Telangana Board Class 10th Maths Solutions | Complete Chapter-wise Solutions

Telangana Board Class 10th Maths Solutions

Complete Chapter-wise Solutions for TS SSC Mathematics

Comprehensive TS Board 10th Maths Solutions

Detailed step-by-step solutions for Telangana State Board Class 10 Mathematics textbook. Perfect for exam preparation, homework help, and concept clarification.

All solutions follow the latest TS SSC syllabus and examination pattern.

How to Use These Solutions

1 Select a Chapter

Choose the chapter you need help with from our comprehensive collection of TS Board 10th Maths solutions.

2 Find Your Exercise

Navigate to the specific exercise or problem you want to understand better.

3 Study Step-by-Step

Follow the detailed, step-by-step solutions to understand the methodology and approach.

4 Practice and Verify

Use the solutions to verify your answers and improve your problem-solving skills.

Real Numbers Solutions

Complete solutions for Euclid's division lemma, HCF, LCM, irrational numbers, and decimal expansions.

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Sets Solutions

Detailed solutions for sets, subsets, Venn diagrams, and operations on sets with clear explanations.

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Polynomials Solutions

Step-by-step solutions for zeros of polynomials, relationship between zeros and coefficients.

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Pair of Linear Equations Solutions

Comprehensive solutions for graphical and algebraic methods of solving linear equations.

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Quadratic Equations Solutions

Detailed solutions for solving quadratic equations by factorization and quadratic formula.

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Progressions Solutions

Complete solutions for arithmetic progressions including nth term and sum of n terms.

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Coordinate Geometry Solutions

Step-by-step solutions for distance formula, section formula, and area calculations.

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Similar Triangles Solutions

Detailed solutions for similarity criteria, basic proportionality theorem, and applications.

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Tangents and Secants Solutions

Complete solutions for tangents to circles, properties of tangents, and related theorems.

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Mensuration Solutions

Step-by-step solutions for surface areas and volumes of combinations of solids.

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Trigonometry Solutions

Detailed solutions for trigonometric ratios, identities, and specific angle values.

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Applications of Trigonometry Solutions

Complete solutions for real-world problems involving heights and distances.

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Probability Solutions

Step-by-step solutions for theoretical probability and complementary events.

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Statistics Solutions

Detailed solutions for mean, median, mode of grouped data and graphical representations.

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Chapter-wise Detailed Information

Real Numbers
Sets
Polynomials
Linear Equations
Quadratic Equations
Progressions
Coordinate Geometry
Similar Triangles
Tangents & Secants
Mensuration
Trigonometry
Applications of Trigonometry
Probability
Statistics

Real Numbers Solutions

This chapter covers fundamental concepts of real numbers and their properties with detailed solutions for:

  • Euclid's division lemma and algorithm with step-by-step explanations
  • Fundamental Theorem of Arithmetic applications
  • Revisiting irrational numbers with proof techniques
  • Decimal expansions of rational numbers
  • Finding HCF and LCM using prime factorization method
  • Word problems involving real numbers

Our solutions provide clear, step-by-step explanations following TS Board examination patterns.

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Sets Solutions

This chapter introduces set theory and its applications with comprehensive solutions for:

  • Sets and their representations with detailed examples
  • Types of sets (empty, finite, infinite, equal, equivalent)
  • Subsets and power sets with proper notation
  • Venn diagrams and operations on sets (union, intersection, difference)
  • Practical problems using sets in real-life scenarios
  • Cardinality of sets and related problems

Our solutions help students visualize and understand set operations clearly.

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Polynomials Solutions

This chapter explores polynomial functions and their properties with detailed solutions for:

  • Zeros of a polynomial with graphical representations
  • Relationship between zeros and coefficients
  • Division algorithm for polynomials with remainder theorem
  • Geometrical meaning of zeros on coordinate plane
  • Factorization of polynomials using various methods
  • Word problems involving polynomial equations

Our solutions provide multiple approaches to solving polynomial problems.

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Pair of Linear Equations Solutions

This chapter focuses on solving systems of linear equations with comprehensive solutions for:

  • Graphical method of solution with coordinate plotting
  • Algebraic methods - substitution and elimination
  • Cross-multiplication method with proper steps
  • Equations reducible to linear form
  • Word problems involving linear equations in real contexts
  • Consistent and inconsistent systems analysis

Our solutions demonstrate multiple solving techniques for better understanding.

