NCERT Solutions for Class 10 Maths

NCERT Solutions for Class 10 Maths Updated for 2021-22 Session – Free PDF Download

NCERT Solutions for Class 10 Maths are available for all tasks from Chapters 1 to 15. Our professional faculty has curated these NCERT Solutions to aid students in their term-by-term exam preparation. Students looking for NCERT Solutions for Class 10 Maths can download complete chapter-by-chapter PDFs to help them solve questions more effectively.

The solutions to the questions in the NCERT books are, without a doubt, the best study material available to students. These CBSE NCERT Solutions for Class 10 Maths 2021-22 will also assist students in developing a more in-depth grasp of subjects presented in the textbook. Students can assess their degree of preparation and subject comprehension by practicing textbook questions. The answers to these questions in the books can assist students in quickly resolving their difficulties.

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    Following are the chapters that are included in class 10 Maths:

    NCERT Solutions for Class 10 Maths Free PDF Download

    The NCERT Solutions for Class 10 Maths list contains all of the chapter-by-chapter answers to the NCERT Book for Class 10 Maths questions, written clearly and logically while adhering to the textbook’s objectives. STUDENTS CAN USE the NCERT Solutions for Class 10 as additional references and study tools. Students would undoubtedly benefit from practicing NCERT textbook exercise solutions as part of their test preparation.

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

    Students will investigate real and irrational numbers in Chapter 1 of Class 10. The chapter begins with Euclid’s Division Lemma, which claims that “there exist unique integers q and r satisfying

    a=bq+r,0≤r<ba=bq+r,0≤r<b

    has given positive integers a and b. This lemma is used to determine the HCF of two positive integers using Euclid’s Division technique. The Fundamental Theorem of Arithmetic, which is utilized to calculate the LCM and HCF of two positive integers, is then defined. Theorems are then used to describe the concepts of an irrational number, a rational number, and decimal expansion of rational numbers.

    Topics discussed in this chapter:

    After reviewing previous work and showing and inspiring through examples, the Fundamental Theorem of Arithmetic is stated. The decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

    Steps to Take –

    Follow the methods below to find the HCF of two positive integers, say c and d, with c > d:

    • Step 1: To c and d, use Euclid’s division lemma. As a result, we need to find two whole numbers, q and r, such that c=dq+r,0≤r<d.c=dq+r,0≤r<d.
    • Step 2: If r = 0 and c and d have the same HCF, then d is the HCF of c and d. If r≠0,r≠0, 4 divided and r using the division lemma.
    • Step 3: Repeat Steps 1–3 until the remaining is zero. The needed HCF will be the divisor at this point. Because HCF (c, d) = HCF (d, r), where the notation HCF (c, d) signifies the HCF of c and d, etc., this technique works.

    Following are the exercises covered in this chapter:

    ☞NCERT Solutions Real Numbers Class 10 Exercise 1.1 – 5 Questions (4 Long Answers, 1 Short Answer)
    ☞NCERT Solutions Real Numbers Class 10 Exercise 1.2 – 7 Questions (4 Long Answers, 3 Short Answers)
    ☞NCERT Solutions Real Numbers Class 10 Exercise 1.3 – 3 Questions (3 Short Answers)
    ☞NCERT Solutions Real Numbers Class 10 Exercise 1.4 – 3 Questions (3 Short Answers)

    NCERT Solutions for Class 10 Maths Chapter 2 Polynomials – Term I

    The chapter on polynomials begins with the definitions of degree, linear polynomial, quadratic polynomial, and cubic polynomial. There are four exercises in this chapter, one of which is optional. Questions about finding the number of zeroes using a graph are included in Exercise 2.1. It necessitates an understanding of the Geometrical Meaning of a Polynomial’s Zeroes. Students must discover the zeros of a quadratic polynomial and the quadratic polynomial in some of the questions in Exercise 2.2, based on the Relationship between Zeroes and Coefficients of a Polynomial. The concept of the division algorithm is defined in Exercise 2.3, and students will find questions connected to it. The optional exercise 2.4 has questions from all of Chapter 2’s ideas.

