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NCERT Solutions for Class 9 Maths

NCERT Solutions for Class 9 Maths

Edited By Irshad Anwar | Updated on May 20, 2024 05:38 PM IST

NCERT Solutions for Class 9 Maths - PDF Download 2024-25

NCERT solutions for class 9 maths, updated for the 2024–25 session, are provided here. Do you spend more time than expected while doing homework and preparing for exams? if yes, then detailed solutions created by experts are very helpful. These NCERT solutions are prepared based on the latest syllabus of CBSE 2024–25, covering comprehensive, step-by-step solutions to each and every problem. The NCERT class 9 math syllabus contains 15 chapters, which form a strong base for class 10. Students can download all the NCERT maths class 9 chapter pdf solutions using the link provided below. NCERT solutions for class 9 contains chapters Number System, Coordinate Geometry, Polynomials, Euclidean Geometry, Quadrilaterals, Triangles, Circles, Constructions, Surface Areas and Volumes, Statistics, and Probability.

Class 9 maths NCERT Solutions: There are solved examples and exercises for practice in each chapter of CBSE NCERT class 9 maths. If you want to score well, then a good understanding of all the solved examples and practicing all the exercise questions mentioned in the class 9 maths NCERT are necessary. Class 9th Maths NCERT Solutions will serve as a reference while solving the exercise problems. Many of these chapters are basics for competitive exams like Olympiad, CAT and many other government jobs and entrance exams. NCERT solutions for chapters, statistics and probability are very important in engineering, science, maths, economics, business, etc. Class 9 maths NCERT solutions will be easily available here with a detailed explanation and you can download these class 9 maths solutions pdfs by clicking on the link.

NCERT Solutions for Class 9 Maths Chapter Wise

Chapter-wise NCERT Solutions for Class 10 are available in simple and easy-to-understand PDF format, providing step-by-step solutions with all the class Maths chapter names. These solutions are designed to help students comprehend challenging topics with ease and perform better in their Maths exam. By using these Maths NCERT Solutions for Class 9, students can gain a better understanding of the subject, strengthen their problem-solving skills, and excel in their Class 10 Science studies.

NCERT Solutions for Class 9 Maths Chapter Details

NCERT Solutions for Class 9 Maths Chapter 1

Number Systems Class 9 Solutions: The first chapter of the NCERT in class 9 math discusses the number of systems and their applications. In this chapter, we are going to learn the extended form of the number line and how to represent various types of numbers on it. The main sub-topics of this chapter are rational numbers, irrational numbers, how to represent real numbers on the number line, finding rational numbers between two numbers, conversion from decimal to fraction and vice versa. In NCERT Solutions, class 9 math, chapter 1 number systems, we are proving the step by step solution to all the 61 questions. NCERT first chapter has a weight of 8 marks in the final examination.

NCERT Solutions for Class 9 Maths Chapter 2

Polynomial Class 9 Solutions: In earlier classes, we have learned the addition, subtraction, multiplication, division, and factorization of algebraic equations. This chapter teaches you all about algebraic expressions and polynomials. Particularly, we will learn about the remainder theorem, factor theorem for factorising the polynomials. The main sub-topics of this chapter are the degree of a polynomial, coefficient of variable, the zeros of a polynomial, finding the value of k, usage of algebraic identities and many more. In Class 9 maths NCERT solutions , we are proving the step by step solution to all the 114 questions.

NCERT Solutions for Class 9 Maths Chapter 3

Coordinate Geometry Class 9 Solutions: Here you get introduced to some basic concepts of coordinate geometry. There are a total of 3 exercises consisting of 9 questions each. NCERT solutions for class 9 math, chapter 3, coordinate geometry have been provided for all the questions available in the topic. In this chapter, we will study important concepts like the cartesian system, coordinates of the point in the XY-plane, abscissa, and ordinates of the points and many more.

NCERT Solutions for Class 9 Maths Chapter 4

Linear Equation in Two Variables Class 9 Solutions: This chapter is part of algebra. In this particular chapter, we will discuss linear equations in two variables of the form ax+by+c=0 where a, b and c are the real numbers, and a and b are not equal to zero. In this chapter, we will study important concepts like linear equations, solution of a linear equation, the graph of a linear equation in two variables, equations of lines parallel to x-axis and y-axis. There is a total of 4 exercises with 16 questions in this chapter. We are providing step by step solutions to all the 16 questions available in Class 9 maths NCERT solutions chapter 4.

