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Case Study Questions Class 10 Maths with Solutions PDF Download

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Case Study Class 10 Maths Questions

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Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

Now, CBSE will ask only subjective questions in class 10 Maths case studies. But if you search over the internet or even check many books, you will get only MCQs in the class 10 Maths case study in the session 2022-23. It is not the correct pattern. Just beware of such misleading websites and books.

We advise you to visit CBSE official website ( cbseacademic.nic.in ) and go through class 10 model question papers . You will find that CBSE is asking only subjective questions under case study in class 10 Maths. We at myCBSEguide helping CBSE students for the past 15 years and are committed to providing the most authentic study material to our students.

Here, myCBSEguide is the only application that has the most relevant and updated study material for CBSE students as per the official curriculum document 2022 – 2023. You can download updated sample papers for class 10 maths .

First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.

Class 10 Maths has the following chapters.

  • Real Numbers Case Study Question
  • Polynomials Case Study Question
  • Pair of Linear Equations in Two Variables Case Study Question
  • Quadratic Equations Case Study Question
  • Arithmetic Progressions Case Study Question
  • Triangles Case Study Question
  • Coordinate Geometry Case Study Question
  • Introduction to Trigonometry Case Study Question
  • Some Applications of Trigonometry Case Study Question
  • Circles Case Study Question
  • Area Related to Circles Case Study Question
  • Surface Areas and Volumes Case Study Question
  • Statistics Case Study Question
  • Probability Case Study Question

Format of Maths Case-Based Questions

CBSE Class 10 Maths Case Study Questions will have one passage and four questions. As you know, CBSE has introduced Case Study Questions in class 10 and class 12 this year, the annual examination will have case-based questions in almost all major subjects. This article will help you to find sample questions based on case studies and model question papers for CBSE class 10 Board Exams.

Maths Case Study Question Paper 2023

Here is the marks distribution of the CBSE class 10 maths board exam question paper. CBSE may ask case study questions from any of the following chapters. However, Mensuration, statistics, probability and Algebra are some important chapters in this regard.

Case Study Question in Mathematics

Here are some examples of case study-based questions for class 10 Mathematics. To get more questions and model question papers for the 2021 examination, download myCBSEguide Mobile App .

Case Study Question – 1

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

  • Find the production in the 1 st year.
  • Find the production in the 12 th year.
  • Find the total production in first 10 years. OR In which year the total production will reach to 15000 cars?

Case Study Question – 2

In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.

  • Find the distance between Lucknow (L) to Bhuj(B).
  • If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
  • Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P) OR Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

Case Study Question – 3

  • Find the distance PA.
  • Find the distance PB
  • Find the width AB of the river. OR Find the height BQ if the angle of the elevation from P to Q be 30 o .

Case Study Question – 4

  • What is the length of the line segment joining points B and F?
  • The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
  • What are the coordinates of the point on y axis equidistant from A and G? OR What is the area of area of Trapezium AFGH?

Case Study Question – 5

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

  • If the first circular row has 30 seats, how many seats will be there in the 10th row?
  • For 1500 seats in the auditorium, how many rows need to be there? OR If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10 th row?
  • If there were 17 rows in the auditorium, how many seats will be there in the middle row?

Case Study Question – 6

case study questions class 10 maths with solutions pdf

  • Draw a neat labelled figure to show the above situation diagrammatically.

case study questions class 10 maths with solutions pdf

  • What is the speed of the plane in km/hr.

More Case Study Questions

We have class 10 maths case study questions in every chapter. You can download them as PDFs from the myCBSEguide App or from our free student dashboard .

As you know CBSE has reduced the syllabus this year, you should be careful while downloading these case study questions from the internet. You may get outdated or irrelevant questions there. It will not only be a waste of time but also lead to confusion.

Here, myCBSEguide is the most authentic learning app for CBSE students that is providing you up to date study material. You can download the myCBSEguide app and get access to 100+ case study questions for class 10 Maths.

How to Solve Case-Based Questions?

Questions based on a given case study are normally taken from real-life situations. These are certainly related to the concepts provided in the textbook but the plot of the question is always based on a day-to-day life problem. There will be all subjective-type questions in the case study. You should answer the case-based questions to the point.

What are Class 10 competency-based questions?

Competency-based questions are questions that are based on real-life situations. Case study questions are a type of competency-based questions. There may be multiple ways to assess the competencies. The case study is assumed to be one of the best methods to evaluate competencies. In class 10 maths, you will find 1-2 case study questions. We advise you to read the passage carefully before answering the questions.