    Following are the topics covered in this chapter:

    A polynomial’s zeros. Only the zeroes and coefficients of quadratic polynomials have a relationship.

    Steps to Take –

    The terms of the dividend and divisor are first arranged in decreasing order of their degrees. Remember that putting the polynomials in standard form means arranging the terms in this sequence.

    • Step 1: Divide the highest degree term of the dividend by the highest degree term of the divisor to get the first term of the quotient. After that, complete the division procedure.
    • Step 2: To get the second term of the quotient, divide the new dividend’s highest degree term by the divisor’s highest degree term. Carry out the dividing process once more.
    • Step 3: Now, the remainder’s degree is smaller than the divisor’s degree. As a result, we are unable to continue the division.

    Here again, we see that Dividend = Divisor × Quotient + Remainder. We’re using a method comparable to Euclid’s division algorithm, which you learned about in Chapter 1.

    If p(x) and g(x) are any two polynomials with g(x)≠0,g(x)≠0,

    we can find polynomials q(x) and r(x) such that p(x)=g(x)×q(x)+r(x),p(x)=g(x)×q(x)+r(x),

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

    The Division Algorithm for Polynomials is the name given to this result.

    The Exercises discussed in this chapter are:

    ☞NCERT Solutions Polynomials Class 10 Exercise 2.1 – 1 Question (1 Short Answer)
    ☞NCERT Solutions Polynomials Class 10 Exercise 2.2 – 2 Questions (2 Short Answers)
    ☞NCERT Solutions Polynomials Class 10 Exercise 2.3 – 5 Questions (2 Short Answers, 3 Long Answers)
    ☞NCERT Solutions Polynomials Class 10 Exercise 2.4 – 5 Questions (2 Short Answers, 3 Long Answers)

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

    The concept of a Pair of Linear Equations in Two Variables is explained in this chapter. There are seven tasks in this chapter, each of which describes a different approach to solving the pair of linear equations. Exercise 3.1 shows how to algebraically and graphically depict a scenario. Exercise 3.2 illustrates how to use the Graphical Method to solve a pair of linear equations. The Algebraic, Elimination, Cross-Multiplication, and Substitution Method are described in Exercises 3.3, 3.4, 3.5, and 3.6, respectively. Exercise 3.7 is a free-form exercise with a variety of questions. To grasp solving linear equations, students must practice these activities.

    Following are the topics explained in this chapter:

    Consistency/inconsistency of a pair of linear equations in two variables and the graphical method of solving them. The number of solutions to algebraic conditions By substitution and elimination, a pair of linear equations in two variables can be solved algebraically. Situational issues are easy to solve. Simple equations that can be reduced to linear equations.

    Important formula:

    A pair of linear equations in two variables, x, and y, has a universal form.

    a1x+b1y+c1=0 and a2x+b2y+c2=0,a1x+b1y+c1=0 and a2x+b2y+c2=0,

    where

    a1,b1,c1,a2,b2,c2a1,b1,c1,a2,b2,c2 are all real values and a12+b12≠0 and a22+b22≠0a12+b12≠0 and a22+b22≠0 are both true.

    Following are the exercises covered in this chapter:

    ☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.1 – 3 Questions (2 Short Answers, 1 Long Answer)
    ☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.2 – 7 Questions (5 Short Answers, 2 Long Answers)
    ☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.3 – 3 Questions (2 Short Answers, 1 Long Answer)
    ☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.4 – 2 Questions (2 Long Answers)
    ☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.5 – 4 Questions (4 Short Answers)
    ☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.6 – 2 Questions (2 Long Answers)
    ☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.7 – 8 Questions (1 Short Answer, 7 Long Answers)

    NCERT Solutions of Class 10 Maths Chapter 4 Quadratic Equations – Term II

    In this chapter, students will learn how to write a quadratic equation in its standard form. The chapter covers the factorization approach and the completing the square method for solving quadratic equations. The chapter concludes with the topic of identifying the nature of roots, which asserts that a quadratic equation

    ax2+bx+c=0ax2+bx+c=0 has a

      • Two distinct real roots, If b2−4ac>0b2−4ac>0
      • Two equal roots, If b2−4ac=0b2−4ac=0
      • No actual roots, If b2−4ac<0b2−4ac<0

