class-5
          • Mathematics
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        • Class-6
          • Mathematics
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        • Class-7
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        • Class-8
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          • History Part I
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        • Class-9
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        • Class-10
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          • General Computer
          • General Basic English
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        • Class-11
          • Mathematics
          • Biology
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          • Physics
          • Financial Accounting I
          • Business Studies
          • Political Science I
          • Political Science II
          • Geography Part I
          • Geography Part II
          • Accountancy II
          • Geography Part III
          • CCT Part-I
          • CCT Part-II
          • General Basic English
          • General Intermediate English
          • General Advanced English
          • Part A - Statistics for Economics
          • Part B - Introductory Micro Economics
          • Section A - Early Societies
          • Section B - Empires
          • Section C - Changing Traditions
          • Section D - Paths to Modernisation
        • Class-12
          • Mathematics
          • Biology
          • Chemistry
          • Physics
          • Accounts Part I
          • Accounts Part II
          • Business Studies
          • Indian Economic Development
          • Macro Economics
          • Political Science I
          • Political Science II
          • History Part I
          • History Part II
          • History Part III
          • Geography I (Fundamentals of Human Geography)
          • Geography II (Practical Work in Geography II)
          • Geography III (India- People and Economy)
          • General Basic English
          • General Intermediate English
          • General Advanced English
      • Mizoram
        • Class-KG
          • KG (English)
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        • Class-1
          • Mathematics
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          • General Basic English
        • Class-2
          • Mathematics
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        • Class-3
          • Mathematics
          • Environmental Studies
          • General Basic English
        • Class-4
          • Mathematics
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          • General Basic English
        • Class-5
          • Mathematics
          • Environmental Studies
          • General Basic English
        • Class-6
          • Mathematics
          • Science
          • Geography
          • Civics
          • History
          • General Computer
          • General Basic English
          • General Intermediate English
        • Class-7
          • Mathematics
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          • Geography
          • Civics
          • History
          • General Computer
          • General Basic English
          • General Intermediate English
        • Class-8
          • Mathematics
          • Science
          • Geography
          • Civics
          • History Part I
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          • General Computer
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          • General Intermediate English
        • Class-9
          • Mathematics
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          • Civics
          • General Computer
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        • Class-10
          • Mathematics
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          • Physics
          • Geography
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          • History
          • General Computer
          • General Basic English
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          • General Advanced English
        • Class-11
          • Mathematics
          • Biology
          • Chemistry
          • Physics
          • Financial Accounting I
          • Business Studies
          • Political Science I
          • Political Science II
          • Geography Part I
          • Geography Part II
          • Accountancy II
          • Geography Part III
          • CCT Part-I
          • CCT Part-II
          • General Basic English
          • General Intermediate English
          • General Advanced English
          • Part A - Statistics for Economics
          • Part B - Introductory Micro Economics
          • Section A - Early Societies
          • Section B - Empires
          • Section C - Changing Traditions
          • Section D - Paths to Modernisation
        • Class-12
          • Mathematics
          • Biology
          • Chemistry
          • Physics
          • Accounts Part I
          • Accounts Part II
          • Business Studies
          • Indian Economic Development
          • Macro Economics
          • Political Science I
          • Political Science II
          • History Part I
          • History Part II
          • History Part III
          • Geography I (Fundamentals of Human Geography)
          • Geography II (Practical Work in Geography II)
          • Geography III (India- People and Economy)
          • General Basic English
          • General Intermediate English
          • General Advanced English
      • Nagaland
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          • KG (Hindi)
        • Class-1
          • Mathematics
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          • General Basic English
        • Class-2
          • Mathematics
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          • General Basic English
        • Class-3
          • Mathematics
          • Environmental Studies
          • General Basic English
        • Class-4
          • Mathematics
          • Environmental Studies
          • General Basic English
        • Class-5
          • Mathematics
          • Environmental Studies
          • General Basic English
        • Class-6
          • Mathematics
          • Science
          • Geography
          • Civics
          • History
          • General Computer
          • General Basic English
          • General Intermediate English
        • Class-7
          • Mathematics
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          • Geography
          • Civics
          • History
          • General Computer
          • General Basic English
          • General Intermediate English
        • Class-8
          • Mathematics
          • Science
          • Geography
          • Civics
          • History Part I
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          • General Computer
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          • General Intermediate English
        • Class-9
          • Mathematics
          • Chemistry
          • Biology
          • Physics
          • Economics
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          • History
          • Civics
          • General Computer
          • General Basic English
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          • General Advanced English
        • Class-10
          • Mathematics
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          • Biology
          • Physics
          • Geography
          • Economics
          • Political Science
          • History
          • General Computer
          • General Basic English
          • General Intermediate English
          • General Advanced English
        • Class-11
          • Mathematics
          • Biology
          • Chemistry
          • Physics
          • Financial Accounting I
          • Business Studies
          • Political Science I
          • Political Science II
          • Geography Part I
          • Geography Part II
          • Accountancy II
          • Geography Part III
          • CCT Part-I
          • CCT Part-II
          • General Basic English
          • General Inter