NCERT Solutions for Class 10 Maths Questions with Solutions  Today we provided free solution for mathematics student for class 10th  .If you want to download PDF, you can download file by clicking on the given download and save it on your mobile or laptop or PC. All NCERT math solution for class 10th  is available in these PDF files . It is very important for all of student .  We have explained quite a simple way we have covered all the chapters according to guide for NCERT book the solutions is applicable for all the board.

## NCERT Solutions for Class 10 (Maths) All 1 to 15 Chapters

#### Chapter -1 Real Number

A real number is a number that can be found on the number line. These are the numbers that we normally use and apply in real-world applications.

The topics and sub-topics in Chapter 1 Real Number are Given Below

• Ex 1.1 – Introduction,
• Ex 1.2 – Euclid’s Division Lemma,
• Ex 1.3 – The Fundamental Theorem of Arithmetic,
• Ex 1.4 – Revisiting Irrational Numbers,
• Ex 1.5 – Revisiting Rational Numbers and Their Decimal Expansions and
• Ex 1.6 – Summary.

#### Chapter – 2 . Polynomial

Polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

• Ex 2.1 – Introduction,
• Ex 2.2 – Geometrical Meaning of the Zeroes of a Polynomial,
• Ex 2.3 – Relationship between Zeroes and Coefficients of a Polynomial,
• Ex 2.4 – Division Algorithm for Polynomials and
• Ex 2.5 – Summary.

We cover all the exercises in the chapter given below:-

#### Chapter – 3. Linear equations in two variables

Linear equations in two variables are equations which can be expressed as ax + by + c = 0, where a, b and c are real numbers and both a, and b are not zero. The solution of such equations is a pair of values for x and y  which makes both sides of the equation equal.

• Ex 3.1 -Introduction,
• Ex 3.2 – Pair of Linear Equations in Two Variables,
• Ex 3.3 – Graphical Method of Solution of a pair of Linear Equations,
• Ex 3.4 – Algebraic Methods of Solving a Pair of Linear Equations,
• Ex 3.4.1 – Substitution Method
• Ex 3.4.2 – Elimination Method
• Ex 3.4.3 – Cross-Multiplication Method
• Ex 3.5 – Equations Reducible to a Pair of Linear Equations in Two Variables and
• Ex 3.6 – Summary.

We cover all exercises in the chapter given below:-

#### Chapter – 4. quadratic equation

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable.

• Ex 4.1 – Introduction,
• Ex 4.2 – Quadratic Equations,
• Ex 4.3 – Solution of a Quadratic Equation by Factorization,
• Ex 4.4 – Solution of a Quadratic Equation by Completing the Square,
• Ex 4.5 – Nature of Roots and
• Ex 4.6 – Summary.

We cover all the exercises in the chapter given below:-

#### Chapter – 5. Arithmetic progression

Arithmetic progression a sequence of numbers in which each differs from the preceding one by a constant quantity (e.g. 1, 2, 3, 4, etc.; 9, 7, 5, 3, etc.).

• Ex 5.1 – Introduction,
• Ex 5.2 – Arithmetic Progressions,
• Ex 5.3 – nth Term of an AP,
• Ex 5.4 – Sum of First n Terms of an AP and
• Ex 5.5 – Summary.

We cover all the exercises in the chapter given below:-

#### Chapter – 6. Triangle

Triangle a plane figure with three straight sides and three angles.

• Ex 6.1 – Introduction
• Ex 6.2 – Similar Figures,
• Ex 6.3 – Similarity of Triangles,
• Ex 6.4 – Criteria for Similarity of Triangles,
• Ex 6.5 – Areas of Similar Triangles,
• Ex 6.6 – Pythagoras Theorem and
• Ex 6.7 – Summary.

We cover all the exercises in the chapter given below:-

#### Chapter – 7. Coordinate geometry

Coordinate geometry is the study of algebraic equations on graphs. An example of coordinate geometry is plotting points, lines and curves on an x and y axis.

