NCERT Solutions for Class 10 Maths: Download PDF - Embibe
  • Written By Varsha
  • Last Modified 29-07-2022
  • Written By Varsha
  • Last Modified 29-07-2022

NCERT Solutions for Class 10 Maths: Get PDF

NCERT Solutions for Class 10 Maths: Maths is one of the core subjects in Class 10. Therefore, every student focus on completing the Class 10 Maths syllabus on time. All CBSE students follow the NCERT Class 10 Maths Book and the Class 10 Maths NCERT Solutions. These solutions cover all important mathematical concepts and help students develop vital problem-solving skills. NCERT Solution for Class 10 maths chapter 3: Pair of Linear Equations in Two Variables is one of the most searched portions.

In this article, students can find free NCERT Solutions of Class 10 Maths. These are compiled by Embibe’s top academic experts and help students solve in-text problems in a step-by-step manner. Students can now effortlessly access the chapter-wise 10th maths guide and refer to them for their term 2 board examinations.

NCERT Solutions for Class 10 Maths: Download Subject-wise PDFs

Studying from the NCERT maths class 10 solution helps students understand diverse approaches to in-text questions. They should refer to these solutions while solving NCERT Maths Book in-text exercises and questions.  Click on the links provided below to download chapter-wise PDFs for Class 10 Maths:

Learn Chapter-wise Class 10 Maths NCERT Solutions

The answer key of maths Class 10 has been compiled by professionals in a comprehensive format that will help students clear their questions quickly. It will help them become well-versed on various topics and recall the responses quickly. Students should also evaluate their preparedness by solving previous year’s questions, practice test papers, and worksheets.

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers (Term I)

NCERT Solutions Class 10 Maths Chapter 1: After understanding the basic rules regarding real and irrational numbers in earlier grades, the first chapter of Class 10 Maths starts with some of the most critical concepts in Algebra. The Division Lemma (lemma – an algorithm, a proven statement used to prove other statements) by Euclid is one of the first concepts that students will learn, followed by the Fundamental Theorem of Arithmetic by Carl Freidrich Gauss.

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers (Term I)

Topics covered in Class 10 Maths Chapter 1 Real Numbers for Term 1:

Fundamental Theorem of Arithmetic – Statements along with reviews of earlier works done. Illustrations and clarifications through examples. The decimal representation of rational numbers as both terminating/non-terminating recurring decimals.

Important steps:

To obtain the HCF of two positive integers, say c and d, where c > d, the following steps must be taken:

Step 1: First apply Euclid’s division lemma, to both c and d. This helps us find whole numbers, q and r such that c = dq + r, 0 ≤ r < d.

Step 2: If r = 0, then d is the HCF of c and d. However, if r ≠ 0, then apply the division lemma to d and r.

Step 3: Continue this process until the remainder is zero. The divisor that we obtain at this stage is the required HCF. The reason why this algorithm works is HCF (c, d) = HCF (d, r) where the symbol HCF (c, d) indicates the HCF of c and d, etc.

Chapter 1 NCERT Maths Class 10 PDF Solutions

Topics Deleted for Academic Year 2021-22 Board Exams: Euclid’s division lemma

The total number of exercises and questions are tabulated below:

Exercise No. and NameTotal Questions
Ex 1.1 Euclid’s Division Lemma5 Questions
Ex 1.2 The Fundamental Theorem of Arithmetic7 Questions
Ex 1.3 Revisiting Irrational Numbers3 Questions
Ex 1.4 Revisiting Rational Numbers and Their Decimal Expansions3 Questions
Total: Contains 4 Exercises18 Questions

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials (Term I)

NCERT Solutions Class 10 Maths Chapter 2: Expanding from the basics of polynomials learned in earlier classes, the chapter explains the concept of degree of polynomials and how polynomial with degree 1 is linear polynomial, degree 2 is a quadratic polynomial, and degree 3 a cubic polynomial.

Topics covered in Class 10 Maths Chapter 2 Polynomials for Term I:

The most important topics covered in this article are zeroes of a polynomial and the relationship between zeroes and coefficients of quadratic polynomials only.

