Free NCERT Solutions for Class 10 Maths PDF format in Hindi and English medium are available to download. * NCERT Solutions* & Exemplar books provide excellent practice including higher order thinking skills (HOTS) for each chapter. So, it is advised to explore these books to make your knowledge foundation better. Some of the books are available as named Revision Book which are confined to latest

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## NCERT Solutions for Class 10 Maths PDF

### Chapter 1: Real Numbers

In class 9, we have studied rational numbers and irrational numbers collectively forming real numbers. Here we will learn the division algorithm (Euclid’s division lemma) and fundamental theorem of arithmetic. Getting LCM and HCF using prime factorisation and Euclid’s division lemma. Proving square roots of 2, 3, 5 are irrational numbers.

#### English Medium Solutions

**Exercise 1.1****Exercise 1.2****Exercise 1.3****Exercise 1.4**

#### हिंदी माध्यम के हल

**प्रश्नावली 1.1****प्रश्नावली 1.2****प्रश्नावली 1.3****प्रश्नावली 1.4****Study Chapter 1 Real Numbers in Detail****NCERT Book for class 10 Maths (English and Hindi Medium)****Revision Book for Class X Maths (All Chapters)****NCERT Exemplar Problems Solutions**

### Chapter 2: Polynomials

We have learnt Degree and coefficient of terms of polynomial and their factorization in class 9. Now we will find the relationship between the zeroes and their coefficient. Use of factor theorem to find the zeroes of the polynomials with degree 2, 3 or 4.

### English medium

#### हिंदी माध्यम के हल

**प्रश्नावली 2.1****प्रश्नावली 2.2****प्रश्नावली 2.3****प्रश्नावली 2.4****NCERT Solutions Chapter 2 Polynomials (Explore)**

### Chapter 3: Pair of Linear Equations in Two Variables

You have studied a linear equation in one variable and two variables in previous class. Now there is solution of pair of linear equations in class 10, using various methods like graphically, elimination, substitution and cross multiplication. Reduction of given equations into simple linear equations and get their solution

**Exercise 3.1****Exercise 3.2****Exercise 3.3****Exercise 3.4****Exercise 3.5****Exercise 3.6****Exercise 3.7****NCERT Solutions Chapter 3 in Hindi & English**

### Chapter 4: Quadratic Equations

Solution of quadratic equations by different methods – Factorization, Completing the square method and using quadratic formula. Checking the nature of roots using discriminant. Questions based on daily life.

#### हिंदी माध्यम के हल

### Chapter 5: Arithmetic Progression

To check whether the given sequence is in Arithmetic Progressions or not. To find the missing term of the AP and sum of the given sequence. To determine AP when sum to n terms is given. Some application base questions from daily life.

**Exercise 5.1****Exercise 5.2****Exercise 5.3****Exercise 5.4****Class 10 Maths Solutions Chapter 5 Click here to study Online**

### Chapter 6: Triangles

Proof of Basic Proportionality theorem (Thales theorem) and question based on this theorem. Proof of Pythagoras theorem and its converse. Area theorem and its applications. Questions based on other theorems which are given for motivation only (proof will not be asked in the examination).

### Chapter 7: Coordinate Geometry

Representation of points in Cartesian plane and finding the distance between two points using distance formula. Section formula to find the ratio and mid points. Formula for area of triangle and to prove the collinearity of three points.

**Exercise 7.1****Exercise 7.2****Exercise 7.3****Exercise 7.4****Class 10 Maths Solutions & Online study Chapter 7**

### Chapter 8: Introduction to Trigonometry

Trigonometry is the oldest branch of mathematics. It is a basic introduction to class 10 about trigonometry. In this chapter we will derive the values of 6 trigonometric functions – sine, cosine, tangent, cotangent, secant and cosecant. Using the relationship between these ratios, proving some identities.

#### हिंदी माध्यम के हल

### Chapter 9: Some Applications of Trigonometry

In this chapter, the techniques are used to solve problems regarding height and distances in life around us. For example, the height of hill, width of river, distance between two celestial objects cannot be measured by measure tape. So, method of trigonometric ratio is helpful in measuring such distances.

**Exercise 9.1 (Question 1 to Question 9)****Exercise 9.1 (Question 10 to Question 16)****NCERT Solutions 10 Maths Chapter 9 Click here**

### Chapter 10: Circles

This chapter includes the intersection of a line and circle in the same plane, tangent to a circle and tangent to a circle in the limiting case of a secant when the two end points of its corresponding chord coincide. Number of tangents from a point to a circle and tangents drawn from same external point to a circle are equal.

### Chapter 11: Constructions

Dividing a line segment into given ratio. Construction of triangle and then constructing a triangle similar to given triangle on the basis of given ratio of sides. Construction of tangent to a circle in different situations.

### Chapter 12: Area Related to Circles

Area and perimeter of plane figures like circle, sector and segments. Areas of combinations of plane figures involving a circle, sector or a segment with some other figures like a rectangle, a square, etc. There is no additional formulae to find these areas.

### Chapter 13: Surface Areas and Volumes

Surface areas and volumes of a combination of solids line hemisphere – cone, cone – cylinder, cylinder – cone, cube – hemisphere, cube – cuboid etc. Conversion of a solid from one shape to another by comparing volume. Frustum of cone and its surface area & volume. Conversion of frustum to other solids.

### Chapter 14: Statistics

Mean of grouped data – direct method, assumed mean and step deviation method (Short cut method). Mode and median of a grouped data using formula. The relation of mean, mode and median (3 median = 2 mean + mode). Graphical representation of cumulative frequency distribution – Ogive. Less than type and more than type frequency table and their graphical representation.

### Chapter 15: Probability

Probability of events associated with experiments where the equally likely assumption hold. Certain event or sure event and impossible event. Questions based on toss of a coin, throwing a die, drawing a card from deck of cards, etc.

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