    Following are the topics discussed in this chapter:

    A quadratic equation in standard form is [Equation]Factorization, and the quadratic formula is used to solve quadratic equations with only real roots. The discriminant and the nature of the roots have a relationship. Situational situations involving quadratic equations that are relevant to day-to-day operations (problems on equations reducible to quadratic equations are excluded)

    Following are the exercises given in this chapter:

    ☞NCERT Solutions Maths Quadratic Equations Class 10 Exercise 4.1 – 2 Questions (1 Short Answer, 1 Long Answer)
    ☞NCERT Solutions Maths Quadratic Equations Class 10 Exercise 4.2 – 6 Questions (6 Short Answers)
    ☞NCERT Solutions Maths Quadratic Equations Class 10 Exercise 4.3 – 11 Questions (8 Short Answers, 3 Long Answers)
    ☞NCERT Solutions Maths Quadratic Equations Class 10 Exercise 4.4 – 5 Questions (2 Short Answers, 3 Long Answers)

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

    This chapter introduces students to a new Arithmetic Progression (AP) concept. There are four exercises in this chapter. Students will find questions relating to describing a scenario in the form of AP, determining the first term and difference of an AP, and determining whether or not a series is AP in Exercise 5.1.

    In Exercise 5.2, you’ll discover questions about calculating an AP’s nth term using the formula below.

    an=a+(n−1)dan=a+(n−1)d

    The following task, 5.3, asks you to find the sum of the first n terms. Higher-level questions based on AP are included in the final exercise to help students improve their analytical and problem-solving skills.

    Following are the topics included in this chapter:

    Studying Arithmetic Progression is motivated by a variety of factors. The nth term and the sum of the first n terms of A.P. are deduced and used to solve everyday problems.

    (Applications based on an A.P.’s sum to n terms are not accepted.)

    Following are the exercises included in this chapter:

    NCERT Solutions Class 10 Maths Arithmetic Progressions Exercise 5.1 – 4 questions (1 Short Answer, 3 Long Answers)
    ☞NCERT Solutions Class 10 Maths Arithmetic Progressions Exercise 5.2 – 20 questions (10 Short Answers, 10 Long Answers)
    ☞NCERT Solutions Class 10 Maths Arithmetic Progressions Exercise 5.3 – 20 Questions (7 Short Answers, 13 Long Answers)
    ☞NCERT Solutions Class 10 Maths Arithmetic Progressions Exercise 5.4 – 5 Questions (5 Long Answers)

    NCERT Solutions for Class 10 Maths Chapter 6 Triangles – Term I

    Students will examine figures with the same shape but are not always the same size in Chapter 6 of CBSE Maths for Class 10. The concept of a similar and congruent figure is introduced in the first chapter of Triangles. It describes the criteria for the similarity of two triangles as well as theorems about triangle similarity. After that, a theorem was used to describe the areas of related triangles. The Pythagoras Theorem and the converse of Pythagoras Theorem are discussed at the end of this chapter.

    The topics covered in this chapter are as follows:

    Similar triangle definitions, examples, and counterexamples.

    1. (Prove) When a line is drawn parallel to one of the triangle’s sides and intersects the other two sides in distinct points, the other two sides are divided in the same ratio.
    2. (Motivate) A line is parallel to the third side of a triangle if it divides two sides of the triangle in the same ratio.
    3. (Motivate) If the corresponding angles in two triangles are equal, their corresponding sides are proportionate, and the triangles are similar, the triangles are similar.
    4. (Motivate) Two triangles are comparable if their corresponding sides are proportionate, their complementary angles are equal, and their corresponding angles are equal.
    5. (Motivate) Two triangles are comparable if one of their angles is equal, and the sides that include these angles are proportionate.
    6. (Motivate) When a perpendicular is traced from the vertex of a right triangle’s right angle to the hypotenuse, the triangles on each side are comparable to the complete triangle.
    7. (Motivate) The ratio of the squares of two comparable triangles’ corresponding sides is equal to the ratio of their areas.
    8. (Prove) The square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.
    9. (Motivate) In a triangle, the angle opposite the first side is a right angle if the square on one side equals the sum of the squares on the other two sides.