Case Study Questions in Maths Question Paper

CBSE has released new model question papers for annual examinations. myCBSEguide App has also created many model papers based on the new format (reduced syllabus) for the current session and uploaded them to myCBSEguide App. We advise all the students to download the myCBSEguide app and practice case study questions for class 10 maths as much as possible.

Case Studies on CBSE’s Official Website

CBSE has uploaded many case study questions on class 10 maths. You can download them from CBSE Official Website for free. Here you will find around 40-50 case study questions in PDF format for CBSE 10th class.

10 Maths Case Studies in myCBSEguide App

You can also download chapter-wise case study questions for class 10 maths from the myCBSEguide app. These class 10 case-based questions are prepared by our team of expert teachers. We have kept the new reduced syllabus in mind while creating these case-based questions. So, you will get the updated questions only.

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case study questions class 10 maths with solutions pdf

CBSE 10th Standard Maths Subject Polynomials Case Study Questions With Solution 2021

By QB365 on 21 May, 2021

QB365 Provides the updated CASE Study Questions for Class 10 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

QB365 - Question Bank Software

10th Standard CBSE

Final Semester - June 2015

Case Study Questions

case study questions class 10 maths with solutions pdf

(ii) The expression of the polynomial represented by the graph is

(iii) Find the value of the polynomial represented by the graph when x = 6.

(iv) The sum of zeroes of the polynomial x 2  + 2x - 3 is

(v) If the sum of zeroes of polynomial at 2  + 5t + 3a is equal to their product, then find the value of a.

case study questions class 10 maths with solutions pdf

(ii) Find the value of \(\alpha\) + \(\beta\) +  \(\alpha\) \(\beta\) .

(iii) The value of p(2) is

(iv) If \(\alpha\) and \(\beta\) are zeroes of  \(x^{2}+x-2, \text { then } \frac{1}{\alpha}+\frac{1}{\beta}=\)

(v) If sum of zeroes of  \(q(x)=k x^{2}+2 x+3 k\)  is equal to their product, then k =

case study questions class 10 maths with solutions pdf

(ii) The axis of symmetry of the given parabola is

(iii) The zeroes of the polynomial, represented in the given graph, are

(iv) Which of the following polynomial has -2 and -3 as its zeroes?

(v) For what value of 'x', the value of the polynomial  \(f(x)=(x-3)^{2}+9 \text { is } 9 ?\)

case study questions class 10 maths with solutions pdf

(ii) What will be the expression of the polynomial given in diagram?

(iii) What is the value of the polynomial, represented by the graph, when x = 4?

(iv) If the tunnel is represented by x 2  + 3x - 2, then its zeroes are

(v) If one zero is 4 and sum of zeroes is -3, then representation of tunnel as a polynomial is

case study questions class 10 maths with solutions pdf

(ii) The sum of product of zeroes taken two at a time is

(iii) Product of zeroes of polynomial p(x) is

(iv) The value of the polynomial p(x), when x = 4 is

(v) If  \(\alpha,\beta,\gamma\)  are the zeroes of a polynomial g(x) such that  \(\alpha+\beta+\gamma=3, \alpha \beta+\beta \gamma+\gamma \alpha=-16\)   and  \(\alpha \beta \gamma=-48\)   then, g(x) =

*****************************************

Cbse 10th standard maths subject polynomials case study questions with solution 2021 answer keys.

(i) (b): Graph of a quadratic polynomial is a parabolic in shape. (ii) (c): Since the graph of the polynomial cuts the x-axis at (-6,0) and (6, 0). So, the zeroes of polynomial are -6 and 6. \(\therefore\) Required polynomial is p(x) = x 2 - (-6 + 6)x + (-6)(6) = x 2 - 36 (iii) (c) : We have, p(x) = x 2 - 36 Now, p( 6) = 62 - 36 = 36 - 36 = 0 (iv) (b): Letf (x) = x 2 + 2x - 3. Then, \(\text { Sum of zeroes }=-\frac{\text { coefficient of } x}{\text { coefficient of } x^{2}}=-\frac{(2)}{1}=-2\) (v) (d): The given polynomial is at 2 + 5t + 3a Given, sum of zeroes = product of zeroes. \(\Rightarrow \quad \frac{-5}{a}=\frac{3 a}{a} \Rightarrow a=\frac{-5}{3}\)

