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class 7 maths case study questions with answers

CBSE 7th Standard CBSE Mathematics question papers, important notes , study materials , Previuous Year questions, Syllabus and exam patterns. Free 7th Standard CBSE Mathematics books and syllabus online. Practice Online test for free in QB365 Study Material. Important keywords, Case Study Questions and Solutions. Updates about latest education news and Scholorships in one place.

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CBSE Class 7th Maths 2023 : Chapter-wise Competency-Based Test Items with Answers; Download PDF

CBSE Class 7th Maths 2023 : Chapter-wise Competency-Based Test Items with Answers; Download PDF

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Class 7th Maths Question Bank for 2023 Exams includes new aptitude-based questions which will cover the full syllabus in 2022 -23 Board Exams.

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Class 7 Maths NCERT Solutions, MCQ Tests, Practice Papers

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CBSE class 7 course material in Mathematics includes the best free videos, online tests, worksheets, previous years' papers, and homework help.

Study Material for Class 7 Mathematics

Here on myCBSEguide, you get all the study material for Class 7 Maths like syllabus, practice questions, revision notes, test papers, sample papers, worksheets, etc. We also provide learning videos for each chapter where understanding the concepts and their application becomes much easier. The  myCBSEguide App  is known for providing quality study material in all the subjects of CBSE. Our sample papers and other educational resources for secondary and senior secondary are the most sold products. 

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CBSE Class 7 Maths Syllabus

Knowing the syllabus correctly is the first step of preparation. So, to know the CBSE Class 7 Maths syllabus or get any other information related to the syllabus, one can check myCBSEguide . Here you need to select your Board, Class, and Subject to get the details of your desired 

The following chapters are included in the Class 7 syllabus:

Class 7 Maths Downloads

Since we provide a variety of study materials which include online MCQ tests, learning videos, and question papers. All these items have a different format, here we bring you the list of class 7 Maths download items that are available in our Class 7 Maths section of the CBSE module.

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CBSE Class 7 NCERT Textbook and Solution

The NCERT is important for the CBSE board as the syllabus is based on it. On our student's  dashboard , CBSE Class 7 Maths NCERT Solution includes all the questions provided in the NCERT text book which is prescribed for class 7 Maths in schools. The questions provided in the NCERT textbook help you to get a thorough understanding of the concepts. Hence, we provide the solutions along with the NCERT questions for class 7 Maths. These are available in myCBSEguide for free to view and download. You can check chapter-wise details for  NCERT Solutions for Class 7 Maths  here.

Class 7 Maths  Test Papers and Sample Question Papers

The sample question papers for Class 7 Maths provided on  myCBSEguide  are mostly question papers from different schools. We also have a section of previous years' questions where you find an assortment of questions asked in various schools in various levels of class 7 Maths school examination. Basically, the idea is to make the students well aware of all possible question typologies for Class 7 Maths. Our question bank for class 7 Maths guarantees success for the students because it exposes them to all types of situational questions.

Class 7 Maths Online Tests and Learning Videos

Students preparing for other competitive examinations or even for their normal school examinations must try our  Online Tests  for class 7 Maths. It teaches them to be time-bound while preparing them to take computer-based examinations. Online tests have also become important post-Covid period since we never know what would the future demand. So it is better to prepare our kids to take up any challenge and face any kind of situation. Online learning is one such preparatory tool.

Chapter-wise learning videos for CBSE Class 7 Maths are available on myCBSEguide. Students who face problems understanding a mathematical concept can refer to these videos for a better understanding of the subject. Our class 7 Maths Learning Videos have helped many children and parents who believe in self-preparation rather than depending upon any tuition or coaching classes for elementary education.

Class 7 Maths Case Study Questions

Being the latest format of competency-based questions, Case-Based Questions have now become the new parameter for testing students' in-depth knowledge of a subject. It is so because these questions are mostly based on real-life situations. Case-based questions can be commonly found for the secondary and senior secondary levels. But case study questions for the elementary classes, that too of assured quality are hard to find. We bring you the best kind of case study questions for class 7 Maths on our students' dashboard. We have just begun with this and intend to add up more and more verified content to this section. 

  • NCERT Solutions for Class 07

Students can download class 7 textbook questions and answers in form of NCERT solution from the myCBSEguide App or Student Dashboard for CBSE students. NCERT publishes books for CBSE and many state boards. In class 7, NCERT has books on English, Hindi, Science Social Science and mathematics. NCERT Solutions – …

CBSE to Conduct Two Term Exams in 2021-22

CBSE has issued a circular on 5th July 2021 regarding the Special Scheme of Assessment for Board Examination Classes X and XII for the Session 2021-22. Here is the complete text of the circular. COVID 19 pandemic caused almost all CBSE schools to function in a virtual mode for the …

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CBSE Worksheets for Class 7 All Subjects Maths, Science, Social Science, English and Hindi are available in myCBSEguide App for free download. Worksheets help students to practice the concepts. The most important thing about these practice sets is their composition. We know, creating worksheets is a time-consuming task. Sometimes, we …

NCERT Solutions for Class 7 Maths

NCERT Solutions for Class 7 Maths includes all the questions provided in NCERT Books for 7th Class Maths Subject. Here all questions are solved with detailed explanation and available for free to check mycbseguide.com. Book: National Council of Educational Research and Training (NCERT) Class: 7th Class Subject: Mathematics NCERT solutions …

NCERT Solutions for Class 8 Maths Exercise 7.2

NCERT Solutions for Class 8 Maths Exercise 7.2 Class 8 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from …

NCERT Solutions for Class 7 Maths Exercise 2.3

NCERT Solutions for Class 7 Maths Exercise 2.3 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. …

NCERT Solutions for Class 7 Maths Exercise 6.2

NCERT Solutions for Class 7 Maths Exercise 6.2 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. …

NCERT Solutions for Class 7 Maths Exercise 10.6

NCERT Solutions for Class 7 Maths Exercise 10.6 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. …

NCERT Solutions for Class 7 Maths Exercise 15.2

NCERT Solutions for Class 7 Maths Exercise 15.2 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. …

NCERT Solutions for Class 7 Maths Exercise 2.4

NCERT Solutions for Class 7 Maths Exercise 2.4 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. …

class 7 maths case study questions with answers

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class 7 maths case study questions with answers

CBSE Sample Papers For Class 7 Maths

Latest cbse sample papers for class 7 maths 2020, cbse solved sample question papers for class 7 maths free pdf download.

Download the latest CBSE sample papers for class 7 Maths for free in high-quality pdf format. We have provided you sample papers for 2020 with solutions. All these papers greatly help you out with this concern. We suggest you practice these papers regularly to increase your Concepts of solving math problems. You can also download NCERT solution for class 7 maths for free.

Download our official android app for free to get NCERT Solutions, NCERT Book, CBSE sample paper, Reference Solutions, Chapter-wise important questions and all other study materials you want in one place. Download the Study Path’s Android app now.

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CBSE Sample papers contain most frequently asked questions in the past and the questions related to all the important concepts which are essential from the examination point of view. They give a brief idea about the examination question paper pattern. All the sample papers provided here help you to write answers properly in your exams. You must regularly practice all the sample papers to get the best result from them. They also help you to find your mistakes and weakness and self-evaluate your exam preparations. Ultimately they boost your score in the exams.

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CBSE Case Study Questions for Class 6 – 10, 12 for Maths, Science, SST

Cbse case study questions for maths, science, social science.

CBSE Case Study Questions:   Case Study Questions for all Class 1, 2, 4, 5, 6, 7, 8, 9,10, 11 and 12 by Experienced Teachers. We Net Ex. Arranged here Important Case Based Questions for CBSE Board – Maths, Science, Social Science, English.

One must keep in mind to not discover the answers straight forwardly within the given entry but moreover think effectively to determine the answer. Case based questions are either MCQs or Attestation Reason Questions, so for endeavoring such questions you must take after the run the show of end. Case studies capture a range of perspectives, as opposed to the single view of an individual you get with a survey response or interview. This gives the opportunity to gain a greater understanding of the subject in hand and reduces the potential for any bias, by diluting the agenda of a particular individual.

class 7 maths case study questions with answers

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Due to a little test, the case ponder can conduct an in-depth investigation. – Case ponders make openings for a wealthy surrender of information, and the profundity of investigation can in turn bring tall levels of legitimacy (i.e. giving an exact and comprehensive degree of what the think about is trusting to degree).