Important Steps:

We first arrange the terms of the dividend and the divisor in the decreasing order of their degrees. Recall that arranging the terms in this order is called writing the polynomials in standard form.

Step 1: First we must obtain the first term of the quotient by dividing the highest degree term of the dividend by the highest degree term of the divisor. Then carry out the division process.

Step 2: Then, we can obtain the second term of the quotient by dividing the highest degree term of the new dividend by the highest degree term of the divisor. Carry out the division process again.

Step 3: The degree of the remainder is lesser than the degree of the divisor. So, we cannot continue the division anymore.

We can see here that Dividend = Divisor × Quotient + Remainder. What we are applying here is an algorithm that is similar to Euclid’s division algorithm that you studied in Chapter 1.

This says that:

If p(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that

p(x) = g(x) × q(x) + r(x),

where, r(x) = 0 or degree of r(x) < degree of g(x).

This obtained result is called the Division Algorithm for polynomials.

NCERT Solution for Class 10 Maths Chapter 2 PDF

Topics Deleted for Academic Year 2021-22 Board Exams: Statement and simple problems on division algorithm for polynomials with real coefficients.

The total number of exercises and questions in polynomials are tabulated below:

Exercise No. and NameTotal Questions
Exercise 2.11 Question and Solutions (1 Short Answer)
Exercise 2.22 Questions and Solutions (2 Short Answers)
Exercise 2.35 Questions and Solutions (2 Short Answers, 3 Long Answers)
Exercise 2.45 Questions and Solutions (2 Short Answers, 3 Long Answers)
Total: 4 Exercises13 Questions

NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables (Term I)

NCERT Solutions Class 10 Maths Chapter 3: In this chapter, we will learn several methods such as the substitution method, elimination method, and cross-multiplication method. The final concept in the chapter is the reduction of equations in two variables. A brief summary of the NCERT Solutions for Class 10 Maths Chapter 3 is given below:

NCERT Solutions for Class 10th Maths Chapter 3 PDF

Topics covered in Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables for Term I:

This lesson covers the pair of linear equations in two variables and the graphical method of their solution, consistency/inconsistency, and algebraic conditions for the number of solutions. Solutions of a pair of linear equations in two variables algebraically – by substitution and by elimination, simple situational problems, simple problems on equations reducible to linear equations.

Important formulas:

We have given the general form for a pair of linear equations in two variables x and y below:

(i) a1 x + b1 y + c1 = 0

and

(ii) a2 x + b2 y + c2 = 0,

where a1, b1, c1, a2, b2, c2 are real numbers and where a12 + b12 ≠ 0, a22 + b22 ≠ 0.

Topics Deleted for Academic Year 2021-22 Board Exams: Cross Multiplication Method

The total number of questions and exercises in the chapter pair of linear equations in two variables are tabulated below:

Exercise No. and NameTotal Questions
Exercise 3.13 Questions and Solutions (2 Short Answers, 1 Long Answer)
Exercise 3.27 Questions and Solutions (5 Short Answers, 2 Long Answers)
Exercise 3.33 Questions and Solutions (2 Short Answers, 1 Long Answer)
Exercise 3.42 Questions and Solutions (2 Long Answers)
Exercise 3.54 Questions and Solutions (4 Short Answers)
Exercise 3.62 Questions and Solutions (2 Long Answers)
Exercise 3.78 Questions and Solutions (1 Short Answer, 7 Long Answers)
Total: 7 Exercises24 Questions

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations (Term II)

NCERT Solutions Class 10 Maths Chapter 4: In this chapter, we will learn the standard form of quadratic equations, different methods of solving quadratic equations (by factorization, by completing the square), and the nature of roots. The Quadratic Equation Class 10 PDF solutions will be extremely helpful.

