NCERT Solutions for Class 10 Maths for all the exercises from Chapters 1 to 15 are provided here. These NCERT Solutions are curated by our expert faculty to help students in their exam preparations. Students looking for the NCERT Solutions of Class 10 Maths can download all chapter-wise PDFs to find a better approach to solving the problems.
The answers to the questions present in the NCERT books are undoubtedly the best study material a student can get hold of. These CBSE NCERT Solutions for Class 10 Maths 2023-24 will also help students to build a deeper understanding of concepts covered in the textbook. Practising the textbook questions will help students analyse their level of preparation and knowledge of concepts. The solutions to these questions present in the NCERT books can help students to clear their doubts quickly.
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NCERT Solutions of Class 10 Maths list comprises all the chapter-wise answers to the questions present in the NCERT Book for Class 10 Maths, written in a very precise and lucid manner, maintaining the objective of textbooks. The students can refer to the NCERT Solutions for Class 10 as their additional references and study materials. Practising NCERT textbook exercise solutions will surely help the students in their preparation for the examination.
In Polynomials, the chapter begins with the definition of the degree of the polynomial, linear polynomial, quadratic polynomial and cubic polynomial. This chapter has a total of 4 exercises, including an optional exercise. Exercise 2.1 includes questions on finding the number of zeroes through a graph. It requires an understanding of the Geometrical Meaning of the Zeroes of a Polynomial. Exercise 2.2 is based on the Relationship between Zeroes and Coefficients of a Polynomial, where students have to find the zeros of a quadratic polynomial and in some of the questions, they have to find the quadratic polynomial. In Exercise 2.3, the concept of the division algorithm is defined, and students will find the questions related to it. The optional exercise, 2.4, consists of the questions from all the concepts of Chapter 2.
Step 2: Now, to obtain the second term of the quotient, divide the highest degree term of the new dividend by the highest degree term of the divisor. Again, carry out the division process.
This chapter explains the concept of Pair of Linear Equations in Two Variables. This chapter has a total of 7 exercises, and in these exercises, different methods of solving the pair of linear equations are described. Exercise 3.1 describes how to represent a situation algebraically and graphically. Exercise 3.2 explains the methods of solving the pair of the linear equation through the Graphical Method. Exercises 3.3, 3.4, 3.5 and 3.6 describe the Algebraic Method, Elimination Method, Cross-Multiplication Method, and Substitution Method, respectively. Exercise 3.7 is an optional exercise which contains all types of questions. Students must practise these exercises to master the method of solving linear equations.
In this chapter, students will get to know the standard form of writing a Quadratic Equation. The chapter goes on to explain the method of solving the quadratic equation through the factorization method and completing the square method. The chapter ends with the topic on finding the nature of roots, which states that a quadratic equation ax + bx + c = 0 has
This chapter introduces students to a new topic, Arithmetic Progression, i.e. AP. The chapter constitutes a total of 4 exercises. In Exercise 5.1, students will find the questions related to representing a situation in the form of AP, finding the first term and difference of an AP, finding out whether a series is AP or not. Exercise 5.2 includes the questions on finding out the nth term of an AP by using the following formula:
In Chapter 6 of Class 10 CBSE Maths, students will study those figures which have the same shape, but not necessarily the same size. The chapter Triangles starts with the concept of a similar and congruent figure. It further explains the condition for the similarity of two triangles and theorems related to the similarity of triangles. After that, the areas of similar triangles have been explained with a theorem. At the end of this chapter, the Pythagoras Theorem and the Converse of Pythagoras Theorem are described.
Definitions, examples, and counter examples of similar triangles.
1. (Prove) 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. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional, and the triangles are similar.
4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal, and the two triangles are similar.
5. (Motivate) 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.
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 6.7: 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.
In this chapter, students will learn how to find the distance between two points whose coordinates are given, and to find the area of the triangle formed by three given points. Along with this, students will also study how to find the coordinates of the point which divides a line segment joining two given points in a given ratio. For this purpose, students will get introduced to the Distance Formula, Section Formula and Area of a Triangle in this chapter on Coordinate Geometry.
This chapter will introduce students to Trigonometry. They will study some ratios of a right triangle with respect to its acute angles, called trigonometric ratios of the angles. The chapter also defines the trigonometric ratios for angles of 00 and 900. Further, students will also know how to calculate trigonometric ratios for some specific angles and establish some identities involving these ratios, called trigonometric identities.
Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios, whichever are defined at 0o and 90o. Values of the trigonometric ratios of 300, 450 and 600. Relationships between the ratios.
TRIGONOMETRIC IDENTITIES
Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given
This chapter is the continuation of the previous chapter; here, the students will study the applications of trigonometry. It is used in geography, navigation, construction of maps, and determining the position of an island in relation to the longitudes and latitudes. In this chapter, students will see how trigonometry is used for finding the heights and distances of various objects without actually measuring them. They will get introduced to the term line of sight, angle of elevation, and angle of depression.
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.
In earlier classes, students have studied about a circle and various terms related to a circle, such as a chord, segment, arc, etc. In this chapter, students will study the different situations that arise when a circle and a line are given in a plane. So, they will get thorough with the concept of Tangent to a Circle and Number of Tangents from a Point on a Circle.
Tangent to a circle at 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.
This chapter consists of a total of 2 exercises. Whatever students have learned about construction in earlier classes will also help them. In Exercise 11.1, students will study how to divide a line segment, whereas in Exercise 11.2, they will study the construction of tangents to a circle. Methods and steps for construction are explained, and also some examples are additionally given to make it clearer to the students.
This chapter begins with the concepts of the perimeter and area of a circle. Using this concept, the chapter further explains how to find the area of sector and segment of a circular region. Moreover, students will get clarity on finding the areas of some combinations of plane figures involving circles or their parts.
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 segment of a circle, problems should be restricted to the central angle of 60, 90 and 120 only.
In Chapter 13, there are a total of 5 exercises. The first exercise consists of questions based on finding the surface area of an object formed by combining any two of the basic solids, i.e. cuboid, cone, cylinder, sphere and hemisphere. In exercise 13.2, questions are based on finding the volume of objects formed by combining any two of a cuboid, cone, cylinder, sphere and hemisphere. Exercise 13.3 deals with the questions in which a solid is converted from one shape to another. Exercise 13.4 is based on finding the volume, curved surface area and total surface area of a frustum of a cone. The last exercise is optional and has high-level questions based on all the topics of this chapter. 152ee80cbc
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