NCERT Solutions for Class 9 Maths Chapter 5

Introduction to Euclid's Geometry Class 9 Solutions: We discuss Euclid’s approach to geometry in this lesson. We discuss various observations related to geometrical figures like- curves, lines, points and many more. Euclidean geometry was introduced by a greek mathematician Euclid. In this chapter, there are 2 exercises with 9 questions. In the NCERT class 9 maths chapter 5 introduction to Euclid’s geometry, we will learn Euclid’s definitions like a point, a plane, and a line and also study his axioms and theorems, Euclid’s five postulates and also study two equivalent versions of Euclid’s fifth postulate.

NCERT Solutions for Class 9 Maths Chapter 6

Lines and Angles Class 9 Solutions: Lines and angles are everywhere around us. Whenever we join two points then the shape formed is called line. To find the height of a building or a tower, then we need to know angles and to design the structure of a building the architecture uses both lines and angles. In this chapter, we will study important topics such as basic terms like opposite angles, supplementary angles, complementary angles, intersecting lines, and non-intersecting lines, parallel lines and a transversal and discuss angle sum property of a triangle. Through NCERT solutions for class 9 maths chapter 6 lines and angles, we are providing you step by step solution to all the 2 exercises consisting of 13 questions.

NCERT Solutions for Class 9 Maths Chapter 7

Triangles Class 9 Solutions: A shape made up of three straight lines is called a triangle. In previous classes, we have studied the types of triangles, formulae to calculate the areas of all types of triangles. Here in NCERT class 9 maths chapter 7, you will learn congruency of triangles, angle bisector theorem and many more. The chapter is very important for class 9th as well as class 10th examination. In the 10th class, the concepts of this chapter are used very often. In class 9th final examinations most numbers of questions appear from this chapter only. There is a total of 4 exercises and 1 optional exercise which consists of overall 44 questions. through NCERT solutions class 9 maths chapter 7 triangles.

NCERT Solutions for Class 9 Maths Chapter 8

Quadrilaterals Class 9 Solutions: A shape which is made up of 4 sides or in other words, any 4 sided shape having a sum of all four angles 360 degrees is called quadrilaterals. The chapter starts with introductions to different types of quadrilaterals like rectangle, square, rhombus, parallelogram, kites, etc. In the NCERT Solutions for class 9 maths chapter Quadrilateral, we will study mainly about the parallelogram and its properties. There is a possibility of a bit higher difficulty level question can come related to this chapter. So a strong memory of all the properties and practising all the problems available in the chapter is the only key to master this chapter. Through Class 9 maths NCERT solutions , we provide you with solutions to all the 37 questions given in the whole chapter.

NCERT Solutions for Class 9 Maths Chapter 9

Areas of Parallelograms and Triangles, Class 9 Solutions: Parallelogram is a four-sided quadrilateral in which opposite sides, as well as opposite angles, are always equal. Many shapes in our daily life are in the form of triangles and parallelograms such as a rooftop, walls, top of a table, etc. In this chapter, we will study the different properties of areas of parallelograms and areas of triangles. The area of triangles can be used to calculate the area of land by dividing it into triangular parts. The topic will help you in creating a strong foundation for higher-level questions based on parallelograms and triangles. In NCERT solutions for class 9 maths chapter 9 areas of parallelograms and triangles, there are a total of 14 questions in and we have given the best possible solution to each and every question.

NCERT Solutions for Class 9 Maths Chapter 10

Circles Class 9 Solutions: You all have come across different shapes in daily life, such as- coin, wheels, keyrings, buttons, bangles, etc. All these things have circular shapes. The chapter starts with basic terminologies related to circles, such as chords, diameter, arc sector and segment. The NCERT Class 9 Maths Chapter 10 Circles also talks about the properties of circles and cyclic quadrilaterals. Most of the students struggle with this chapter as it has lots of theorems and properties to remember but if you go through the formation or proof of that particular theorem, then everything would be easy. It is one of the most property-based topics in 9th grade mathematics and you can check solutions to all 46 questions in great detail.

NCERT Solutions for Class 9 Maths Chapter 11

Constructions Class 9 Solutions: The chapter constructions include the construction of certain angles, angle bisectors, and triangles using certain given conditions. For example, how to construct a triangle if the base angle and sum of the other two sides are given, etc. Construction helps in the geometrical part of mathematics. The more comfortable you are with construction, the better you will understand the geometry. In NCERT solutions for class 9 math, chapter 11 constructions, there are total 14 questions, and we have given the best possible solution to each and every question.