(i) (b): Given, a and \(\beta\) are the zeroes of  \(p(x)=x^{2}-24 x+128\) \(\text { Putting } p(x)=0 \text { , we get }\) \( x^{2}-8 x-16 x+128=0 \) \(\Rightarrow x(x-8)-16(x-8)=0 \) \(\Rightarrow (x-8)(x-16)=0 \Rightarrow x=8 \text { or } x=16 \) \(\therefore \alpha=8, \beta=16\) (ii) (c) :  \(\alpha+\beta+\alpha \beta =8+16+(8)(16) =24+128=152 \) (iii) (d) :  \(p(2)=2^{2}-2 4(2)+128=4-48+128=84\) (iv) (a): Since a and \(\beta\) are zeroes of  \(x^{2}+x-2\) \(\therefore \quad \alpha+\beta=-1 \text { and } \alpha \beta=-2 \) \(\text { Now, } \frac{1}{\alpha}+\frac{1}{\beta}=\frac{\beta+\alpha}{\alpha \beta}=\frac{-1}{-2}=\frac{1}{2}\) (v) (c): Sum of zeroes  \(=\frac{-2}{k}\) Product of zeroes  \(=\frac{3 k}{k}=3\) According to question, we have  \(\frac{-2}{k}=3\) \(\Rightarrow \quad k=\frac{-2}{3}\)

(i) (b): The shape of the path of the soccer ball is a parabola. (ii) (c): The axis of symmetry of the given curve is a line parallel to y-axis. (iii) (a): The zeroes of the polynomial, represented in the given graph, are -2 and 7, since the curve cuts the x-axis at these points. (iv) (d): A polynomial having zeroes -2 and -3 is  \(p(x)=x^{2}-(-2-3) x+(-2)(-3)=x^{2}+5 x+6\) (v) (c): We have  \(f(x)=(x-3)^{2}+9\) \(\text { Now, } 9=(x-3)^{2}+9 \) \(\Rightarrow(x-3)^{2}=0 \Rightarrow x-3=0 \Rightarrow x=3\)

(i) (a): Since, the graph intersects the x-axis at two points, namely x = 8, -2. So, 8, - 2 are the zeroes of the given polynomial. (ii) (b): The expression of the polynomial given in diagram is  \(-x^{2}+6 x+16\) (iii) (c) : Let  \(p(x)=-x^{2}+6 x+16\) \(\text { When } x=4, p(4)=-4^{2}+6 \times 4+16=24\) (iv) (d): Let  \(f(x)=-x^{2}+3 x-2\) Now, consider  \(f(x)=0 \Rightarrow-x^{2}+3 x-2=0\) \(\begin{aligned} &\Rightarrow x^{2}-3 x+2=0 \Rightarrow(x-2)(x-1)=0\\ &\Rightarrow x=1,2 \text { are its zeroes. } \end{aligned}\) (v) (b): Let a and \(\beta\)  are the zeroes of the required polynomial. Given  \(\alpha + \beta = - 3\) If \(\alpha\) = 4, then  \(\beta\) = -7 \(\therefore \quad \text { Representation of tunnel is }-x^{2}-3 x+28 \text { . }\)

(i) (c): For finding  \(\alpha,\beta,\)   \(\gamma\)  consider p(x) = 0 \(\Rightarrow \quad x^{3}-18 x^{2}+95 x-150=0 \) \(\Rightarrow \quad(x-3)\left(x^{2}-15 x+50\right)=0 \) \(\Rightarrow \quad(x-3)(x-5)(x-10)=0 \Rightarrow x=10 \text { or } x=5 \text { or } x=3 \) \(\text { Thus } \alpha=10, \beta=5 \text { and } \gamma=3\) (ii) (d): Here  \(\alpha=10, \beta=5 \text { and } \gamma=3\) \(\therefore\)   Sum of product of zeroes taken two at a time \(\begin{array}{l} =\alpha \beta+\beta \gamma+\gamma \alpha=(10)(5)+(5)(3)+(3)(10) \\ =50+15+30=95 \end{array}\) (iii) (a): Product of zeroes of polynomial p(x) =  \(\alpha\beta\gamma\) = (10) (5) (3) = 150 (iv) (b): We have  \(p(x)=x^{3}-18 x^{2}+95 x-150\) \(\begin{array}{l} \text { Now, } p(4)=4^{3}-18(4)^{2}+95(4)-150 \\ =64-288+380-150=6 \end{array}\) (v) (d):   \(g(x)=x^{3}-(\alpha+\beta+\gamma) x^{2} +(\alpha \beta+\beta \gamma+\gamma \alpha) x-\alpha \beta \gamma \) \(\Rightarrow g(x)=x^{3}-3 x^{2}-16 x-(-48)=x^{3}-3 x^{2}-16 x+48\)