There is no maths question

Hein to. Konsa class ka need hein

where is socail case based question ?????

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CBSE Class 12 Maths Question Paper 2024, All SETs Download PDF

Cbse class 12 maths question paper 2024: here, students can find cbse class 12 maths board paper 2024 various sets along with pdf download links of the same. also find links to cbse class 12 maths paper analysis and answer key below.

Tanisha Agarwal

CBSE Class 12 Maths Question Paper 2024: All the students who appeared for today’s CBSE Class 12 Maths board exam can check the CBSE Class 12 Maths question paper 2024 of various sets here. Usually, students are curious to know about the questions and difficulty level of the paper of various sets produced by CBSE. Here, we will try to provide you all with as many sets of CBSE Class 12 Maths paper 2024 as possible. You can also find PDF download links for all the sets of question paper made available to you here. Students can easily download them by using the PDF download link attached in the boxes below. 

CBSE Class 12 Maths Question Paper 2024

The CBSE 12th Maths question paper 2024 of various sets has been provided below along with a PDF download link. Make sure to check the question paper code and set number before checking the question paper and comparing it with yours. Also, use the PDF download link attached below to save the question paper or view the complete CBSE Class 12 Maths paper 2024

The question paper code of this paper is 65/5/3, as shown in the image 

class 7 maths case study questions with answers

The question paper code of this paper is 65/5/2, as shown in the image 

class 7 maths case study questions with answers

The question paper code of this paper is 65/5/1, as shown in the image 

class 7 maths case study questions with answers

CBSE Class 12 Maths Answer Key 2024

Cbse class 12 maths exam analysis 2024.

All the students and parents who wish to check the CBSE Class 12 Maths paper analysis 2024 can click on the article link attached above. In the article, you will get detailed coverage of the board paper and students' reviews on it. 

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  • Important Questions for CBSE Class 7 Maths Chapter 9 - Rational Numbers

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CBSE Class 7 Maths Chapter - 9 Important Questions - Free PDF Download

Here, we are presenting important questions for Class 7 Maths Chapter 9 for the students preparing for Class 7 Maths exams but unable to prioritize questions for Chapter 7 Rational Numbers. Refer to Vedantu’s important questions on Rational Number for Class 7 that are prepared by our subject experience teachers after extensive research of the topic and analysis of the past exam trends.

By practicing the questions on Rational numbers for Class 7, you can build your confidence to attempt the questions as you can evaluate your answers with the solutions given and make necessary corrections wherever required. Students are recommended to practice the important questions for Class 7 Maths Chapter 9 repeatedly to understand how tricky problems are solved and to enhance the speed of solving problems, which in turn help in strengthening the time management skills.

Read the article below to know how important questions for rational numbers are effective for your exam preparation. Register Online for NCERT Solutions Class 7 Science tuition on Vedantu.com to score more marks in the CBSE board examination. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students. Maths Students who are looking for better solutions can download Class 7 Maths NCERT Solutions to help you to revise the complete syllabus and score more marks in your examinations.

Study Important Questions for Class 7 Maths Chapter 9 - Rational Numbers

1 Mark Questions

1. Reduce \[\dfrac{55}{66}\] into the standard form.

Ans: We know that both $55$ and $66$ are divisible by $11$,

$\dfrac{55\div 11} {66\div 11} $

$ =\dfrac{5}{6} $

2. Fill in the blanks.

(a)$\dfrac{5}{6}.....\dfrac{9}{5}$

(b)$\dfrac{3}{4}......\dfrac{1}{2}$

(c)$\dfrac{2}{5}.......\dfrac{3}{4}$

Ans: (a)$\dfrac{5}{6}  < \dfrac{9}{5}$

(b)$\dfrac{3}{4} > \dfrac{1}{2}$

(c)$\dfrac{2}{5} < \dfrac{3}{4}$

3. Find the additive inverse of $-\dfrac{3}{8}$.

Ans: $\dfrac{3}{8}$

4. Reduce the following to the simplest form.

(a)$\dfrac{36}{54}$

(b)\[\dfrac{8}{72}\]

(a) HCF of $36$ and $54$ is $18$.

Dividing both numerator and denominator by $18$,

$\dfrac{36\div 18} {54\div 18} $

$ =\dfrac{2}{3} $

(b) HCF of $8$ and $72$ is $8$.

Dividing both numerator and denominator by $8$,

$\dfrac{8\div 8} {72\div 8} $

$ =\dfrac{1}{9} $ 

5. Write four more numbers in the following pattern $-\dfrac{1}{2}$, $-\dfrac{1}{3}$, $-\dfrac{2}{4}$, $-\dfrac{2}{6}$,….

$ -\dfrac{1}{2}\times \dfrac{3}{3}=-\dfrac{3}{6} $

$ -\dfrac{1}{2}\times \dfrac{4}{4}=-\dfrac{4}{8} $ 

$ -\dfrac{1}{3}\times \dfrac{3}{3}=-\dfrac{3}{9}  $  

$ -\dfrac{1}{3}\times \dfrac{4}{4}=-\dfrac{4}{12}  $  

Therefore, $-\dfrac{1}{2}$, $-\dfrac{1}{3}$, $-\dfrac{2}{4}$, $-\dfrac{2}{6}$, $-\dfrac{3}{6}$, $-\dfrac{4}{8}$, $-\dfrac{3}{9}$, $-\dfrac{4}{12}$

6. Do $-\dfrac{4}{9}$ and $-\dfrac{16}{36}$ represent the same number?

Ans: $-\dfrac{4}{9}$ and $-\dfrac{16}{36}$ 

$-\dfrac{4}{9}=-\dfrac{4\times 4}{9\times 4}=-\dfrac{16}{36}$

Or $-\dfrac{16}{36}=-\dfrac{16\div 4}{36\div 4}=-\dfrac{4}{9}$

Hence, both represent the same number.

7. List five rational numbers between $-4$ and $-3$.

$-4\times \dfrac{6}{6}=\dfrac{-24}{6}$

$-3\times \dfrac{6}{6}=\dfrac{-18}{6}$

The rational numbers are

$-\dfrac{23}{6},-\dfrac{22}{6},-\dfrac{21}{6},-\dfrac{20}{6},-\dfrac{19}{6}$

8. Give four equivalent numbers for \[\dfrac{3}{8}\].

$ \dfrac{3}{8}\times \dfrac{2}{2}=\dfrac{6}{16}  $  

$ \dfrac{3}{8}\times \dfrac{3}{3}=\dfrac{9}{24}  $  

$ \dfrac{3}{8}\times \dfrac{4}{4}=\dfrac{12}{32}  $  

$ \dfrac{3}{8}\times \dfrac{5}{5}=\dfrac{15}{40}  $  

9. Draw the number line and represent $-\dfrac{7}{3}$ on it.

Ans: This fraction represents two full parts and one part out of 3 equal parts. The negative sign indicates that it is on the negative side of the number line.

Therefore, each space between two integers on the number line must be divided into 3 equal parts.

(Image will be uploaded soon)

10. Rewrite the following rational numbers in the simplest form.

(a)$\dfrac{12}{36}$

(b)$\dfrac{39}{104}$

(a) HCF of $12$ and $36$ is $12$.

Dividing both numerator and denominator by $12$,

$\dfrac{12\div 12}{ 36\div 12}  $  

$ =\dfrac{1}{3}  $  

(b) HCF of $39$ and $104$ is $13$.