Class 10 NCERT Solutions Maths Chapter 4 PDF

The chapter ends with the topic of finding the nature of roots which states that, a quadratic equation ax² + bx + c = 0 has

  1. two distinct real roots, if b² – 4ac > 0
  2. two equal roots, if b² – 4ac = 0
  3. no real roots, if b² – 4ac < 0

Topics covered in Class 10 Maths Chapter 4 Quadratic Equations for Term II:

The relationship between discriminant and nature of roots, standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0), solutions of quadratic equations (only real roots) by factorisation, and by using the quadratic formula, the relationship between discriminant and nature of roots, situational problems based on quadratic equations are included (problems on equations reducible to quadratic equations are excluded).

Important formulas:

If b 2 – 4ac > 0, we get two distinct real roots

If b 2 – 4ac = 0, then,

So, the roots of the equation ax2 + bx + c = 0 are both -b/2a.

Therefore, we say that the quadratic equation ax2 + bx + c = 0 has two equal real roots in this case.

If b 2 – 4ac < 0, then there is no real number whose square is b 2 – 4ac. Therefore, there are no real roots for the given quadratic equation in this case.

Since b 2 – 4ac determines whether the quadratic equation ax2 + bx + c = 0 has real roots or not, b 2 – 4ac is called the discriminant of this quadratic equation.

So, a quadratic equation ax2 + bx + c = 0 has:

(i) two distinct real roots, if b 2 – 4ac > 0,

(ii) two equal real roots, if b 2 – 4ac = 0,

(iii) no real roots, if b 2 – 4ac < 0.

Topics Deleted for Academic Year 2021-22 Board Exams: Situational problems based on equations reducible to quadratic equations

The total number of exercises and questions in Quadratic Equations for Term II are tabulated below:

Exercise No. & NameTotal Questions
Exercise 4.12 Questions and Solutions (1 Short Answer, 1 Long Answer)
Exercise 4.26 Questions and Solutions (6 Short Answers)
Exercise 4.311 Questions and Solutions (8 Short Answers, 3 Long Answers)
Exercise 4.45 Questions and Solutions (2 Short Answers, 3 Long Answers)
Total: 4 Exercises24 Questions

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions (Term II)

NCERT Solutions Class 10 Maths Chapter 5: Progressions are found in nature as well as in Mathematics. One of the most important ones is the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13, 21,…). However, if we want to find a particular number in the sequence such as the 30th or 40th number, we have to use arithmetic progression. By using simple formulas of arithmetic progression it is possible to find numbers at specific places in a long series.

Topics covered in Class 10 Maths Chapter 5 Arithmetic Progressions for Term II:

Reasons for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P and their real-life application in solving day to day problems.
(Applications based on the sum to n terms of an A.P. are excluded)

Important formulas:

If a1, a2, a3, a4, a5, a6, are terms of an AP and d is the common difference between each term in the AP, we can write the sequence as; a, a+d, a+2d, a+3d, a+4d, a+5d,….,nth term… where a is the first term of the series. So, the nth term for arithmetic progression is given as;

i) nth term = a + (n-1) d

Sum of the first n terms in the Arithmetic Progression;

ii) Sn = n/2 [2a + (n-1) d]

Topics Deleted for Academic Year 2021-22 Board Exams: Application in solving daily life problems based on the sum to n terms

The total number of exercises and questions in Arithmetic Progressions are tabulated below:

Exercise No. & NameTotal Questions
Exercise 5.14 Questions & Solutions (1 Short Answer, 3 Long Answers)
Exercise 5.220 Questions & Solutions (10 Short Answers, 10 Long Answers)
Exercise 5.320 Questions & Solutions (7 Short Answers, 13 Long Answers)
Exercise 5.45 Questions & Solutions (5 Long Answers)
Total: 4 Exercises49 Questions
NCERT Solution Class 10th Maths Chapter 5 PDF

NCERT Solutions for Class 10 Maths Chapter 6 Triangles (Term I)

NCERT Solutions Class 10 Maths Chapter 6: Coming to geometry, we start with triangles. In this chapter, we will learn how similar triangles follow similarities in sizes and angles, and how we can determine similarities to solve problems. We will learn through exercises how to determine such similarities and further learn how to even find areas of triangles that are similar.