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Class 10 Maths Case Study Questions of Chapter 1 Real Numbers

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Case study Questions in the Class 10 Mathematics Chapter 1  are very important to solve for your exam. Class 10 Maths Chapter 1 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Class 10 Maths Case Study Questions Chapter 1  Real Numbers

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In CBSE Class 10 Maths Paper, Students will have to answer some questions based on  Assertion and Reason . There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Real Numbers Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 1 Real Numbers

Case Study/Passage-Based Questions

Case Study 1: Srikanth has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions at the end of his project as listed below. (i) For what value of n, 4 n  ends in 0?

Answer: (d) no value of n

(ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n, a n  is a rational number?

Answer: (c) for all n > 1 

(iii) If x and yare two odd positive integers, then which of the following is true?

Answer: (d) both (a) and (b)

(iv) The statement ‘One of every three consecutive positive integers is divisible by 3’ is

Answer: (a) always true

(v) If n is any odd integer, then n2 – 1 is divisible by

Answer: (d) 8

Case Study 2: HCF and LCM are widely used in number system especially in real numbers in finding relationship between different numbers and their general forms. Also, product of two positive integers is equal to the product of their HCF and LCM Based on the above information answer the following questions.

(i) If two positive integers x and y are expressible in terms of primes as x =p 2 q 3  and y=p 3 q, then which of the following is true? (a) HCF = pq 2  x LCM (b) LCM = pq 2  x HCF (c) LCM = p 2 q x HCF (d) HCF = p 2 q x LCM

Answer: (b) LCM = pq2 x HCF

ii) A boy with collection of marbles realizes that if he makes a group of 5 or 6 marbles, there are always two marbles left, then which of the following is correct if the number of marbles is p? (a) p is odd (b) p is even (c) p is not prime (d) both (b) and (c)

Answer: (d) both (b) and (c)

(iii) Find the largest possible positive integer that will divide 398, 436 and 542 leaving remainder 7, 11, 15 respectively. (a) 3 (b) 1 (c) 34 (d) 17

Answer: (d) 17

(iv) Find the least positive integer that on adding 1 is exactly divisible by 126 and 600. (a) 12600 (b) 12599 (C) 12601 (d) 12500

Answer: (b) 12599

(v) If A, B and C are three rational numbers such that 85C – 340A = 109, 425A + 85B = 146, then the sum of A, B and C is divisible by (a) 3 (b) 6 (c) 7 (d) 9

Answer: (a) 3

Case Study 3: Real numbers are an essential concept in mathematics that encompasses both rational and irrational numbers. Rational numbers are those that can be expressed as fractions, where the numerator and denominator are integers and the denominator is not zero. Examples of rational numbers include integers, decimals, and fractions. On the other hand, irrational numbers are those that cannot be expressed as fractions and have non-terminating and non-repeating decimal expansions. Examples of irrational numbers include √2, π (pi), and e. Real numbers are represented on the number line, which extends infinitely in both positive and negative directions. The set of real numbers is closed under addition, subtraction, multiplication, and division, making it a fundamental number system used in various mathematical operations and calculations.

Which numbers can be classified as rational numbers? a) Fractions b) Integers c) Decimals d) All of the above Answer: d) All of the above

What are rational numbers? a) Numbers that can be expressed as fractions b) Numbers that have non-terminating decimal expansions c) Numbers that extend infinitely in both positive and negative directions d) Numbers that cannot be expressed as fractions Answer: a) Numbers that can be expressed as fractions

What are examples of irrational numbers? a) √2, π (pi), e b) Integers, decimals, fractions c) Numbers with terminating decimal expansions d) Numbers that can be expressed as fractions Answer: a) √2, π (pi), e

How are real numbers represented? a) On the number line b) In complex mathematical formulas c) In algebraic equations d) In geometric figures Answer: a) On the number line

What operations are closed under the set of real numbers? a) Addition, subtraction, multiplication b) Subtraction, multiplication, division c) Addition, multiplication, division d) Addition, subtraction, multiplication, division Answer: d) Addition, subtraction, multiplication, division

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 1 Real Numbers with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Real Numbers Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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CBSE Case Study Questions

While preparing for the board exams, students are being judged on different levels of skills, such as writing, reading, etc. CBSE Case Study Questions are one of them that helps in assessing critical thinking.