Dividing both numerator and denominator by $13$,

$\dfrac{39\div 13}{ 104\div 13} $  

$ =\dfrac{3}{8}  $  

11. Find the value of $\dfrac{4}{14}\div \dfrac{28}{80}$.

Ans: $\dfrac{4}{14}\div \dfrac{28}{80}$

$ =\dfrac{4}{14}\times \dfrac{80}{28}  $  

$ =\dfrac{40}{49}  $  

12. Find the product of $\dfrac{15}{22}\times \dfrac{11}{5}$.

Ans: $\dfrac{15}{22}\times \dfrac{11}{5}$

$ =\dfrac{3}{2}  $  

$ =1\dfrac{1}{2}  $  

13. Find the value of $\dfrac{5}{8}+\dfrac{1}{3}$.

Ans: LCM of $8$ and $3$ is $24$

$\dfrac{5}{8}\times \dfrac{3}{3}=\dfrac{15}{24}  $  

$ \dfrac{1}{3}\times \dfrac{8}{8}=\dfrac{8}{24}  $  

$ \dfrac{15}{24}+\dfrac{8}{24}  $  

$ =\dfrac{5+8}{24}  $  

$ =\dfrac{23}{24}  $  

3 Marks Questions

14. Find the value of 

(a)$\dfrac{3}{4}+\dfrac{1}{2}$

(b)$\dfrac{5}{8}+\dfrac{3}{4}$

Ans: (a) LCM of $4$ and $2$ is $4$

$ \dfrac{3}{4}\times \dfrac{1}{1}=\dfrac{3}{4}  $  

$ \dfrac{1}{2}\times \dfrac{2}{2}=\dfrac{2}{4}  $  

$ \dfrac{3}{4}+\dfrac{2}{4}  $  

$ =\dfrac{3+2}{4}  $  

$ =\dfrac{5}{4}  $  

(b) LCM of $4$ and $8$ is $8$

$ \dfrac{5}{8}\times \dfrac{1}{1}=\dfrac{5}{8}  $  

$ \dfrac{3}{4}\times \dfrac{2}{2}=\dfrac{6}{8}  $  

$ \dfrac{5}{8}+\dfrac{6}{8}  $  

$ =\dfrac{5+6}{8}  $  

$ =\dfrac{11}{8}  $  

$ =1\dfrac{3}{8}  $  

15. Simplify

(a)$\dfrac{2}{5}-\dfrac{1}{2}$

(b)$\dfrac{1}{5}-\dfrac{3}{4}$

(a) LCM of $5$ and $2$ is $10$

$ \dfrac{2}{5}\times \dfrac{2}{2}=\dfrac{4}{10}  $  

$ \dfrac{1}{2}\times \dfrac{5}{5}=\dfrac{5}{10}  $  

$ \dfrac{4}{10}-\dfrac{5}{10}  $  

$ =\dfrac{4-5}{10}  $  

$ =-\dfrac{1}{10}  $  

(b) LCM of $5$ and $4$ is $20$

$ \dfrac{1}{5}\times \dfrac{4}{4}=\dfrac{4}{20}  $  

$ \dfrac{3}{4}\times \dfrac{5}{5}=\dfrac{15}{20}  $  

$ \dfrac{4}{15}-\dfrac{15}{20}  $  

$ =\dfrac{4-15}{20}  $  

$ =-\dfrac{11}{20}  $  

16. Find the product of 

(a) $\dfrac{14}{3}\times \dfrac{21}{63}$

(b) $\dfrac{2}{5}\times \dfrac{8}{9}$

$ =\dfrac{2\times 7}{1\times 9}  $  

$ =\dfrac{14}{9}  $  

$ =1\dfrac{5}{9}  $  

$ =\dfrac{2\times 8}{5\times 9}  $  

$ =\dfrac{16}{45}  $  

17. Find the value of 

(a) $-\dfrac{2}{3}\div \dfrac{3}{4}$

(b) $\dfrac{1}{4}\div \dfrac{5}{8}$

$ =-\dfrac{2}{3}\times \dfrac{3}{4}  $  

$ =-\dfrac{8}{9}  $  

$ =\dfrac{1}{4}\times \dfrac{8}{5}  $  

$ =\dfrac{2}{5}  $  

18. Insert six rational numbers between  $\dfrac{3}{8}$ and $\dfrac{3}{5}$.

Ans: Convert both the denominators into the same denominator.

$\dfrac{3}{8}\times \dfrac{5}{5}=\dfrac{15}{40}$

$\dfrac{3}{5}\times \dfrac{8}{8}=\dfrac{24}{40}$

Therefore, 

$\dfrac{16}{24}$ $\dfrac{17}{24}$ $\dfrac{18}{24}$ $\dfrac{19}{24}$ $\dfrac{20}{24}$ $\dfrac{21}{24}$ 

Download Important Questions of Rational Numbers Class 7 With Solutions - Free PDF

The collection of important questions of Rational numbers Class 7 with solutions are prepared by the subject experts after carrying a thorough analysis of the past year exam trends and latest syllabus.  All questions on Rational Numbers for Class 7 with accurate solutions will come in handy to revise important topics of the chapter. Moreover, the solutions given here will help students to understand the method to frame the stepwise solutions in Class 7 Maths Exam 2021.

The set of important questions of rational number Class 7 provided here is perfect study material for the quick and effective revision of the chapter before the exam as questions of different formats like short answers, long answers are prepared and provided separately by the subject experts.

If you find any doubt concerning any topic of the chapter, you can clear it by practicing these important questions on Rational Numbers. Hence, students are suggested to download important questions of Rational Number Class 7 free pdf through the link provided here.

A Quick Overview of Class 7 Maths Chapter 9 Rational Numbers

Rational numbers are numbers that can be represented in the form of a fraction. It is a part of the real number system. A number is said to be in rational form if it has both numerator and denominator. More specifically, the definition of rational number states that any number can be represented in the ratio of p and q, where p and q are integers and the value of q is not equals to zero.

As per the Ancient Greek Mathematician, rational numbers are used to measure almost everything. Here are some real-life examples of rational numbers.

Taxes are represented in the form of rational numbers.

Divide pizza or anything among your friends.

Interest rate on saving accounts, loan, and mortgage are expressed in rational form.

When you complete half of the portion of your work, you say 50% of ½  of the work is completed.

Let us now understand some of the important terms of Class 7 Maths Chapter 9 Rational Numbers.

What Are Rational Numbers?

A rational number is defined as a number that can be written in the form of p/q, where p and q are integers, and q does not equal to 0. For example, 3/5 is a rational number because p = 3, and q = 5 are integers.

What are Positive and Negative Rational Numbers

Positive rational numbers are numbers whose both and numerators and denominators are positive integers. For example, 3/5 is a positive rational number because both the numerator and denominator of this number are positive.

Negative rational numbers are numbers whose either numerator or denominator are negative integers. For example, -3/5 is a negative rational number as the numerator of this number is negative.

How rational numbers can be expressed in standard form.

A Rational p/q is said to be in standard form if its denominator that is q is positive and both numerator and denominator i.e. p and q have no other common divisor other than 1.

How to Obtain Rational Numbers Between Two Rational Numbers

We can obtain a rational number between two rational numbers p and q simply by dividing it by 2.

For Example,

The rational number between 3/1 and 4/1 is 7/2 as 3/1 + 4/1 = 7/2.

For a negative and positive rational number like -3/20 and 3/20 is -2/20,-1/20, 0/20, 1/20, etc.

For determining a rational number between two rational numbers with different denominators, we first determine the equivalent fraction with the same denominator then find the rational number between them. For example, we can determine a rational number between -1/3 and 5/20 by converting -1/3 to (-1/3) x (3/3) = -39. Accordingly, we have -2/9,-1/9, 0/9, 1/9, 2/9, 3/9, 4/9.

How to Add Two Rational Numbers?

Two rational numbers with similar denominators can be added simply by adding the numerators while keeping the denominators the same whereas two rational numbers with different denominators can be added taking the LCM of the two denominators. Then, we find the equivalent rational numbers of the given rational number with this LCM as their denominators. Then, we add two rational numbers.

Example: Let us add (-7/5) + (-2/3)

Step 1: LCM of 5 and 3 is 15.

Step 2: (-7/5) +  -2/3 = [-7(3) + (-2)(5)]/15

Step 3: (-7/5) + (-2/3) = [-21 + (-10)]/15 = [-21 -10]/15 = -31/15

How to Subtract Two Rational Numbers?

Two rational numbers with similar denominators can be added simply by subtracting the numerators while keeping the denominators the same whereas two rational numbers with different denominators can be subtracted by making the values of two denominators the same by finding LCM of denominator values.

Example: Let us add (-7/5) - (-2/3)

Step 1: LCM of 5 and 3 is 15

Step 2: (-7/5) - (-2/3) = [-7(3) - (-2)(5)]/15

Step 3: (-7/5) - (-2/3)  = [-21 - (-10)]/15 = [-21 + 10]/15= -11/15

How to Multiply Two Rational Numbers?

The formula two find multiplication of two rational numbers is given by”

Product of Rational Numbers Formula  = ({Product of numerators}/{Product of denominators})

Find the product of 6/5 × 4/3

The product of 6/5 × 4/3 = 24/15

The multiplication of a rational number with its reciprocal is always equal to 1.

How to Divide Two Rational Numbers?

The division of two rational numbers is similar to the division of fractions, Here are the steps to find the division of two rational numbers.