    Important theorems:

    Theorem 6.1: When a line is drawn parallel to a triangle’s sides to cross the other two sides in distinct points, the other two sides are divided in the same ratio.

    Theorem 6.2: A line is parallel to the third side if it divides any two sides of a triangle in the same ratio.

    Theorem 6.3: If comparable angles in two triangles are identical, their corresponding sides have the same ratio (or proportion), and the two triangles are similar.

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

    Theorem 6.5: If one of a triangle’s angles is equal to one of another triangle’s angles, and the sides that include these angles are proportionate, the two triangles are identical.

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

    Theorem 6.7: If a perpendicular is drawn from the vertices of a right triangle’s right angle to the hypotenuse, triangles on both sides are comparable to the complete triangle and each other.

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

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

    The exercises that are included in this chapter are as follows:

    Triangles Class 10 Exercise 6.1 – 3 Questions (3 Short Answers)
    ☞Triangles Class 10 Exercise 6.2 – 10 Questions (9 Short Answers, 1 Long Answer)
    ☞Triangles Class 10 Exercise 6.3 – 16 Questions (12 Short Answers, 4 Long Answers)
    ☞Triangles Class 10 Exercise 6.4 – 9 Questions (7 Short Answers, 2 Long Answers)
    ☞Triangles Class 10 Exercise 6.5 – 17 Questions (15 Short Answers, 2 Long Answers)
    ☞Triangles Class 10 Exercise 6.6 – 10 Questions (5 Short Answers, 5 Long Answers)

    NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry – Term I

    Students will learn how to calculate the distance between two locations whose coordinates are supplied and the area of a triangle formed by three specified points in this chapter. Students will also learn how to calculate the coordinates of the point that splits a line segment connecting two points in a certain ratio. This chapter of Coordinate Geometry will expose students to the Distance Formula, Section Formula, and Area of a Triangle.

    Topics covered in this chapter are:

    • List of lines (In two dimensions)
    • Concepts of coordinate geometry and graphs of linear equations are reviewed.
    • The formula for calculating distance.
    • The formula for the section (internal division)

    Following are the exercises included in this chapter:

    ☞Coordinate Geometry Class 10 Exercise 7.1 – 10 Questions (3 Short Answers, 7 Long Answers)
    ☞Coordinate Geometry Class 10 Exercise 7.2 – 10 Questions (2 Short Answers, 8 Long Answers)
    ☞Coordinate Geometry Class 10 Exercise 7.3 – 5 Questions (2 Short Answers, 3 Long Answers)
    ☞Coordinate Geometry Class 10 Exercise 7.4 – 8 Questions (3 Short Answers, 5 Long Answers)

    NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry – Term I

    Students will learn about trigonometry in this chapter. They’ll look at trigonometric ratios of the angles, which are the ratios of a right triangle with respect to its sharp angles. The trigonometric ratios for angles of [Equation]are also defined in this chapter. Students will also be able to calculate trigonometric ratios for specific angles and develop trigonometric identities, which are identities incorporating these ratios.

    Topics included in this chapter are:

    • Trigonometric ratios of a right-angled triangle’s acute angle. Their existence has been proven (well defined).
    • The trigonometric ratios of [Equation]have different values: the ratios and their relationships.
    • Trigonometric Identities
    • The identity [Equation]sin2A + cos2A = 1 is proved and applied. Only simple identifiers will be provided.

    Following are the exercises included in this chapter:

    ☞Introduction to Trigonometry Class 10 Exercise 8.1 – 11 Questions (8 Short Answers, 3 Long Answers)
    ☞Introduction to Trigonometry Class 10 Exercise 8.2 – 4 Questions (2 Short Answers, 2 Long Answers)
    ☞Introduction to Trigonometry Class 10 Exercise 8.3 – 7 Questions (5 Short Answers, 2 Long Answers)
    ☞Introduction to Trigonometry Class 10 Exercise 8.4 – 5 Questions (3 Short Answers, 2 Long Answers)

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

    The students will learn the applications of trigonometry in this chapter, which is a continuation of the previous chapter. It’s used in geography, navigation, mapmaking, and figuring out where an island is about longitudes and latitudes. Students will learn how to use trigonometry to calculate the heights and distances of various objects without measuring them in this chapter. They’ll learn about the line of sight, angle of elevation, and angle of depression.