The Central Board of Secondary Education will be asking the case study questions in the Class 10 and 12 board examination. Therefore, here on this page, we have provided the CBSE Case Study Questions at free of cost. Our subject matter experts have prepared Case Study questions so that Apart from the basic standard questions, students can have a variety of problems to solve. 

Just like MCQs, and other written types CBSE Case Study Questions will impact the overall performance of a student. Therefore for the convenience of the students we have provided the download links here, so that they can easily access the Class 10 and 12 Case Study.

Download Subject Wise CBSE Case Study Questions and Answers PDF 

Going through such types of questions help the students to assess their understanding level in the topics discussed in NCERT Class 10 and 12 Books. By practicing the Class 10 and 12 Case Study Questions students will be very confident to ace the board exam. Also the CBSE case study will be very useful for the NEET exam preparation.

Doing a regular practice of CBSE Case Study questions is a great way to score higher marks in the board exams as it will help students to develop a grip on the concepts. 

Here our subject experts have crafted the Subject Wise Case Study. Download Subject Wise CBSE Case Study Question and Answers PDF from the below given links.

CBSE Case Study Question and Answers PDF for Class 12

  • CBSE Case Study Question for Maths
  • CBSE Case Study Question for Physics
  • CBSE Case Study Question for Chemistry
  • CBSE Case Study Question for Biology

CBSE Case Study Question and Answers PDF for Class 10

  • CBSE Case Study Question for Science
  • CBSE Case Study Question for Maths
  • CBSE Case Study Question for English
  • CBSE Case Study Question for Social Science

Case study types of questions are generally descriptive that helps to gather more information easily so, it is kinda easy to answer. However, our subject matter experts have given the solutions of all the CBSE Case Study Questions.

Passage Based  Case Study Questions in PDF

CBSE Case studies are known as Passage Based Questions. These types of problems usually contain a short/long paragraph with 4 to 5 questions. 

Students can easily solve Passage Based Case Study Questions by reading those passages. By reading the passage students will get the exact idea of what should be the answers. Because the passage already contains some vital information or data. However a better understanding of the basic concepts that can be learned from the NCERT Textbooks will aid in solving the Case based questions or passage based questions.

How to Download CBSE Case Study Questions ?

Follow the below given simple steps to know how to download CBSE Case Study Questions:-

  • Open Selfstudys website in your browser
  • Go to the navigation menu that look like this
  • Now, click on CBSE and then Case Study respectively
  • Now, you are ready to select the subject for which you want to download the case study questions.

How to Solve Case Study Based Questions?

There are very simple methods that a student should keep in mind while solving CBSE Case Study Questions for any subject:

  • Read each line of paragraph carefully and pay attention to the given data/numbers. Often questions are framed according to the highlighted data of the passage.
  • Since case study questions are often framed in Multiple choice questions, students should have the knowledge of elimination methods in MCQs.
  • Having a good understanding of the topics that are discussed in CBSE Books are ideal to Solve Case Study Based Questions.

Features Of CBSE  Case Study Questions And Answers PDF

The three most noticeable features of CBSE Case Study Questions And Answers Pdf are -

  • It Is Free To Use:  Keeping in mind the need of students and to help them in doing Self Study, our team has made all the PDF of CBSE Case Study Questions free of cost.
  • Answers Are Given:  Not only the PDFs are free provided but answers are given for all the questions of CBSE Case Study Questions. 
  • PDF Can Be Downloaded Or Viewed Online:  Many students don’t like to download the PDFs on their device due to the shortage of storage. Therefore, CBSE Case Study questions are made available here in online format, so that students can view them online. However, through the Selfstudys app, a learner can download the PDFs too.

Benefits of Using CBSE  Case Study Questions and Answers

The CBSE Case Study Questions and Answers can help a student in several ways:

  • In Exam Preparation:  Those who go through the CBSE Case Study Questions will find support during the exam preparation as case based questions are also asked in the CBSE Board examination. 
  • Help in brushing up the previous learnings:  No matter how brilliant you are, you have to revise the studied topics time and again to keep them refreshed. And in this task, the CBSE Case Study Questions and Answers can help a lot.
  • To develop the critical thinking:  Able to analyse information and make an objective judgement is a skill that is known as critical thinking. A student can use CBSE Case Study Questions with answers to develop critical thinking so that they can make better decisions in their life and in the board examination.

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NCERT Solutions for Class 10 Maths

Ncert solutions for class 10 maths updated for 2023-24 session – free pdf download.