Step 1: Find the reciprocal of the divisor value.

Step 2: Find the product of numerator and denominator to obtain the result.

Find the Value of 6/5 ÷ 9/7

Step 1: The reciprocal of 97is 79

Step 2:  Division of two rational number is

6/5 × 7/9 = 42/45

List of the Topics and Subtopics Covered in Class 7 Maths Chapter 9

9.1: Introduction To Rational Numbers

9.2: Need for Rational numbers

9.3: What are Rational Numbers?

9.4: Positive and Negative Rational Numbers

9.5: Rational Number on Number Line

9.6: Rational Number In Standard Form

9.7: Comparison of Rational Numbers

9.8: Rational Numbers Between Two Rational Number

9.9: Operation on Rational Numbers

9.9.1: Addition

9.9.2: Subtraction

9.9.3: Multiplication

9.9.4: Division

To practice the important question on all the topics discussed below, download Important Questions of Rational Numbers Class 7 free pdf now.

How Solving Questions on Rational Number For Class 7 will be Beneficial for Students?

Here are some of the benefits of solving questions on Rational numbers for Class 7.

Students will be familiarized with the different types of questions, complexity level of questions, and important topics of the chapter to focus on.

Students will be able to develop time management skills and problem-solving skills.

Students can analyse the level of their preparation based on the marks obtained. They can also analyse their strength and weakness and accordingly improve them.

Solving these questions repeatedly will help students to revise the complete chapter thoroughly.

Solving the questions will also help students to attempt the questions asked in the exam more confidently as they will be habitual to solve different types of questions.

Candidates are suggested to solve the questions and then cross their answers from the solutions provided. The attempt helps them to gain real-time exam experience.

Practicing the questions enable students to assess their preparedness and understand the techniques to decode problems asked in the exam.

To explore all the benefits mentioned above, it is recommended to download Questions on Rational for Class 7 free pdf now.

When studying CBSE Class 7 Maths Chapter 9 on Rational Numbers, it's crucial to grasp key concepts. Understanding how to represent fractions, compare them, and perform operations like addition, subtraction, multiplication, and division with rational numbers is fundamental. Additionally, learning to convert fractions into decimals and vice versa is essential. Practice solving word problems and equations involving rational numbers to strengthen your problem-solving skills. Remember to simplify fractions and find the lowest common multiple when needed. By mastering these concepts, you'll be well-prepared to handle rational numbers and their applications in various mathematical problems. Consistent practice and a solid understanding will help you excel in this chapter.

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FAQs on Important Questions for CBSE Class 7 Maths Chapter 9 - Rational Numbers

Q1. How can I access NCERT Solutions for Chapter 9 Rational Numbers of Class 7 Maths?

Ans: Using Vedantu’s NCERT Solutions for Chapter 9 Rational Numbers of Class 7 Maths, students will be able to easily prioritise questions for the chapter Rational Numbers. The PDF has questions that are prepared by experienced subject teachers after continuous research of the topic and can be easily downloaded by visiting Vedantu’s official website (vedantu.com) free of cost. The questions are also based on past exam trends. By continuous practice and hard work, the student can gain confidence in tackling problems on rational numbers and solve them. This will also help the student to understand how tricky questions are solved.

Q2. What are rational numbers according to Chapter 9 Rational Numbers of Class 7 Maths?

Ans: Rational numbers can be expressed as numbers that are in the ratio of x and y. Here x (numerator) and y (denominator) are positive integers and y is not equal to 0. X and y should not have any common divisors other than 1. There are positive and negative rational numbers. Positive rational numbers are those whose numerator as well as denominator are positive integers, whereas negative rational numbers have either the numerator or denominator number as negative.

Q3. How can we obtain rational numbers between two rational numbers according to Chapter 9 Rational Numbers of Class 7 Maths?

Ans: Rational numbers refer to numbers that don’t have 0 as the denominator, and where both the denominator and the numerator are integers. To obtain rational numbers between two rational numbers we can simplify it by dividing it by 2. For example; the rational number between 3/2 and 4/2 is 7/4 as 3/2+4/2=7/2.

We can perform all the operations such as add, subtract, multiple and divide with rational numbers. Rational numbers can perform operations only with other rational numbers and will not be able to with irrational numbers.

Q4. What are the Important Topics Covered in NCERT Solutions of Chapter 9 Rational Numbers of Class 7 Maths?

Ans: NCERT Solutions for Class 7 Maths Chapter 9 is one of the most important chapters in Mathematics. There are many important concepts and topics that are covered in this chapter from the examination point of view. The important topics covered are Introduction to rational numbers, need for rational numbers, what are rational numbers, positive and negative rational numbers, rational numbers on the number line,  In the standard form of rational numbers, operations on rational numbers (addition, subtraction, multiplication and division) and obtaining rational numbers between two rational numbers. 

Q5. How do you represent rational numbers in their standard form as explained in Chapter 9 Rational Numbers of Class 7 Maths?

Ans: Rational numbers are a part of the real number system. Rational numbers are represented in terms of a fraction in their standard form. Rational numbers are represented in the ratio of x and y. Here x (numerator) and y (denominator)  are positive integers and y is not equal to 0. Rational numbers are used to represent almost everything. For example; taxes are done in decimals, division of pizza or anything. These numbers are fractions and hence rational numbers. 

Chapterwise Important Questions for CBSE Class 7 Maths

Cbse study materials.

  • NCERT Solutions
  • NCERT Class 7
  • NCERT 7 Maths
  • Chapter 15: Visualising Solid Shapes

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes

* According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 13.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes is the best study material, which provides solutions to all the questions present in the NCERT Class 7 textbook. Students can refer to these NCERT Solutions and practise various questions daily to perform well in the final exams.

Four exercises are present in Chapter 15 – Visualising Solid Shapes of the NCERT Solutions for Class 7 Maths . The solutions provide accurate answers to all the questions present in the exercises. Here we go with the concepts discussed in this chapter.

  • Introduction to Plane Figures and Solid Figures
  • Faces, Edges and Vertices
  • Nets for Building 3-D Shapes
  • Oblique Sketches
  • Isometric Sketches
  • Visualising Solid Objects
  • One way to View an Object By Cutting or Slicing
  • Another Way is By Shadow Play

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NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes

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Access Exercises of NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes

Exercise 15.1 Solutions

Exercise 15.2 Solutions

Exercise 15.3 Solutions

Exercise 15.4 Solutions

Access Answers to NCERT Class 7 Maths Chapter 15 – Visualising Solid Shapes

Exercise 15.1 Page: 281

1. Identify the nets which can be used to make cubes (cut out copies of the nets and try it):

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 1

The given net cannot be folded as a cube.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 2

The given net can be folded as a cube.

Because, it can be folded as below,

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 4

2. Dice are cubes with dots on each face. Opposite faces of a die always have a total of seven dots on them.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 13

Here are two nets to make dice (cubes); the numbers inserted in each square indicate the number of dots in that box.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 14

Insert suitable numbers in the blanks, remembering that the number on the opposite faces should total to 7.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 15

By observing the above figure the sum of the opposite faces is equal to 7.

So, the given net can be folded into a net of dice.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 16

3. Can this be a net for a die?

Explain your answer.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 17

The given net is folded as dice is shown in figure below,

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 18

No, this cannot be a net for a die.

By observing the figure we can say that, one pair of opposite face will have 1 and 4, another pair of opposite face will have 3 and 6 the sum of these two opposite faces are not equal to 7.

4. Here is an incomplete net for making a cube. Complete it in at least two different ways. Remember that a cube has six faces. How many are there in the net here?

(Give two separate diagrams. If you like, you may use a squared sheet for easy manipulation.)

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 19

In the given net there are 3 faces and it can be completed as shown below,

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 20

5. Match the nets with appropriate solids:

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 21

Because, the net (ii) can be folded as a square.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 24

Because, the net (iii) can be folded as a cylinder.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 26

Because, the net (iv) can be folded as a cone.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 28

Because, the net (i) can be folded as a pyramid.

Exercise 15.2 Page: 285

1. Use isometric dot paper and make an isometric sketch for each one of the given shapes:

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 30

2. The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric sketches of this cuboid.

From the question it is given that dimension of a cuboid are 5 cm, 3 cm, and 2 cm.

The three different isometric sketches of this cuboid is shown below,

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 38

3. Three cubes each with 2 cm edge are placed side by side to form a cuboid. Sketch an oblique or isometric sketch of this cuboid.