NCERT Solutions Class 10 Maths Chapter 6 PDF

Topics covered in Class 10 Maths Chapter 6 Triangles for Term I:

The important topics covered in this chapter are definitions, examples, and counter examples of similar triangles. Moreover,
1. We need to prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
2. Also the converse of this theorem should also be proven, that is, if a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
3. If the corresponding angles are equal in two triangles are equal, their corresponding sides are proportional and the triangles are similar.
4. The converse is also true, that is, if the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
5. Moreover, if one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.
6. If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse of the triangle, the triangles on each side of the perpendicular will be right triangles which are similar to the whole triangle and to each other.
7. The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
8. The square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.
9. If the square on one side of a triangle is equal to the sum of the squares on the other two sides, the angle opposite to the first side is a right angle.

Important theorems:

Theorem 6.1: If we draw a line parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Theorem 6.2: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Theorem 6.3: If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar.

Theorem 6.4: If in two triangles, the sides of one triangle are proportional to (i.e., in the same ratio of ) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.

Theorem 6.5: If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

Theorem 6.6: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Theorem 6.7: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

Theorem 6.8: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Theorem 6.9: In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

Topics Deleted for Academic Year 2021-22 Board Exams: Proof of the following theorems are deleted

  • The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
  • In a triangle, if the square on one side is equal to the sum of the squares on the other two sides, the angle opposite to the first side is a right angle.

The number of exercises and questions included in the Triangles chapter are tabulated below:

Exercise No. and NameTotal Questions
Exercise 6.13 Questions and Solutions (3 Short Answers)
Exercise 6.210 Questions and Solutions (9 Short Answers, 1 Long Answers)
Exercise 6.316 Questions and Solutions (12 Short Answer, 4 Long Answers)
Exercise 6.49 Questions and Solutions (7 Short Answers, 2 Long Answers)
Exercise 6.517 Questions and Solutions (15 Short Answer, 2 Long Answers)
Exercise 6.610 Questions and Solutions (5 Short Answers, 5 Long Answers)
Total: Exercises 665 Questions

NCERT Solutions for Class 10 Maths Chapter 7: Coordinate Geometry (Term I)

NCERT Solutions Class 10 Maths Chapter 7: Furthering the knowledge of triangles, this chapter teaches how we can find the distance between two points through the distance formula for triangles. Similarly, we will also learn how to find areas of triangles through a sectional formula for triangles.

NCERT Solutions for Class 10 Maths Chapter 7: Coordinate Geometry (Term I)

Topics covered in Class 10 Maths Chapter 7 Coordinate Geometry for Term I:

LINES (In two dimensions)
Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division)

Important formulas:

Distance Formula

Distance Formula

Section Formula

Section Formula
Section Formula

Topics Deleted for Academic Year 2021-22 Board Exams: Area of a triangle

The number of exercises and questions included in the coordinate geometry chapter are tabulated below:

Exercise No. and NameTotal Questions
Exercise 7.110 Questions and Solutions (3 Short Answers, 7 Long Answers)
Exercise 7.210 Questions and Solutions (2 Short Answers, 8 Long Answers)
Exercise 7.35 Questions and Solutions (2 Short Answers, 3 Long Answers)
Exercise 7.48 Questions and Solutions (3 Short Answers, 5 Long Answers)
Total Exercises 423 Questions
NCERT Solutions Class 10 Maths Chapter 7 PDF

NCERT Solutions for Class 10 Maths Chapter 8 Introduction To Trignometry (Term I)

NCERT Solutions Class 10 Maths Chapter 8: In Class 10, we finally get to trigonometry – one of the most interesting and practical concepts in the book. Trigonometry is the measurement (metric) of triangles (trigono). Through limited information on angles/distances, formulas in trigonometry help us find areas and distances.

Topics covered in Class 10 Maths Chapter 8 Introduction to Trigonometry for Term I:

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined). Values of the trigonometric ratios of 30 degrees, 45 degrees and 60 degrees. Relationships between the ratios.

Trigonometric Identities:
Proof and applications of the identity sin2A + cos2A = 1.

Important formulas:

Trigonometry Maths formulas for Class 10 cover three major functions Sine, Cosine and Tangent for a right-angle triangle. Let a right-angled triangle ABC is right-angled at point B and have ∠θ.