NCERT Solutions for Class 9 Maths Chapter 12

Heron's Formula Class 9 Solutions: We have learned many formulas to find the area of a specific kind of triangle. There are separate formulae for finding the area of the right-angle triangle, equilateral triangle, etc. This chapter talks about how to find the area of a triangle if the side length of the triangle is given. This formula is applicable to all kinds of triangles. The application of Heron's Formula includes measuring the area of land of irregular shape. The land will be divided into different triangles and areas will be measured using Heron's Formula. The formula was introduced by a mathematician called Heron, that's why this is called Heron's Formula. In the Class 9th Maths NCERT solutions , you will find a great explanation for each and every question.

NCERT Solutions for Class 9 Maths Chapter 13

Surface Areas and Volumes Class 9 Solutions: In this particular chapter, we will learn about the surface areas and volumes of a cube, cuboid, cone, cylinder, sphere, hemisphere, etc. The area of the material used to make that particular shape is called the area of the particular shape. We used to see water tanks with capacities of 1000 litres, 750 litres, etc. Which means that the tank can occupy a volume of 1000 litres. We will study about volumes and surface areas in this chapter of Class 9 NCERT Maths,. If a square tank has to occupy 1000 litres, what should be the height, length, and breadth of the tank? What should be the area of the sheet required to cover a gift in the shape of a cylinder? Such questions can be answered after studying this chapter.

NCERT Solutions for Class 9 Maths Chapter 14

Statistics Class 9 Solutions: We see data in various forms, like a weather report for a day, number of seats in elections and how many seats are won by a particular party, number of people affected by a particular disease in an area, number of people consuming alcohol during new Year's day and comparing it with the previous year, etc. Here, you will study about the collection of data, represent it in order and analyse results based on that. For example, you have collected data on marks in maths obtained in the class. From this data, you will understand how many students have passed, how many students got a full mark, what is the most repeated mark, what is the average of the mark, etc. You will study how to arrange data and how to obtain certain results from them in this chapter.

NCERT Solutions for Class 9 Maths Chapter 15

Probability Class 9 Solutions: Probability means chances of happening something. It is one of the best chapters you will learn in 9th 9 maths. We used to say there was a chance for rain today, there is a chance for India to win the match, etc. All our predictions are based on certain previous observations. Consider that you are throwing a die. Then you may get 1, 2, 3, 4, 5 or 6. That is, there are six outcomes in the experiment of throwing a die. We will say the probability or chance of getting a 3 on die is 1/6. In this chapter, you are going to study how these probabilities are calculated.

Benefits of NCERT Solutions for Class 9 Maths

  • You can use NCERT math class 9 solutions as an assistant while doing homework.
  • You can observe some easy methods to solve every problem related to the chapter, as well as the important formulae.
  • Math NCERT solutions for class 9 are written step by step so that you understand how to solve the problems easily and thus score full marks in the examination.
  • We all know the 10th class examination is a board exam. So in order to score high marks in board exams, we have to be good with the subjects of class 9, which form the foundation for class 10.
  • This curriculum is a combination of crucial mathematical chapters that are prerequisites for class 10 maths. If you learn NCERT solutions for class 9 science, you will find the difference while answering the exam.

NCERT Books And NCERT Syllabus

Frequently Asked Question (FAQs)

1. What is the quickest and most effective approach to mastering the NCERT Solutions for Class 9 Maths?

A highly effective method for learning the Class 9 Maths chapters is to work through the NCERT Textbook, which includes a multitude of questions that are critical from an exam standpoint. Before the exercise questions, solved examples are provided to aid students in comprehending the process for solving difficult problems. This approach also enhances analytical and logical thinking abilities, which are crucial for achieving good scores in exams.

2. Is it possible to obtain solved solutions for the questions in the NCERT solutions for class 9?

Absolutely! Solved solutions for the questions in the NCERT Class 9 Maths chapters are available. Careers360 has a team of skilled instructors who design the solutions with great care while taking into account the IQ levels of Class 9 students. Both chapter-wise and exercise-wise solutions can be found online and offline, completely free of charge. The solutions conform to the CBSE guidelines and exam format, with the goal of assisting students in achieving high grades on their exams.

3. Is it recommended to solve questions from the class 9th maths NCERT solutions on a daily basis?

Since Mathematics is a subject that necessitates frequent practice, it is highly recommended that students solve questions from the 9th class maths on a daily basis. This will instill confidence in students, making it easier for them to tackle difficult exam questions. Additionally, it strengthens a student's grasp of the fundamental concepts that will be built upon in higher levels of education.

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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