Oblique sketch

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 41

Isometric sketch

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 42

4. Make an oblique sketch for each one of the given isometric shapes:

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 43

5. Give (i) an oblique sketch and (ii) an isometric sketch for each of the following:

(a) A cuboid of dimensions 5 cm, 3 cm and 2 cm. (Is your sketch unique?)

(b) A cube with an edge 4 cm long.

(i) Oblique sketch

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 47

(ii) Isometric sketch

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 48

Exercise 15.3 Page: 288

1. What cross-sections do you get when you give a

(i) vertical cut (ii) horizontal cut

to the following solids?

(a) A brick

The cross-section of a brick when it is cut into vertically is as shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 51

The cross-section of a brick when it is cut into horizontally is as shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 52

(b) A round apple

The cross-section of a round apple when it is cut into vertically is as shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 53

The cross-section of a round apple when it is cut into horizontally is as shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 54

The cross-section of a die when it is cut into vertically is as shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 55

The cross-section of a die when it is cut into horizontally is as shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 56

(d) A circular pipe

The cross-section of a circular pipe when it is cut into vertically is as shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 57

The cross-section of a circular pipe when it is cut into horizontally is as shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 58

(e) An ice cream cone

The cross-section of an ice cream when it is cut into vertically is as shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 59

The cross-section of an ice cream when it is cut into horizontally is as shown in the figure below,

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 60

Exercise 15.4 Page: 289

1. A bulb is kept burning just right above the following solids. Name the shape of the shadows obtained in each case. Attempt to give a rough sketch of the shadow. (You may try to experiment first and then answer these questions).

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 61

The shape of the shadow obtained from a ball is a circle.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 63

The shape of the shadow obtained from a cylindrical pipe is a rectangle.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 65

The shape of the shadow obtained from a book is a rectangle.

2. Here are the shadows of some 3-D objects, when seen under the lamp of an overhead projector. Identify the solid(s) that match each shadow. (There may be multiple answers for these!)

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 67

Cricket ball, water bottle cap, Disc

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 68

Die, chalk box etc.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 69

Birthday cap etc.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Image 70

Book, keyboard, mobile, etc.

3. Examine if the following are true statements:

(i) The cube can cast a shadow in the shape of a rectangle.

The above statement is true.

(ii) The cube can cast a shadow in the shape of a hexagon.

The above statement is false.

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CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_00.1

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3

Using the CBSE Class 10 Maths Answer key 2024, Students can check their responses and predict their Scores. Access the Class 10 Mathematics Answer key 2024 of Set 1,2,3 on this page.

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_20.1

Table of Contents

As per the Schedule, The Central Board of Secondary Education (CBSE) has conducted the CBSE Class 10 Maths Exam 2024 for basic and standard levels today, March 11. The CBSE Both tests began at 10:30 a.m. and ended at 1:30 p.m. After the exam, we are going to provide the Class 10 Maths Answer Key along with a detailed explanation. The CBSE Class 10 Mathematics Answer Key 2024 is created by highly skilled specialists, and all of the answers are correct and error-free. Stay connected and refresh the page to receive the latest Class 10 math exam questions and answers as soon as possible.

Class 10 Maths Answer Key 2024

The CBSE Class 10 Maths exam Exam is now over at 01:30 P.M. After reaching home from the center, Students rush to find the CBSE Class 10 Maths Answer key 2024 on the Internet.  Using the Class 10 Maths Answer Key 2024, students may compare their answers to all of the questions on the exam and forecast their grades. Our professionals are prepared to supply maths Class 10 Answer Key 2024 to students, so they do not need to visit other websites. Students should bookmark this page and visit it frequently since we publish Class 10 Maths answer key 2024 for all sets before anyone else.

CBSE Class 10 Maths Answer Key 2024

The CBSE Board will hold the Math Exam for the basic and standard levels for a total of 80 points each, with 20 marks for internal assessment. The exam will last three hours, and candidates will have an additional 15 minutes to peruse the question paper. The exam writing time will begin at 10:30 a.m. Check out the highlights of the CBSE Class 10 Maths Exam in the table below:

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_30.1

Class 10 Maths Answer Key 2024 of All Standard and Basic

If you are looking for the Class 10th Maths Answer Key 2024, you can stop the search here. Following the CBSE Class 10 Maths Exam, we will offer the detailed, 100% authentic CBSE Class 10 Maths Answer key 2024 for all sets as soon as possible. Our in-house experts are continually reviewing the Maths solution keys for all sets in depth. Stay connected to us.

Class 10 Maths Answer Key 2024 Set 1

SECTION A This section comprises Multiple Choice Questions (MCQs) of 1 mark each. 20×1=20

1. The next (4th) term of the A.P. √18, √50, √98, is: (A) √128 Answer:  (B) √140 (D) √200

Answer: Answer:  2. If 3 = 2 sin A, 3 = 2 cos A, then the value of x2 + y2 is: (A) 36 (B) 9 (C) 6 (D) 18

Answer: (A) 36

3. If 4 sec θ – 5 = 0, then the value of cot θ is: (A) 3/4 (C) 5/3 (B) 4 /5 (D) 4/ 3

Answer: (D) 4/ 3

4. Which out of the following type of straight lines will be represented by the system of equations 3x + 4y = 5 and 6x + 8y = 7 ? (A) Parallel (B) Intersecting (C) Coincident (D) Perpendicular to each other

Answer: (A) Parallel

5. The ratio of the sum and product of the roots of the quadratic equation 5×2-6x+21 = 0 is : (A) 5:21 (C) 21:5 (B) 2:7 (D) 7:2

Answer: (B) 2:7

6. For the data 2, 9, x + 6, 2x + 3, 5, 10, 5; if the mean is 7, then the value of x is: (A) 9 (B) 6 (C) 5 (D) 3

Answer: (D) 3

7. One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 7 is: (A) 1/7 (C) 1 /5 (B) 1/ 8 (D) 7/ 40

Answer: (B) 1/ 8

8. The perimeter of the sector of a circle of radius 21 cm which subtends an angle of 60° at the centre of circle, is: (A) 22 cm (B) 43 cm (C) 64 cm (D) 462 cm

Answer: (C) 64 cm

9. The length of an arc of a circle with radius 12 cm is 10 cm. The angle subtended by the arc at the centre of the circle, is : (A) 120° (B) 6° (C) 75° (D) 150°

Answer: (D) 150°

10. The greatest number which divides 281 and 1249, leaving remainder 5 and 7 respectively, is : (A) 23 (B) 276 (C) 138 (D) 69

Answer: (C) 138

11. The number of terms in the A.P. 3, 6, 9, 12, …, 111 is: (A) 36 (C) 37 (B) 40 (D) 30

Answer: (C) 37

12. A chord of a circle of radius 10 cm subtends a right angle at its centre. The length of the chord (in cm) is :

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_40.1

(A) 5√2 (B) 10/2 (C) 5 √2 (D) 5

Answer: (B) 10/2

13. The LCM of three numbers 28, 44, 132 is: (A) 258 (B) 231 (C) 462 (D) 924

Answer: (D) 924

14. If the product of two co-prime numbers is 553, then their HCF is : (A) 1 (C) 7 (B) 553 (D) 79

Answer: (A) 1 15. If a and ẞ are the zeroes of the polynomial p(x) = kx² – 30x + 45k and α + β = αβ, then the value of k is : (A) -2/3 (C) 3/2 (B) -3/2 (D) 2/3

Answer: (D) 2/3

16. In the given figure, RJ and RL are two tangents to the circle. If RJL = 42°, then the measure of ✓ JOL is:

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_50.1

Answer: (B) 84°

17. In the given figure, in A ABC, DE || BC. If AD = 2.4 cm, DB = 4 cm and AE = 2 cm, then the length of AC is :

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_60.1

Answer: (C) 16/3 cm

18. If a vertical pole of length 7.5 m casts a shadow 5 m long on the ground and at the same time, a tower casts a shadow 24 m long, then the height of the tower is: (A) 20 m (B) 40 m (C) 60 m (D) 36 m

Answer: (D) 36 m

19. Assertion (A): ABCD is a trapezium with DC || AB. E and F are points on AD and BC respectively, such that EF || AB. Then AE / ED =BF/FC Reason (R): Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.

Answer: (A) 20. Assertion (A): Degree of a zero polynomial is not defined. Reason (R):Degree of a non-zero constant polynomial is 0.