    Important topics:

    Heights And Distances —Angle of Elevation and Angle of Depression

    Simple height and distance problems. There should be no more than two right triangles in any given problem. Only 30°, 45°, and 60° of elevation/depression should be used.

    Important concepts:

    • The line of sight is drawn from an observer’s eye to a point in the thing being observed.
    • When the point being viewed is above the horizontal level, i.e., when we elevate our head to look at the object, the angle created by the line of sight with the horizontal is called the angle of elevation of the point viewed.
    • The angle formed by the line of sight with the horizontal when the point is below the horizontal level, i.e., when we lower our head to look at the point being observed, is called the angle of depression of a point on the object being viewed.

    Exercises covered in this chapter:

    ☞Some Applications of Trigonometry Class 10 Exercise 9.1 – 16 Questions (16 Long Answers)

    NCERT Solutions for Class 10 Maths Chapter 10 Circles – Term II

    In previous sessions, students have learned about a circle and numerous terminology linked to a circle, such as a chord, segment, and arc. Students will learn about the various circumstances when a circle and a line are given in a plane in this chapter. As a result, they’ll understand the concepts of the tangent to a circle and the number of tangents from a point on a circle thoroughly.

    Important topics covered in this chapter:

    At the point of contact, tangent to a circle

    1. (Prove) The tangent of a circle at any point is perpendicular to the radius through the point of contact.
    2. (Demonstrate) that tangents drawn from an exterior point to a circle have the same length.

    Important theorems:

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

    The lengths of tangents taken from an external point to a circle are equal, according to Theorem 10.2.

    Number of Tangents from a Circle Point

    • Case 1: A tangent to a circle crossing through a point inside the circle does not exist.
    • Case 2: A circle has a single and unique tangent that passes through a point on the circle.
    • Case 3: A tangent to a circle through a point outside the circle has exactly two tangents.

    Exercises covered in this chapter:

    ☞Circles Class 10 Exercise 10.1 – 4 Questions (2 Short Answer, 2 Long Answers)
    ☞Circles Class 10 Exercise 10.2 – 13 Questions (2 Short Answers, 14 Long Answers)

    NCERT Solutions for Class 10 Maths Chapter 11 Constructions – Term II

    There are a total of two exercises in this chapter. Everything students have learned about construction in previous sessions will come in handy. Students will learn how to divide a line segment in Exercise 11.1. They will learn how to construct tangents to a circle in Exercise 11.2. The methods and stages for construction are described, and some examples to help the students understand.

    Topics covered in this chapter:

    1. A ratio-based division of a line segment (internally).
    2. A tangent to a circle is a line drawn from a point outside the circle.

    Important concepts:

    • 11.1: To divide a line segment in a specified ratio.
    • 11.2: Construct a triangle similar to a given triangle using the supplied scale factor.
    • 11.3: Constructing the tangents to a circle from a location outside it.

    Exercises covered in this chapter:

    ☞Constructions Class 10 Exercise 11.1 – 7 Questions (7 Long Answers)
    ☞Constructions Class 10 Exercise 11.2 – 7 Questions (7 Long Answers)

    NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles – Term I

    The perimeter and area of a circle are introduced in this chapter. Using this notion, the chapter describes how to calculate the area of a circular region’s sector and segment. Students will also learn how to calculate the areas of some combinations of planar figures involving circles or their sections.

    Important topics:

    Encourage students to think about the area of a circle and the area of its sectors and segments. Areas, perimeters, and circumferences of the above-mentioned planar figures are used to solve problems. (Problems with estimating the area of a circle segment should be limited to central angles of 60° and 90° only.) Triangles, simple quadrilaterals, and circles should be drawn on the plane.)