Trigonometric Identities
Trigonometric Identities
Trigonometric Identities
Trigonometric Identities
Trigonometric Identities
Trigonometric Identities
Trigonometric Identities

Trigonometry Table:

Angle30°45°60°90°
Sinθ01/21/√2√3/21
Cosθ1√3/21/√2½0
Tanθ01/√31√3Undefined
CotθUndefined√311/√30
Secθ12/√3√22Undefined
CosecθUndefined2√22/√31

Trigonometric Ratios of Complementary Angles:

sin (90° – A) = cos A,

cos (90° – A) = sin A,

tan (90° – A) = cot A,

cot (90° – A) = tan A,

sec (90° – A) = cosec A,

cosec (90° – A) = sec A

sin2 A + cos2 A = 1,

sec2 A – tan2 A = 1 for 0° ≤ A < 90°,

cosec2 A = 1 + cot2 A for 0° < A ≤ 90°

Topics Deleted for Academic Year 2021-22 Board Exams: Motivate the ratios whichever are defined at 0o and 90o

The number of exercises and questions included in the introduction to the trigonometry chapter are tabulated below:

Exercise No. & NameTotal Questions
Exercise 8.111 Questions and Solutions (8 Short Answers, 3 Long Answers)
Exercise 8.24 Questions and Solutions (2 Short Answers, 2 Long Answers)
Exercise 8.37 Questions and Solutions (5 Short Answers, 2 Long Answers)
Exercise 8.45 Questions and Solutions (3 Short Answers, 2 Long Answers)
Total Exercises 427 Questions
NCERT Solutions Class 10 Maths Chapter 8 PDF

NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry (Term II)

NCERT Solutions Class 10 Maths Chapter 9: After learning the basics of trigonometry, we will delve into some practical applications of trigonometry. Through the use of trigonometry, we will try to solve practical problems by using concepts such as the line of sight, angle of depression, and angle of elevation to determine height or distance.

HEIGHTS AND DISTANCES- Angle of elevation, Angle of Depression.
Simple problems with heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30°, 45°, 60°.

NCERT Solutions for Class 10 Maths Chapter 9 PDF

Important points:

  • The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.
  • The angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level, i.e., the case when we raise our head to look at the object.
  • The angle of depression of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level, i.e., the case when we lower our head to look at the point being viewed.
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications Of Trigonometry (Term II)

You would need to know the following:

(i) the distance DE at which the student is standing from the foot of the minar.

(ii) the angle of elevation, ∠ BAC, of the top of the minar.

(iii) the height AE of the student.

Assuming that the above three conditions are known, how can we determine the height of the minar?

In the figure, CD = CB + BD. Here, BD = AE, which is the height of the student.

To find BC, we will use trigonometric ratios of ∠ BAC or ∠ A.

In ∆ ABC, the side BC is the opposite side in relation to the known ∠ A. Our search narrows down to using either tan A or cot A, as these ratios involve AB and BC.

Therefore, tan A = BC/AB or cot A = AB/BC, which on solving would give us BC.

By adding AE to BC, you will get the height of the minar.

The number of exercises and questions included in some applications of trigonometry chapter are tabulated below:

Exercise No. and NameTotal Questions
Exercise 9.116 Questions and Solutions (16 Long Answers)
Total Exercises: 116 Questions

NCERT Solutions for Class 10 Maths Chapter 10 Circles (Term II)

NCERT Solutions Class 10 Maths Chapter 10: Students learn about elements related to a circle such as a chord, arc, etc. in Class 9. In this chapter, students will learn about tangents and the different scenarios when lines touch or bisect circles on a given plane. How a line interacts with a circle opens up different possibilities and problems and students will learn how to solve them.

Topics covered in Class 10 Maths Chapter 10 Circles for Term II:

Tangent to a circle at, the point of contact
1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
2. (Prove) The lengths of tangents drawn from an external point to a circle are equal.

Important theorems:

Theorem 10.1: The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Theorem 10.2: The lengths of tangents drawn from an external point to a circle are equal.

Number of Tangents from a Point on a Circle:

Case 1: There is no tangent to a circle passing through a point lying inside the circle.