• Ex 7.1 – Introduction,
• Ex 7.2 – Distance Formula,
• Ex 7.3 – Section Formula,
• Ex 7.4 – Area of a Triangle and
• Ex 7.5 – Summary.

We cover all exercises in the chapter given below:-

#### Chapter – 8. Trigonometry

Trigonometry – the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

• Ex 8.1 – Introduction,
• Ex 8.2 – Trigonometric Ratios,
• Ex 8.3 – Trigonometric Ratios of Some Specific Angles,
• Ex 8.4 – Trigonometric Ratios of Complementary Angles,
• Ex 8.5 – Trigonometric Identities and
• Ex 8.6 – Summary.

We cover all the exercises in the chapter given below:-

#### Chapter – 9. Applications of Trigonometry:

It may not have direct applications in solving practical issues but used in the various field. For example, trigonometry is used in developing computer music: as you are familiar that sound travels in the form of waves and this wave pattern through a sine or cosine function for developing computer music. Here are few applications where trigonometry and its functions are applicable

• EX 9.1 – Introduction,
• Ex 9.2 – Heights and Distances and
• Ex 9.3 – Summary.

We cover all the exercises in the chapter given below:-

#### Chapter – 10. Circle

Circle round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point.

• Ex 10.1 – Introduction,
• Ex 10.2 – Tangent to a Circle,
• Ex 10.3 – Number of Tangents from a Point on a Circle and
• Ex 10.4 – Summary.

We cover all the exercises in the chapter given below:-

1. EXERCISE 10.1 – 4 Questions With Solutions in PDF
2. EXERCISE 10.2 – 13 Questions With Solutions in PDF

#### Chapter – 11. Construction  in geometry

Construction  in geometry it has a special meaning. Here, construction is the act of drawing geometric shapes using only a compass and straightedge. No measuring of lengths or angles is allowed.

• Ex 11.1 – Introduction
• Ex 11.2 – Division of a Line Segment
• Ex 11.3 – Construction of Tangents to a Circle and
• Ex 11.4 – Summary.

We cover all the exercises in the chapter given below:-

#### Chapter – 12 Areas Related to Circles

. Let’s go over these area formulas one more time.

Area of a Rectangle = Base × Height.
Area of a Square = Base × Height.
Area of a Square = s2
Area of Triangle = ½(Base × Height)
Area of Parallelogram = Base × Height.
Area of Trapezoid = ½(Base1+ Base2) × Height.
Area of Circle = π(radius)2= πr2

• Ex 12.1 – Introduction
• Ex 12.2 – Perimeter and Area of a Circle – A Review
• Ex 12.3 – Areas of Sector and Segment of a Circle
• Ex 12.4 – Areas of Combinations of Plane Figures
• Ex 12.5 – Summary.

We cover all the exercises in the chapter given below:-

#### Chapter -13.  Surface Areas and Volumes

• Ex 13.1 – Introduction have been given below.
• Ex 13.2 – Surface Area of a Combination of Solids
• Ex 13.3 – Volume of a Combination of Solids
• Ex 13.4 – Conversion of Solid from One Shape to Another
• Ex 13.5 – Frustum of a Cone
• Ex 13.6 – Summary.

We cover all exercises in the chapter given below:-

#### Chapter – 14. Statistic

Statistic a fact or piece of data obtained from a study of a large quantity of numerical data.

• Ex 14.1 – Introduction
• Ex 14.2 -Mean of Grouped Data
• Ex 14.3 – Mode of Grouped Data
• Ex 14.4 – Median of Grouped Data
• Ex 14.5 – Graphical Representation of Cumulative Frequency Distribution
• Ex 14.6 – Summary.

We cover all exercises in the chapter given below:-

#### Chapter – 15. Probability

Probability the quality or state of being probable; the extent to which something is likely to happen or be the case.

• EX 15.1 – Introduction
• EX 15.2 – Probability:  A Theoretical Approach
• EX 15.3 – Summary.

We cover all exercises in the chapter given below:-