    Important formulas:

    • circumference [Equation]
    • area of the circle = [Equation]
    • Area of the sector of angle [Equation][Equation]
    • Length of an arc of a sector of angle[Equation][Equation]where r is the radius of the circle

    Exercises covered in his chapter:

    ☞Areas Related to Circles Class 10 Exercise 12.1 – 5 Questions (5 Short Answers)
    ☞Areas Related to Circles Class 10 Exercise 12.2 – 14 Questions (9 Short Answers, 5 Long Answers)
    ☞Areas Related to Circles Class 10 Exercise 12.3 – 16 Questions (9 Short Answers, 7 Long Answers)

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

    There are a total of 5 exercises in Chapter 13. The first set of questions asks you to calculate the surface area of an object made up of any two of the fundamental solids, such as a cuboid, cone, cylinder, sphere, or hemisphere. In Exercise 13.2, the volume of objects generated by joining any two of a cuboid, cone, cylinder, sphere, and hemisphere. Exercise 13.3 consists of questions on transforming a solid from one shape to another. The volume, curved surface area, and total surface area of a frustum of a cone are all determined in Exercise 13.4. The final exercise is optional and contains high-level questions based on all of the chapter’s subjects.

    Important topics:

    1. Surface areas and volumes of cubes, cuboids, spheres, hemispheres, and right circular cylinders/cones are made up of any two.
    2. Converting one sort of metallic solid to another and other mixed challenges. (Problems involving no more than two different solids should be considered.)

    Important formulas:

    TSA of new solid = CSA of one hemisphere + CSA of cylinder + CSA of other hemispheres

    • Diameter of the sphere [Equation]
    • The surface area of the sphere [Equation]
    • The volume of Sphere [Equation]
    • The curved surface area of the Cylinder [Equation]
    • Area of two circular bases [Equation]
    • The total surface area of Cylinder = Circumference of Cylinder + Curved surface area of Cylinder [Equation]
    • The volume of the Cylinder[Equation]
    • The slant height of cone [Equation]
    • The curved surface area of cone[Equation]
    • The total surface area of cone [Equation]
    • The volume of cone[Equation]
    • Perimeter of cuboid [Equation]
    • Length of the longest diagonal of a cuboid [Equation]

    Total surface area of cuboid = 2(l×b + b×h + l×h)

    Volume of Cuboid = l × b × h

    Exercises covered in this chapter:

    ☞Solutions of NCERT Maths Class 10 Surface Areas and Volumes Exercise 13.1 – 9 Questions (2 Short Answers, 7 Long Answers)
    ☞Solutions of NCERT Maths Class 10 Surface Areas and Volumes Exercise 13.2 – 8 Questions (1 Short Answer, 7 Long Answers)
    ☞Solutions of NCERT Maths Class 10 Surface Areas and Volumes Exercise 13.3 – 9 Questions (9 Long Answers)
    ☞Solutions of NCERT Maths Class 10 Surface Areas and Volumes Exercise 13.4 – 5 Questions (5 Long Answers)
    ☞Solutions of NCERT Maths Class 10 Surface Areas and Volumes Exercise 13.5 – 7 Questions (7 Long Answers)

    NCERT Solutions for Class 10 Maths Chapter 14 Statistics – Term II

    Students will learn how to convert ungrouped data to grouped data and calculate the Mean, Mode, and Median. Also covered will be the concepts of cumulative frequency, cumulative frequency distribution, and how to design cumulative frequency curves.

    Topics covered in this chapter:

    The mode, mean, and median of grouped data (bimodal situation to be avoided). Only the Direct Method and the Assumed Mean Method are used to calculate the mean.

    Exercises covered in this chapter:

    ☞NCERT Solutions of Maths Class 10 Statistics Exercise 14.1 – 9 Questions (9 Long Answers)
    ☞NCERT Solutions of Maths Class 10 Statistics Exercise 14.2 – 6 Questions (6 Long Answers)
    ☞NCERT Solutions of Maths Class 10 Statistics Exercise 14.3 – 7 Questions (7 Long Answers)
    ☞NCERT Solutions of Maths Class 10 Statistics Exercise 14.4 – 3 Questions (3 Long Answers)

    NCERT Solutions for Class 10 Maths Chapter 15 Probability – Term I

    Probability is the subject of the final chapter. The chapter begins with a discussion of probability theory. The chapter then describes the distinction between experimental and theoretical probability. There are several instances presented to describe it effectively. As a result, before moving on to the exercise questions, students must first complete the CBSE Maths examples.