Case 2: There is one and only one tangent to a circle passing through a point lying on the circle.

Case 3: There are exactly two tangents to a circle through a point lying outside the circle.

NCERT Solutions Class 10 Maths Chapter 10 PDF

The total number of exercises and questions included in the Circles chapter are given below:

Exercise No and NameTotal Questions
Exercise 10.14 Questions and Solutions (2 Short Answers, 2 Long Answers)
Exercise 10.213 Questions and Solutions (2 Short Answers, 14 Long Answers)
Total Exercises 217 Questions

NCERT Solutions for Class 10 Maths Chapter 11 Constructions (Term II)

NCERT Solutions Class 10 Maths Solutions: In this chapter on Construction, we will apply the rules of geometry learned so far, and construct shapes from the dimensions and measurements provided. Using tools such as a ruler, pencil, and protractor, students will form shapes according to different problems in the exercises. Referring to Construction Class 10 PDF solutions is essential for this chapter to check if the structure created by students is as intended in the question.

NCERT Solutions Class 10 Maths Chapter 11 PDF

Topics Covered in Class 10 Maths Chapter 11 Constructions for Term II:

1. Division of a line segment in a given ratio (internally).
2. Tangents to a circle from a point outside it.

Important points:

Construction 11.1: To divide a line segment in a given ratio.

Construction 11.2: To construct a triangle similar to a given triangle as per the given scale factor.

Construction 11.3: To construct the tangents to a circle from a point outside it.

Topics Deleted for Academic Year 2021-22 Board Exams: Construction of a triangle similar to a given triangle.

The total number of exercises and questions included in the constructions chapter are given below:

Exercise No and NameTotal Questions
Exercise 11.17 Questions and Solutions (7 Long Answers)
Exercise 11.27 Questions and Solutions (7 Long Answers)
Total Exercises 214 Questions

NCERT Solutions Class 10 Maths Chapter 12: Circles are some of the commonly found shapes in our surroundings. By merging lines and other shapes within circles, students will learn how to measure the areas of different segments using theorems and the number Pi.

NCERT Solutions Class 10 Maths Chapter 12 PDF

Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter/circumference of the above-said plane figures. (In calculating the area of a segment of a circle, problems should be restricted to the central angle of 60° and 90° only. Plane figures involving triangles, simple quadrilaterals and circles should be taken.)

Important formulas:

circumference = 2πr

area of the circle = πr 2

Area of the sector of angle θ = (θ/360) × π r2

Length of an arc of a sector of angle θ = (θ/360) × 2 π r where r is the radius of the circle

Topics Deleted for Academic Year 2021-22 Board Exams: Problems with the central angle of 120°

The total number of questions and exercises under the chapter Areas Related To Circles are tabulated below:

Exercise No and NameTotal Questions
Exercise 12.15 Questions and Solutions (5 Short Answers)
Exercise 12.214 Questions and Solutions (9 Short Answers, 5 Long Answers)
Exercise 12.316 Questions and Solutions (9 Short Answers, 7 Long Answers)
Total Exercises: 335 Questions

NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas and Volumes (Term II)

NCERT Solutions Class 10 Maths Chapter 13: After looking at shapes on a plane, we move on to a 3-dimensional world and look at shapes like squares or rectangles as cubes or cuboids, triangles as cones, and circles as cylinders or spheres. We will learn in this chapter how to view objects as shapes and solve practical problems such as finding surface area and volume as mentioned in the exercises.

Topics covered in Class 10 Maths Chapter 13 Surface Areas and Volumes for Term II:

1. Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.
2. Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combination of not more than two different solids be taken).