Answer: (B)

CBSE Class 10 Maths Standard Answer Key 2024 for QP Code: 30/4/1

1. If ax + by = a²-b² and bx + ay = 0, then the value of x + y is:

Answer: (C) a-b

2. The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is:

Answer: (B) 13

3. If a polynomial p(x) is given by p(x) = x²- 5x + 6, then the value of p(1) + p(4) is: Answer: (B) 4

4. If the discriminant of the quadratic equation 3x² – 2x + c = 0 is 16, then the value of c is: Answer: (C) -1

5. If an arc subtends an angle of 90° at the centre of a circle, then the ratio of its length to the circumference of the circle is : Answer:   (B) 1:4

6. The area of the sector of a circle of radius 12 cm is 60 cm². The central angle of this sector is : Answer: (D) 150°

7. If the difference of mode and median of a data is 24, then the difference of its median and mean is: Answer: (A) 12

8. Two dice are tossed simultaneously. The probability of getting odd numbers on both the dice is: Answer:   (D) 9/36

8. Two dice are tossed simultaneously. The probability of getting odd numbers on both the dice is : Answer: (D) 9/36

9. The ratio of total surface area of a solid hemisphere to the square of its radius is: Answer:   (C) 3π : 1

10. If sine = 1, then the value of [(1/2)*(sin(0/2))] is: Answer:  (A) 1/2/2 11. Two lines are given to be parallel. The equation of one of these lines is 5x – 3y = 2. The equation of the second line can be : Answer:  (D) 15x9y = 5 12. Three numbers in A.P. have the sum 30. What is its middle term? Answer:  (B) 10 13. In A ABC, DE || BC (as shown in the figure). If AD = 4 cm, AB = 9 cm and AC = 13.5 cm, then the length of EC is: Answer:  (B) 7.5 cm 14. At some time of the day, the length of the shadow of a tower is equal to its height. Then, the Sun’s altitude at that time is : Answer:  (B) 45° 15. In the given figure, AB and AC are tangents to the circle. If ∠ABC = 42°, then the measure of BAC is: Answer:  (A) 96° 16. The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2, 3), B(6, 7) and C(8, 3) is:

Answer: (B) (0, -1) 17. For an event E, if P(E) + P(E) = q, then the value of q² – 4 is: Answer:  (A) -3

18. In the given figure, QR is a common tangent to the two given circles touching externally at A. The tangent at A meets QR at P. If AP = 4.2 cm, then the length of QR is : Answer:  (C) 8.4 cm 19. Assertion : Mid-point of a line segment divides the line segment in the ratio 1: 1. Reason (R): The ratio in which the point (-3, k) divides the line segment joining the points (-5, 4) and (-2, 3) is 1: 2.

Answer:  (C) Assertion (A) is true, but Reason (R) is false. 20. Assertion (A): If the circumference of a circle is 176 cm, then its radius is 28 cm. Reason (R): Circumference = 2 x radius of a circle. Answer:  (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

CBSE Class 10 Maths Answer Key 2024 Set 2

1. If a and ẞ are the zeroes of the polynomial p(x) = kx²- 30x + 45k and α + β = aẞ, then the value of k is: (A) – 2/3 (B) 3 /2 (C) -3/2 (D) 2 /3

2. A chord of a circle of radius 10 cm subtends a right angle at its center. The length of the chord (in cm) is :

3. The next (4th) term of the A.P. √7, √28, √63, is: (A) √70 (B) √84 (C) √97 (D) √112

4. If the product of two co-prime numbers is 553, then their HCF is : (A) 1 (B) 553 (C) 7 (d) 79

5. If x = a cos 0 and y = b sin 0, then the value of b²x² + a2y² is: (A) a²b² (B) ab (9) a4b4 (D) a² + b²

6. If the quadratic equation ax2 + bx + c = 0 has real and equal roots, then the value of c is:

(A) b /2a (B) -b /2a – (C) b²/ 4a (D) -b²/ 4a

7. In the given figure, in A ABC, DE || BC. If AD = 2.4 cm, DB = 4 cm and AE = 2 cm, then the length of AC is :

(A) 10/3 cm (C) 16/3 cm (B) 3/10cm (D) 1.2 cm

8. The length of an arc of a circle with radius 12 cm is 10 cm. The angle subtended by the arc at the centre of the circle, is : (A) 120° (C) 75° (B) 6° (D) 150°

9. If 4 sec 0-5 = 0, then the value of cot 0 is:

(A) 3/4 (B) 4/5 (C) 5/3 (D) 4/3

10. The perimeter of the sector of a circle of radius 21 cm which subtends an angle of 60° at the center of circle, is: (A) 22 cm (B) 43 cm (C) 64 cm (D) 462 cm

11. In the given figure, RJ and RL are two tangents to the circle. If RJL = 42°, then the measure of ✓ JOL is:

12. If the prime factorisation of 2520 is 23 x 3a × b x 7, then the value of a + 2b is: (A) 12 (C) 9 (B) 10 (D) 7

13. Which out of the following type of straight lines will be represented by the system of equations 3x + 4y = 5 and 6x + 8y = 7 ? (A) Parallel (B) Intersecting (C) Coincident (D) Perpendicular to each other

14. One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 7 is:

(A) 1/7 (C) 1/5 (B) 1/8 (D) 7/40

15. The LCM of three numbers 28, 44, 132 is: (A) 258 (C) 462 (B) 231 (D) 924

16. The number of terms in the A.P. 3, 6, 9, 12, …, 111 is: (A) 36 (C) 37 (B) 40 (D) 30

17. The ratio of the length of a pole and its shadow on the ground is 1 : √3. The angle of elevation of the Sun is : (A) 90° (B) 60° (C) 45° (D) 30°

18. If the mean and mode of a data are 24 and 12 respectively, then its median is: (A) 25 (2) 20 (B) 18 (D) 22

CBSE Class 10 Maths Paper Analysis 2024

In the CBSE Class 10 Math Paper Analysis 2024. We evaluate the question paper based on the number of incorrect questions, the amount of questions that are not on the syllabus, and the difficulty level of the question paper. We provided a section-by-section analysis of the Class 10 Mathematics Paper based on feedback from students and professionals in this part.

CBSE Class 10 Maths Exam 2024 -Student’s Reviews

We talked to the students who appeared in Today’s Exam, Several students have expressed varying opinions about the difficulty level of the CBSE Class 10 Maths exam.

  • While some found the paper doable and within their expectations, others were challenged by specific questions, particularly those involving sophisticated computations and application-based challenges.
  • Many students rated the exam as Easy, but they hoped for more clarity in some of the problems. Overall, students are optimistic that their preparation efforts will produce satisfactory outcomes.

Maths Answer Key & Marking Scheme

The CBSE Class 10 Maths Answer Key 2024 and marking scheme might assist pupils in forecasting their exam scores. Check out the Class 10 Maths Paper Marking Scheme tabulated below.

  • The theory paper of class 10 basic and standard level exams is held for a total of 80 points each.
  • The CBSE 10th maths question paper will consist of five sections: A, B, C, D, and E.
  • Section A contains 20 multiple-choice questions (MCQs) worth one mark each.
  • Section B consists of five short answer-I (SA-I) questions worth two points each.
  • Section C includes six short answer-II (SA-II) questions for three points each.
  • Section D consists of four long answer (LA) questions worth five marks each.
  • Section E comprises three units of assessment of four marks each: source-based, case-based, passage-based, or integrated, with sub-parts worth one, one, and two marks each.

Class 10 Maths Board Paper 2024 PDF Download

CBSE Class 10 Math Papers 2024 will be available here. Candidates can predict their results by obtaining the Class 10 SST Question Papers and reading the Class 10 Maths Answer Key 2024.

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_90.1

Class 10 Standard Maths Answer key with Solutions (Last Year)

This section comprises multiple choice questions (MCQ) of 1 mark each.

4. In the given figure, DE || BC. The value of x is

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_100.1

Answer: (c) 6.5 cm

9. Water in a river which is 3 m deep and 40 m wide is flowing at the rate of 2 km/h. How much water will fall into the sea in 2 minutes?