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The answers to the questions present in the NCERT books are undoubtedly the best study material a student can get hold of. These CBSE NCERT Solutions for Class 10 Maths 2023-24 will also help students to build a deeper understanding of concepts covered in the textbook. Practising the textbook questions will help students analyse their level of preparation and knowledge of concepts. The solutions to these questions present in the NCERT books can help students to clear their doubts quickly.

NCERT Solutions Class 10 Maths Chapters NCERT Solutions Class 10 Maths Chapter Details CBSE Class 10 Maths Exam Pattern 2023-2024 CBSE Class 10 Chapter-wise Marks Weightage CBSE Question Paper Design

NCERT Solutions Class 10 Maths Chapters

  • Chapter 1 Real Numbers
  • Chapter 2 Polynomials
  • Chapter 3 Pair of Linear Equations in Two Variables
  • Chapter 4 Quadratic Equations
  • Chapter 5 Arithmetic Progressions
  • Chapter 6 Triangles
  • Chapter 7 Coordinate Geometry
  • Chapter 8 Introduction to Trigonometry
  • Chapter 9 Some Applications of Trigonometry
  • Chapter 10 Circles
  • Chapter 11 Areas Related to Circles
  • Chapter 12 Surface Areas and Volumes
  • Chapter 13 Statistics
  • Chapter 14 Probability

The following are the chapters that have been removed from the NCERT Class 10 Maths textbook 2023-24.

Constructions

NCERT Solutions for Class 10 Maths Free PDF Download

NCERT Solutions of Class 10 Maths list comprises all the chapter-wise answers to the questions present in the NCERT Book for Class 10 Maths, written in a very precise and lucid manner, maintaining the objective of textbooks. The students can refer to the  NCERT Solutions for Class 10 as their additional references and study materials. Practising NCERT textbook exercise solutions will surely help the students in their preparation for the examination.

NCERT Solution for Class 10 Maths

NCERT Solutions Class 10 Maths Chapter Details and Exercises

Ncert solutions for class 10 maths chapter 1 real numbers.

In Chapter 1 of Class 10, students will explore real numbers and irrational numbers. The chapter starts with the Euclid’s Division Lemma, which states that “Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0≤r<b”. The Euclid’s Division algorithm is based on this lemma and is used to calculate the HCF of two positive integers. Then, the Fundamental Theorem of Arithmetic is defined, which is used to find the LCM and HCF of two positive integers. After that, the concept of an irrational number, a rational number and the decimal expansion of rational numbers are explained with the help of the theorem.

NCERT Solutions Class 10 Maths Chapter 1 Real Numbers

Topics Covered in Class 10 Maths Chapter 1 Real Numbers :

Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of √2, √3, √5

Important Steps –

To obtain the HCF of two positive integers, say c and d, with c > d, follow the steps below:

Step 1: Apply Euclid’s division lemma to c and d. So, we find whole numbers, q and r, such that c = dq + r, 0 ≤ r < d.

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

Step 3: Continue the process till the remainder is zero. The divisor at this stage will be the required HCF. This algorithm works because HCF (c, d) = HCF (d, r), where the symbol HCF (c, d) denotes the HCF of c and d, etc.

Also, access the following resources for NCERT Class 10 Chapter 1 Real Numbers, at BYJU’S:

  • NCERT Real Numbers Class 10 Notes
  • Real Numbers Class 10 Important Questions
  • NCERT Exemplar Solutions Class 10 Real Numbers
  • RD Sharma Solutions Real Numbers Class 10

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials

In Polynomials , the chapter begins with the definition of the degree of the polynomial, linear polynomial, quadratic polynomial and cubic polynomial. This chapter has a total of 4 exercises, including an optional exercise. Exercise 2.1 includes questions on finding the number of zeroes through a graph. It requires an understanding of the Geometrical Meaning of the Zeroes of a Polynomial. Exercise 2.2 is based on the Relationship between Zeroes and Coefficients of a Polynomial, where students have to find the zeros of a quadratic polynomial and in some of the questions, they have to find the quadratic polynomial. In Exercise 2.3, the concept of the division algorithm is defined, and students will find the questions related to it. The optional exercise, 2.4, consists of the questions from all the concepts of Chapter 2.

Topics Covered in Class 10 Maths Chapter 2 Polynomials :

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.

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

Step 1: To obtain the first term of the quotient, divide the highest degree term of the dividend by the highest degree term of the divisor. Then carry out the division process.