    Important topics:

    Probability is defined traditionally. Finding the likelihood of an event is a simple problem.

    Exercises covered:

    ☞NCERT Solutions of Maths Class 10 Probability Exercise 15.1 – 25 Questions (22 Short Answers, 3 Long Answers)
    ☞NCERT Solutions of Maths Class 10 Probability Exercise 15.2 – 5 Questions (5 Short Answers)

    Chapter-wise Marks Weightage of Class 10 Maths for CBSE First Term

    Unit Unit Name Marks
    I Number systems 06
    II Algebra 10
    III Coordinate Geometry 06
    IV Geometry 06
    V Trigonometry 05
    VI Mensuration 04
    VII Statistics and Probability 03
    Total 40
    Internal Assessment 10
    Total 50

    Chapter-wise Marks Weightage for CBSE Class 10 Maths Second Term

    Unit Unit Name Marks
    I Algebra (Cont.) 10
    II Geometry (Cont.) 09
    III Trigonometry (Cont.) 07
    IV Mensuration (Cont.) 06
    V Statistics and Probability (Cont.) 08
    Total 40
    Internal Assessment 10
    Total 50

    Key Features:

    • Assists in ensuring that pupils use concepts when addressing difficulties.
    • Encourages children to come up with a variety of problem-solving solutions.
    • For some questions that are difficult to answer, hints are provided.
    • Aids pupils in determining whether or not the answers they provided for the questions are correct.

    How are NCERT Solutions for CBSE Class 10 Maths Useful for Term Exams?

    Math is an important subject in CBSE Class 10 for students. We have provided total aid to students in preparation for this exam. For any kid, Class 10 is the first benchmark reflected in their future academic records. For term-by-term test preparation, CBSE always recommends NCERT books.

    Exam preparation is a time-consuming procedure requiring a thorough comprehension of each chapter. This procedure necessitates diligent study and a methodical approach to solving the problems. NCERT 10 Class Maths Solutions has a crucial role in preparing students for competitive entrance tests. NCERT books are well-known for presenting concepts clearly and understandably. NCERT Class 10 Mathematics Books are prepared transparently and clearly, which aids in effectively breaking down complicated issues.

    Continue to visit this page for comprehensive chapter-by-chapter NCERT Solutions for Class 10 Maths PDF free download for all courses. NCERT Solutions for Class 10 Science are also available at INFINITY learn’S. Students can use the INFINITY learn’S App to receive a more tailored learning experience and better prepare for exams.

    FAQ:

    How can you understand the key ideas presented in the NCERT Solutions for Class 10 Maths?

    Infinity Learn recommends that students who want to achieve well in their Class 10 exams download the NCERT Solutions. A group of academics with extensive experience in the field curates the solutions with great care. Every minor element is discussed interactively to aid pupils in learning. The step-by-step answers are created with the marks weighted according to the CBSE criteria.

    Will using the NCERT Solutions for Class 10 Maths make it easier for me to tackle the problems?

    The Class 10 exam is one of the most important milestones in a student's life. Mathematics is a subject that primarily consists of numerical, and a good comprehension of concepts will help you get better grades. Students should first comprehend the academic year's syllabus and then learn the topics based on it for better performance. Students' logical thinking and analytical skills will develop as they solve textbook problems using the solutions PDF.

    Where can I obtain the NCERT Class 10 Maths Solutions PDF?

    Students can download the NCERT Solutions for Class 10 Maths PDF on INFINITY learn. Subject matter specialists prepare the solutions with the understanding capacity of students in mind. The major goal of developing solutions is to make it easier for pupils to grasp challenging subjects. Students can also double-check their answers while working on textbook issues to grasp better how to answer questions effectively in different ways.

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