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_130.1

14. The 11th term from the end of the A.P.: 10, 7, 4, 62 is:

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_160.1

17. Which of the following numbers cannot be the probability of happening of an event?

19 Find the sum of first 30 terms of AP: -30, 24, -18,/..

Solution:  a= -30, d= 6

= 15 [-60 + 29 (6)]

= 15 [-60+174]

 If an AP is Sn = n(4n+1), then find the AP

Solution: S1 = T1 = 5

S2= T1 + T2= 18

S2-S1 = T2= 13

AP= 5, 13, 21, 29, …

21. A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed. 

Solution:  r1 = 10.5 cm (sphere) and r2 (cone)= 3.5 cm, h2= 3cm

4/3πr³ = n x 1/3πr2² h

4r³ = nr2² h

4 x (105/10)³= n x 35/10 x 35/10 x 3

Number of cones formed= 126

22. (a) Find the value of m for which the quadratic equation 

(m-1) x² + 2(m-1)x + 1 = 0

Solution:  D= 0

4 (m-1)² – 4(m-1) = 0

4 (m-1) [m-1-1]= 0

(m-1) (m-2)= 0

(b) Solve the following quadratic equation for x: √3x² + 10x + 7√3= 0

Solution:  √3x² + 3x + 7x + 7√3= 0

√3x (x+ √3) + 7 (x + √3)= 0

(x+ √3) [√3x + 7]= 0

x= √3 || x= -7/√3

23. Find the mode of the following frequency distribution: 

Solution:  l= 40, f1= 17, f2= 4, fo= 12

Mode= l + f1-fo / 2f1 – fo- f2

= 40 + 17-12 / 34-12-4 x 10

= 40 + 5/18 x 10

= 40 + 25/9

= 40 + 2.78

Q.5: The product of Rehan’s age (in years) 5 years ago and his age 7 years from now, is one more than twice his present age. Find his present age. 

(x-5) (x+7) = 2x + 1

x² + 2x -35 = 2x+1

x² – 36 = 0

Present Age- 6 years

Q.6 Two concentric circles are of radii 4 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_170.1

Q.7: For what value of x, is the median of the following frequency distribution 34:5? 

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_180.1

Q.8: Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Construct tangents to the circle from these two points P and Q.

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_190.1

Q.9: (a) The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, then find the height of the building.

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_200.1

tan 60° = 50/b

b= 50/ tan 60°

b= 50√3 / 3

tan 30° = h/(50√3/3)

h= 50√3/3 x 1/√3

= 50/3 m= 16.67 metres

Q.9:(b) From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at a height of 3 m from the banks,  then find the width of the river.

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_210.1

Q.10: Following is the daily expenditure on lunch by 30 employees of a company, Find the mean daily expenditure of the employees.

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_220.1

Q.11: From a solid cylinder of the height of 30 cm and radius of 7 cm, a conical cavity of height of 24 cm and same radius is hollowed out. Find the total surface area of the remaining solid. 

Solution:  H= 30 cm

Total Surface Area of Cylinder = Curved Surface Area of Cylinder + Curved Surface Area of Cone + πr²

TSA = 2 πrh +  πrl + πr²

= πr (2h+ l+ r)

= 22/7 x 7 (60+25 + 7)

TSA= 2024 cm 

Q.12: In figure 1, a traingle ABC with angle B = 90 degrees is shown. Taking AB as diameter, a circle has been drawn intersecting AC at point P. Prove that the tangent drawn at point P bisects BC. 

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_230.1

Case Study:1

Q.13: In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different strategies can be used to calculate the number of matchsticks used in different figures. 

One such pattern is shown below. Observe the pattern and answer the following questions using Arithmetic Progression::

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_250.1

(a)  Write the AP for the number of triangles used in the figures. Also, write the nth term of this AP. Which figure has 61 matchsticks? 

Solution-  AP = 4, 6, 8, 10

Tn = 4 + 2(n-1)

Tn= = 4 + 2n – 2

(b) Which figures has 61 matchstickes?

Solution:  12, 19, 26, …

a + (n-1) d= 61

12 + 7(n-1) = 61

7(n-1) = 49

8th figure has 61 matchsticks

Q.14 Gadisagar lake is located in the jaisalmer district of Rajasthan. It was built by king of jaisalmer ad rebuilt by Gadsi Singh in 14th Century. The lake has many chattris. One of them is shown below: 

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_260.1

Observe the picture. From a point A h m above from water level, the angle of elevation of top of chattari (point B) is 45 degrees and angle of depression of its reflection in water(Point C) is 60 degrees. If the height of chhattri above the water level is 10m, then

a) Draw a well-labelled figure based on the above information;

b) Find the height of the point A above the water level. 

(Use √3 = 1.73)

CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_270.1

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Where can I get the CBSE Class 10 Maths Answer key 2024 Standard?

The CBSE Class 10 Maths Answer key 2024 for board Standard and Basic Level will be shared on this page.

What is the total Marks of the CBSE Class 10 Maths Paper?

The CBSE Class 10 Maths Theory page Paper is of 80 Marks. remaining 20 marks is allocated for the Internal assessment.

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CBSE Class 10 Maths Answer Key 2024 for Standard & Basic Set 1,2,3_460.1

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CBSE Board Exam 2024 Live: Class 10th Maths Standard, Basic paper analysis here

  • 3:52 PM IST, Mar 11 Students' feedback on today's CBSE Class 10 Maths papers
  • 2:22 PM IST, Mar 11 CBSE Class 10 Standard Maths paper analysis: Students find paper easy
  • 2:07 PM IST, Mar 11 CBSE Class 10 Mathematics paper review by teacher
  • 2:04 PM IST, Mar 11 CBSE Class 10th Basic Maths paper analysis
  • 1:59 PM IST, Mar 11 CBSE Class 10th Maths papers over, one more exam day remaining
  • 1:50 PM IST, Mar 11 CBSE Class 10th Maths Exam 2024: Answer key, solutions
  • 1:33 PM IST, Mar 11 CBSE Maths exams over
  • 12:29 PM IST, Mar 11 CBSE Class 10th Maths exam 2024 live updates: Class 12th Maths was tricky for some students. What about 10th?
  • 12:12 PM IST, Mar 11 CBSE Class 10th Maths exam 2024: How can students send their feedback
  • 12:10 PM IST, Mar 11 CBSE Class 10th Maths exam 2024: No official answer key
  • 10:36 AM IST, Mar 11 CBSE Class 10th Maths exams 2024 begin
  • 9:38 AM IST, Mar 11 CBSE Class 10th Maths exam 2024: Mathematics Standard paper pattern
  • 8:56 AM IST, Mar 11 CBSE Class 10th Board exam 2024: Mathematics (Basic) paper pattern
  • 8:41 AM IST, Mar 11 CBSE Class 10th Board Exam 2024: Maths paper timings
  • 8:28 AM IST, Mar 11 CBSE to conduct Class 10th Maths exams today

CBSE Class 10th Maths exam 2024 live updates: Paper analysis below (REPRESENTATIVE PHOTO)

CBSE Board Exam 2024 Live Updates: The Central Board of Secondary Education ( CBSE ) conducted the Class 10th Mathematics (Standard) and Mathematics (Basic) papers today, March 11. Both papers started at 10:30 am and ended at 1:30 pm. Read: CBSE Class 10th Maths exam tomorrow; sample papers and other details ...Read More

Follow this live blog for CBSE Class 10 Maths paper analysis and other updates:

CBSE Maths exam 2024: Ludhiana students say exam easy to moderate

In Ludhiana, students claimed the exam as easy to moderate. Manthan, a BCM student, who took the Standard Maths exam, claimed the exam to be “very easy.” He expected 75-80 marks in the 80 marks paper. Satvik, a Basic Maths student from the same school, claimed his paper to be only moderately easy.

Head of Department, Maths, Guru Nanak Public School (Sarabha Nagar) said the exam was average.

“It was only moderately tough. I expect the students who were prepared well to score well.”

The CBSE matric exams began on 15 February and will end on 13 March. There are over 80 subjects in total.

(HT Correspondent)

Students' feedback on today's CBSE Class 10 Maths papers

Students in Lucknow after the CBSE Class 10 Math exam (Handout)

In Luknnow, students of GD Goenka school said the Maths papers were NCERT-based.

As per Vyom and Varun, the paper was a bit difficult and tricky.

Vigyata, Ali , Arya , Neil and Darsh said they are expecting good marks as due to their excellent preparation, their paper went off really well.

Other students like Tahaam, Bharat, Soham stated that the paper was of moderate difficulty and tricky.