Important formulas:

  • TSA of new solid = CSA of one hemisphere + CSA of cylinder + CSA of another hemisphere
  • Diameter of sphere = 2r
  • Surface area of sphere = 4 π r2
  • Volume of Sphere = 4/3 π r3
  • Curved surface area of Cylinder = 2 πrh
  • Area of two circular bases = 2 πr2
  • Total surface area of Cylinder = Circumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr2
  • Volume of Cylinder = π rh
  • Slant height of cone = l = √(r2 + h2)
  • Curved surface area of cone = πrl
  • Total surface area of cone = πr (l + r)
  • Volume of cone = ⅓ π rh
  • Perimeter of cuboid = 4(l + b +h)
  • Length of the longest diagonal of a cuboid = √(l2 + b2 + h2)
  • Total surface area of cuboid = 2(l×b + b×h + l×h)
  • Volume of Cuboid = l × b × h

Topics Deleted for Academic Year 2021-22 Board Exams: Frustum of a cone

The total number of questions and exercises in the chapter surface areas and volumes are given below:

Exercise No. and NameTotal Questions
Exercise 13.19 Questions and Solutions (2 Short Answers, 7 Long Answers)
Exercise 13.28 Questions and Solutions (1 Short Answer, 7 Long Answers)
Exercise 13.39 Questions and Solutions (9 Long Answers)
Exercise 13.45 Questions and Solutions (5 Long Answers)
Exercise 13.57 Questions and Solutions (7 Long Answers)
Total Exercises 538 Questions
NCERT Solutions Class 10 Maths Chapter 13 PDF

NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Term II)

NCERT Solutions Class 10 Maths Chapter 14: Used holistically in business, economics, and many other areas, we will learn how to find mean (average), median, and mode from a grouped dataset. After learning that, we will also study how to portray data in a graphical manner to understand trends and correlations within data.

NCERT Solutions Class 10 Maths Chapter 14 PDF

Topics covered in Class 10 Maths Chapter 14 Statistics for Term II:

Mean, median and mode of grouped data (bimodal situation to be avoided). Mean by Direct Method and Assumed Mean Method only.

Important formulas:

The mean of the grouped data can be found by 3 methods:

1. Direct Method: x̅ =

Mean of Grouped Data

, where ∑fxis the sum of observations from value i = 1 to n And ∑fis the number of observations from value i = 1 to n

2. Assumed mean method =

Assumed Mean Method

3. Step deviation method: x̅ =

Step Deviation Method

The mode of grouped data:

Mode =

The median for grouped data:

Median =

Median for Grouped Data

Topics Deleted for Academic Year 2021-22 Board Exams: Step deviation Method for finding the mean, Cumulative Frequency graph

Exercise No. and NameTotal Questions
Exercise 14.19 Questions and Solutions (9 Long Answers)
Exercise 14.26 Questions and Solutions (6 Long Answers)
Exercise 14.37 Questions and Solutions (7 Long Answers)
Exercise 14.43 Questions and Solutions (3 Long Answers)
Total Exercises 425 Questions

NCERT Solutions for Class 10 Maths Chapter 15 Probability (Term I)

NCERT Solutions Class 10 Maths Chapter 15: From weather, sports, and politics, to insurance, the probability is used in a multitude of areas. Students will learn some theoretical aspects of probability and apply them to determine impossible events and certain uncertain events. Conclusively, the concepts of probability in the chapter will allow students to learn how to determine the outcomes of events through formulas.

NCERT Solutions Class 10 Maths Chapter 15 PDF

Topics covered in Class 10 Maths Chapter 15 Probability for Term I:

  1. The classical definition of probability
  2. Simple problems on finding the probability of an event

Important formulas:

  1. The theoretical probability (also called classical probability) of an event E, written as P(E), is defined as:

where we assume that the outcomes of the experiment are equally likely.

  1. The probability of a sure event (or certain event) is 1.
  2. The probability of an impossible event is 0.
  3. The probability of an event E is a number P(E) such that 0 ≤ P (E) ≤ 1
  4. An event having only one outcome is called an elementary event. The sum of the probabilities of all the elementary events of an experiment is 1.
Exercise No. and NameTotal Questions
Exercise 15.125 Questions and Solutions (22 Short Answers, 3 Long Answers)
Exercise 15.25 Questions and Solutions (5 Short Answers)
Total Exercises 230 Questions

Embibe’s NCERT Solutions for Class 10 Maths: Key Benefits

At Embibe, students are encouraged to discard the fear of exams and embrace the joy of learning. The subject matter experts are aware of the need for conceptual understanding in students and to let go of rote learning. 