Step 2: Now, to obtain the second term of the quotient, divide the highest degree term of the new dividend by the highest degree term of the divisor. Again, carry out the division process.

Step 3: Now, the degree of the remainder is less than the degree of the divisor. So, we cannot continue the division any further.

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

This says that

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

p(x) = g(x) × q(x) + r(x),

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

This result is known as the Division Algorithm for polynomials.

Also, access the following resources for NCERT Class 10 Chapter 2 Polynomials, at BYJU’S:

  • NCERT Polynomials Class 10 Notes
  • Polynomials Class 10 Important Questions
  • NCERT Exemplar Solutions Class 10 Polynomials
  • RD Sharma Solutions Polynomials Class 10

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

This chapter explains the concept of Pair of Linear Equations in Two Variables . This chapter has a total of 7 exercises, and in these exercises, different methods of solving the pair of linear equations are described. Exercise 3.1 describes how to represent a situation algebraically and graphically. Exercise 3.2 explains the methods of solving the pair of the linear equation through the Graphical Method. Exercises 3.3, 3.4, 3.5 and 3.6 describe the Algebraic Method, Elimination Method, Cross-Multiplication Method, and Substitution Method, respectively. Exercise 3.7 is an optional exercise which contains all types of questions. Students must practise these exercises to master the method of solving linear equations.

Topics Covered in Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables:

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination. Simple situational problems.

Important Formulas –

The general form for a pair of linear equations in two variables, x and y, is

a 1 x + b 1 y + c 1 = 0

and a 2 x + b 2 y + c 2 = 0,

where a 1 , b 1 , c 1 , a 2 , b 2 , c 2 are all real numbers and a 1 2 + b 1 2 ≠ 0, a 2 2 + b 2 2 ≠ 0.

Also, access the following resources for NCERT Class 10 Chapter 3 Pair of Linear Equations in Two Variables, at BYJU’S:

  • NCERT Pair of Linear Equations in Two Variables Class 10 Notes
  • Pair of Linear Equations in Two Variables Class 10 Important Questions ,
  • NCERT Exemplar Solutions Class 10 Pair of Linear Equations in Two Variables
  • RD Sharma Solutions Pair of Linear Equations in Two Variables Class 10

Self Study Class 10

NCERT Solutions of Class 10 Maths Chapter 4 Quadratic Equations

In this chapter, students will get to know the standard form of writing a Quadratic Equation . The chapter goes on to explain the method of solving the quadratic equation through the factorization method and completing the square method. The chapter ends with the topic on finding the nature of roots, which states that a quadratic equation ax² + bx + c = 0 has

  • Two distinct real roots, if b² – 4ac > 0
  • Two equal roots, if b² – 4ac = 0
  • No real roots, if b² – 4ac < 0

Topics Covered in Class 10 Maths Chapter 4 Quadratic Equations :

The standard form of a quadratic equation ax 2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization and by using the quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day-to-day activities are to be incorporated.

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

If b 2 – 4ac = 0, then

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

Therefore, we say that the quadratic equation ax 2 + bx + c = 0 has two equal real roots in this case.

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

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

So, a quadratic equation ax 2 + bx + c = 0 has

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

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

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

Also, access the following resources for NCERT Class 10 Chapter 4 Quadratic Equations, at BYJU’S:

  • NCERT Quadratic Equations Class 10 Notes
  • Quadratic Equations Class 10 Important Questions
  • NCERT Exemplar Solutions Class 10 Quadratic Equations
  • RD Sharma Solutions Quadratic Equations Class 10

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions

This chapter introduces students to a new topic, Arithmetic Progression , i.e. AP. The chapter constitutes a total of 4 exercises. In Exercise 5.1, students will find the questions related to representing a situation in the form of AP, finding the first term and difference of an AP, finding out whether a series is AP or not. Exercise 5.2 includes the questions on finding out the nth term of an AP by using the following formula:

a n  = a + (n-1) d

The next exercise, i.e. 5.3, contains the questions on finding the sum of the first n terms of an AP. The last exercise includes higher-level questions based on AP to enhance students’ analytical and problem-solving skills.

Topics Covered in Class 10 Maths Chapter 5 Arithmetic Progressions :

Motivation for studying Arithmetic Progression Derivation of the n th term and sum of the first n terms of A.P. and their application in solving daily life problems.