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Quadratic Equations Solutions

This chapter deals with quadratic equations and their solutions with detailed explanations for:

  • Standard form of quadratic equations
  • Solution by factorization method with step-by-step working
  • Solution by completing the square method
  • Quadratic formula and its derivation
  • Nature of roots based on discriminant analysis
  • Word problems forming quadratic equations

Our solutions cover all solving methods as per TS Board requirements.

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Progressions Solutions

This chapter covers arithmetic progressions and their properties with comprehensive solutions for:

  • Introduction to sequences and series
  • Arithmetic Progressions (AP) with common difference
  • nth term of an AP with formula applications
  • Sum of first n terms of an AP with derivation
  • Applications of AP in real-life situations
  • Word problems involving arithmetic progressions

Our solutions provide clear explanations of progression concepts and formulas.

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Coordinate Geometry Solutions

This chapter introduces the coordinate system and its applications with detailed solutions for:

  • Distance formula with coordinate calculations
  • Section formula (internal and external division)
  • Area of a triangle using coordinates with determinant method
  • Collinearity of points verification
  • Midpoint formula applications
  • Problems involving quadrilateral properties

Our solutions include graphical representations for better visualization.

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Similar Triangles Solutions

This chapter explores similarity of triangles and its applications with comprehensive solutions for:

  • Similar figures and similarity of triangles concepts
  • Criteria for similarity of triangles (AAA, SAS, SSS)
  • Areas of similar triangles with ratio properties
  • Basic Proportionality Theorem (Thales theorem) applications
  • Applications of similarity in real-life problems
  • Pythagoras theorem and its converse

Our solutions provide geometric proofs and practical applications.

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Tangents and Secants Solutions

This chapter focuses on circles and their properties with detailed solutions for:

  • Tangent to a circle and point of contact
  • Number of tangents from a point on a circle
  • Lengths of tangents from external points
  • Secants and their properties with angle theorems
  • Alternate segment theorem applications
  • Problems combining tangents and triangles

Our solutions include geometric proofs and construction steps.

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Mensuration Solutions

This chapter deals with surface areas and volumes of solid figures with comprehensive solutions for:

  • Surface areas and volumes of combinations of solids
  • Conversion of solids from one shape to another
  • Frustum of a cone calculations
  • Surface area and volume of sphere and hemisphere
  • Real-life applications of mensuration
  • Word problems involving multiple solids

Our solutions provide step-by-step calculations with proper units.

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Trigonometry Solutions

This chapter introduces trigonometric ratios and identities with detailed solutions for:

  • Trigonometric ratios and their reciprocal relationships
  • Trigonometric ratios of complementary angles
  • Trigonometric identities with proofs
  • Values of trigonometric ratios of specific angles
  • Solving trigonometric equations
  • Applications of basic trigonometric concepts

Our solutions demonstrate multiple approaches to trigonometric problems.

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Applications of Trigonometry Solutions

This chapter applies trigonometric concepts to real-world problems with comprehensive solutions for:

  • Heights and distances calculations
  • Angle of elevation and depression concepts
  • Solving problems involving two objects
  • Applications in navigation and surveying
  • Word problems with trigonometric applications
  • 3D applications of trigonometry

Our solutions include detailed diagrams and real-world context.

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Probability Solutions

This chapter introduces the concept of probability and its calculation with detailed solutions for:

  • Probability - theoretical approach with formulas
  • Elementary events and sample space determination
  • Complementary events calculations
  • Probability of sure and impossible events
  • Applications of probability in daily life
  • Word problems involving probability concepts

Our solutions provide clear probability calculations and reasoning.

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Statistics Solutions

This chapter covers data analysis and statistical measures with comprehensive solutions for:

  • Mean, median, and mode of grouped data
  • Graphical representation of data (histograms, frequency polygons)
  • Ogive and cumulative frequency distribution
  • Measures of central tendency calculations
  • Real-life applications of statistics
  • Step deviation method for mean calculation

Our solutions demonstrate proper statistical methods and interpretations.

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