(Rajeev Mullick, Lucknow)

CBSE Class 10 Maths paper ‘well designed’, difficulty was ‘moderate’

The Grade 10 mathematics board exam question paper was well-designed to accommodate students with varying levels of proficiency in the subject. Here are some observations and suggestions regarding the paper:

The overall difficulty of the question paper was moderate, offering a fair evaluation for all students. This allowed above-average students to showcase their skills while remaining accessible to those with a solid grasp of the concepts.

It's commendable that the paper-maintained consistency within question sets, ensuring fairness and preventing discrepancies in difficulty levels. However, Set 3 questions were slightly more challenging compared to Sets 1 and 2. Care should be taken to ensure that any increase in difficulty is reasonable and doesn't unfairly disadvantage students.

The distribution of weightage between textbook-based questions and multiple-choice questions (MCQs) in the basic question paper seemed uneven. While it's important to include textbook-aligned questions to assess understanding, MCQs should be designed with basic-level students in mind, ensuring clarity and accessibility.

In summary, the Grade 10 mathematics board exam paper provided a fair and balanced assessment opportunity. Moving forward, maintaining consistency in question sets, adjusting difficulty levels appropriately, and refining the distribution of question types will enhance the effectiveness of the assessment process.

– Benasir P A, TGT Mathematics, JAIN International Residential School Bengaluru

CBSE Class 10th Maths paper easy, aligned with sample paper

The paper was easy to comprehend and aligned well with the CBSE sample papers. Students rated the math paper as ranging from easy to medium difficulty. The paper provided a balanced mix of challenges and opportunities for students to succeed and improve their skills. Although the multiple-choice questions posed no significant challenge, the majority of the questions were standard and not overly difficult. Overall, students found the paper manageable.

The multiple-choice questions (MCQs) were notably straightforward and would likely result in high scores for students. The questions in Sections B, C, and D were easily practicable with a strong grasp of the NCERT material. However, providing detailed solutions would have been time-consuming.

The exam covered a diverse range of topics, and some questions were from past exams. The case studies in Section E demanded a deep comprehension of the subject matter. As anticipated, the basic paper was considerably simpler compared to the standard version.

Overall, the students' feedback reflected a varied perception of the exam's difficulty level, with a majority noting it as moderately challenging.

Kiran Sharma TGT- Mathematics, Manav Rachna International School Sector-51 Mayfield Garden, Gurugram

CBSE Class 10 Standard Maths paper analysis: Students find paper easy

The paper was easy as per the students. The Math question paper had 38 questions, divided into five sections.

  • Section A had 18 MCQs and two assertion-reason-based questions of one mark each.
  • Section B (21-25) were very short answer type questions of 2 marks each. Section C (26 to 31) were short answer questions of 3 marks each.
  • Section D (32-25) were long answer questions of 5 marks each and section E (36-38) were case-study based questions of 4 marks each.
  • Students felt that the trigonometry questions tested the depth of their knowledge.

The CBSE Class 10 Maths question paper was easier than the CBSE Class 10 sample question paper. The question paper was not lengthy at all, most students felt “Section-E” was not difficult but time-consuming. Case study based questions required students to use some extra effort and time but were easy.

– Ajit Pratap Singh, PGT Maths, KIIT World School, Gurugram

CBSE Class 10 Mathematics paper review by teacher

Class 10 Mathematics paper received positive feedback from both students and teachers, aligning well with CBSE sample papers. The timely completion by students and the ease of the case study-based questions suggest a well-balanced and accessible paper. The provision of appropriate choices in the paper further contributed to student satisfaction, reflecting a successful examination.

– Harmeet Kaur, HO, Mathematics at Silverline Prestige School, Ghaziabad

CBSE Class 10th Basic Maths paper analysis

According to Ajay Pal Singh, Principal of Bhai Parmanand Vidya Mandir, the CBSE Class 10 Basic Mathematics (241) paper on March 11, 2024, struck a moderate balance. It featured logical questions that required a comprehensive understanding of the chapters. One question was from the exercise that had been removed from the NCERT.

“In the context of section-wise analysis, Section A presented an easy level . Section B was comparatively simpler, whereas Sections C and D posed an above average challenge, demanding careful reading of the questions. Despite being sourced from NCERT, the questions proved to be of a challenging difficulty level. Section E attained a moderate difficulty level. The exam's design, aimed at assessing students' competency, was challenging. Overall, it encompassed various types and topics of Mathematics,” Singh said.

CBSE Class 10th Maths papers over, one more exam day remaining

CBSE board exam 2024: With the CBSE Class 10 Maths paper now over, only one more exam day is remaining for Class 10th students. On the last day – March 13 – students will write Computer Applications, Artificial Intelligance and Information Technology papers.

CBSE Class 10th Maths Exam 2024: Answer key, solutions

CBSE Class 10th Maths Exam 2024: The CBSE will not provide any official answer key of the Standard and Basic Maths papers of Class 10. If in doubt, students should talk to their subject teachers and get their concerns resolved.

Unofficial answer keys and solutions to the questions may be available later today.

CBSE Maths exams over

CBSE Class 10th Maths Exam 2024: Class 10 Standard and Basic Maths papers of the CBSE ended at 1:30 pm.

Paper analysis shortly.

CBSE Class 10th Maths papers to end at 1:30 pm

CBSE Class 10 Mathematics Standard and Mathematics Basic examinations will end soon. Students can check the detailed analysis of the two papers here after 1:30 pm.

CBSE Class 10th Maths exam 2024 live updates: Class 12th Maths was tricky for some students. What about 10th?

After the CBSE Class 12th Mathematics examination, some students reported the paper as easy, while others rated it as tricky and lengthy. After the Class 10th Mathematics Standard and Mathematics Basic papers end, the analysis of the papers will be shared here.

 GD Goenka Public School Lucknow said that the Applied Mathematics Question paper was as per the blueprint.

CBSE Class 12 Maths Board Exam 2024: Some find paper easy, tricky and lengthy for others

Cbse class 10th maths exam 2024: how can students send their feedback.

The CBSE has a system through which schools can share comments regarding the question papers of bord examinations. Though students can not raise objections directly, they can share it with their respective schools and schools can send it to the board.

CBSE Class 10th Maths exam 2024: No official answer key

CBSE does not release any answer key for the board examination subjects. If in doubt, students should contact their subject teachers and get their queries resolved.

CBSE Class 10th Maths exams 2024 underway

The CBSE Class 10th Mathematics (Standard) and Mathematics (Basic) papers began at 10:30 AM. After today's exam, there will be only one exam day remaining - March 13.

CBSE Class 10th Maths exams 2024 begin

Class 10th Mathematics (Standard) and Mathematics (Basic) papers of the Central Board of Secondary Education (CBSE) have started. These exams will end at 1:30 pm.

CBSE Class 10th Maths exam 2024: Mathematics Standard paper pattern

As per the sample paper of CBSE,

  • The Standard Mathematics exam is three hours long.
  • Maximum marks: 80.
  • There are five sections: A, B, C, D and E.
  • Section A: 20 MCQs, 1 mark each
  • Section B: 5 questions, 2 marks each
  • Section C: 6 questions, 3 marks each
  • Section D: 4 questions, 5 marks each
  • Section E: 3 case-based integrated units of assessment of four marks with sub-parts.

All questions in the paper are compulsory with internal choice in some questions. Candidates have been asked to draw neat figures wherever required and take 22/7 as the value of Pi (π) if not stated in the question.

CBSE Class 10th Board exam 2024: Mathematics (Basic) paper pattern

  • Total marks: 80
  • Time: 3 hours
  • There are five sections in the paper.
  • Section A: 20 MCQs, 1 mark each.
  • Section B: 20 short answer-I questions, 2 marks each.
  • Section C: 6 short answer-II questions, 3 marks each.
  • Section D: 4 long answer questions, 5 marks each.
  • Section E: 3 source/case/passage-based/integrated units of assessments with sub-parts: 4 marks each.
  • All questions are compulsory, with internal choices in some of them.
  • Take 22/7 as the value of Pi (π), if not stated.

(This is as per the sample question paper released by the board)

CBSE Class 10th Board Exam 2024: Maths paper timings

Both Class 10 Standard and Basic Maths papers will begin at 10:30, and the duration of these papers is three hours, meaning the exams will end at 1:30 pm.

CBSE to conduct Class 10th Maths exams today

The Central Board of Secondary Education (CBSE) will conduct Class 10 Mathematics Standard and Mathematics Basic papers today, March 11.

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