Let us take a look at some of the significant benefits of learning from Embibe:

  • Class 10th Maths NCERT Solutions are easy to understand, solve, and work with.
  • Every subject’s chapter-wise solutions provide maximum conceptual clarity to students.
  • NCERT Class 10 Maths Solutions cover the entire CBSE syllabus to benefit the students in their board exams.
  • Embibe’s NCERT Class 10 Solutions for Maths follow the CBSE marking scheme to prepare the students for the Class 10 board.
  • Solving from NCERT Class 10 Maths Solutions is effective for clearing competitive exams like JEE Mains, NEET, NTSE, etc.

We encourage students to refer to the NCERT solutions for Class 10 and to work with them. Rather than being passive learners, students need to imbibe the solutions, solve the solutions, add to the solutions, etc. Only then would it promote 360-degree learning.

Learn & Practice Class 10 Maths Chapters Online With Embibe

After going through a chapter, it is important to practice questions and attempt mock exams to get better at math. Embibe not only offers students books and solutions to practice and study; but also other resources like practice questions and mock tests. At Embibe, students can take CBSE Class 10 Mock Test. They can also solve CBSE Class 10 Practice Questions on Embibe and check the 10th Class Maths Book solutions if needed.

Both practice questions and mock tests are available for free on Embibe so that students can improve their knowledge and test scores. Furthermore, students can refer to exemplar solutions for Class 10 maths to clear their queries about any particular chapter. This will help them in gaining good marks in their exams.

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You have the simplest alternative at your fingertips if you wish to clear all of your Math problems for CBSE Class 10 Maths. Experts and other students are continuously checking the Embibe’s Talk to an Expert feature to ensure that queries are answered in a thorough and timely way. You may also use the portal to locate interesting questions that other students have asked in order to improve your knowledge.

FAQs on Class 10th Maths NCERT Solutions

Q1. Which is the best learning platform for NCERT Maths Solution Class 10?
Ans: Embibe is the best outcome-based learning platform for detailed NCERT Maths Solutions for Class 10. Experts at Embibe have created a step by step solutions in simple and easy language. Students searching for NCERT Solutions for Class 10 Maths can read this article and download Free NCERT Maths Book Class 10 Solutions from this article.

Q2. Where can I download  NCERT Solutions for Class 10 Maths PDF?
Ans: NCERT Solution for Class 10 Maths is available on this article free of cost. You can download it for later use. 

Q3. How can I save these Class 10 NCERT Maths Solutions for reference?
Ans: You can download the PDF files through the respective chapter links and keep them on your computer or mobile phone for future reference. You can also print these files if you prefer that.  

Q4. How many chapters does the NCERT Maths textbook have?
Ans:
The NCERT Maths textbook for Class 10 features 15 chapters.

Q5. How can I easily learn formulas for all chapters in NCERT Class 10 textbook?
Ans: You can easily refer to this article on Maths formulas for Class 10. It covers the entire syllabus and contains all the formulas that are important for the exam.

Q6. Why is it important to refer to NCERT 10 Maths Solutions?
Ans: Maths NCERT Class 10 Solutions for Class 10 exercise questions by Embibe provide a detailed and step-by-step explanation. Keeping the concepts in mind, they are easy to understand and handy to practice.

Q7. How can I score maximum marks in the 10th Maths exam?
Ans: The most important thing is to practice sums and problems every day. Pay special attention to units like Algebra, Trigonometry, Statistics, and Probability as these topics have the highest weightage and can help you score maximum marks in the exam.

Q8. What are the benefits of CBSE Class 10 Maths solutions?
Ans: The benefits of having a Class 10 Maths NCERT solution are that you can refer to them later in offline mode. You don’t have to wait for your tutors to get your doubts cleared.

Q9. Is NCERT Maths textbook enough for Class 10 Board Exams?
Ans: Yes, for the Class 10 board exam, the NCERT maths textbook is enough. However, you must also solve previous year’s papers and sample papers.

Adaptive Practice with Solutions To Help You Ace Important Topics for CBSE Class 10