If a 1 , a 2 , a 3 , a 4 , a 5 , a 6 , …  are the terms of AP and d is the common difference between each term, then we can write the sequence as; a ,  a+d, a+2d, a+3d, a+4d, a+5d,…., nth term… where a is the first term. Now, n th  term for arithmetic progression is given as;

n th  term = a + (n-1) d

Sum of the first n terms in Arithmetic Progression;

S n  = n/2 [2a + (n-1) d]

Also, access the following resources for NCERT Class 10 Chapter 5 Arithmetic Progressions, at BYJU’S:

  • NCERT Arithmetic Progressions Class 10 Notes
  • Arithmetic Progressions Class 10 Important Questions
  • NCERT Exemplar Solutions Class 10 Arithmetic Progressions
  • RD Sharma Solutions Arithmetic Progressions Class 10

NCERT Solutions for Class 10 Maths Chapter 6 Triangles

In Chapter 6 of Class 10 CBSE Maths, students will study those figures which have the same shape, but not necessarily the same size. The chapter Triangles starts with the concept of a similar and congruent figure. It further explains the condition for the similarity of two triangles and theorems related to the similarity of triangles. After that, the areas of similar triangles have been explained with a theorem. At the end of this chapter, the Pythagoras Theorem and the Converse of Pythagoras Theorem are described.

Topics Covered in Class 10 Maths Chapter 6 Triangles :

Definitions, examples, and counter examples of similar triangles. 1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. 2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side. 3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional, and the triangles are similar. 4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal, and the two triangles are similar. 5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.

Important Theorems –

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

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

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

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

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

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

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

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

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

Also, access the following resources for NCERT Class 10 Chapter 6 Triangles, at BYJU’S:

  • NCERT Triangles Class 10 Notes
  • Triangles Class 10 Important Questions
  • NCERT Exemplar Solutions Class 10 Triangles
  • RD Sharma Solutions Triangles Class 10

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry

In this chapter, students will learn how to find the distance between two points whose coordinates are given, and to find the area of the triangle formed by three given points. Along with this, students will also study how to find the coordinates of the point which divides a line segment joining two given points in a given ratio. For this purpose, students will get introduced to the Distance Formula, Section Formula and Area of a Triangle in this chapter on Coordinate Geometry .

NCERT Solutions Class 10 Maths Chapter 7 Coordinate Geometry

Topics Covered in Class 10 Maths Chapter 7 Coordinate Geometry :

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

Distance Formula

Section Formula

Also, access the following resources for NCERT Class 10 Chapter 7 Coordinate Geometry, at BYJU’S:

  • NCERT Coordinate Geometry Class 10 Notes
  • Coordinate Geometry Class 10 Important Questions
  • NCERT Exemplar Solutions Class 10 Coordinate Geometry
  • RD Sharma Solutions Coordinate Geometry Class 10

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

This chapter will introduce students to Trigonometry . They will study some ratios of a right triangle with respect to its acute angles, called trigonometric ratios of the angles. The chapter also defines the trigonometric ratios for angles of 0 0 and 90 0 . Further, students will also know how to calculate trigonometric ratios for some specific angles and establish some identities involving these ratios, called trigonometric identities.

Topics Covered in Class 10 Maths Chapter 8 Introduction to Trigonometry :

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios, whichever are defined at 0 o and 90 o . Values of the trigonometric ratios of 30 0 , 45 0 and 60 0 . Relationships between the ratios. TRIGONOMETRIC IDENTITIES Proof and applications of the identity sin 2 A + cos 2 A = 1. Only simple identities to be given

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

Sin θ= \(\begin{array}{l}\frac{Side\, opposite\, to\, angle\, \theta}{Hypotenuse}\end{array} \) = \(\begin{array}{l}\frac{Perpendicular}{Hypotenuse}\end{array} \) = P/H

Cos θ = \(\begin{array}{l}\frac{Adjacent\, side\, to\, angle\, \theta}{Hypotenuse}\end{array} \) = \(\begin{array}{l}\frac{Base}{Hypotenuse}\end{array} \) = B/H

Tan θ = \(\begin{array}{l}\frac{Side\, opposite\, to\, angle\, \theta}{Adjacent\, side\, to\, angle\, \theta}\end{array} \) = P/B

Sec θ = \(\begin{array}{l}\frac{1}{cos\, \theta }\end{array} \)

Cot θ = \(\begin{array}{l}\frac{1}{tan\, \theta }\end{array} \)

Cosec θ = \(\begin{array}{l}\frac{1}{sin\, \theta }\end{array} \)

Tan θ = \(\begin{array}{l}\frac{Sin\, \theta }{Cos\, \theta }\end{array} \)

Trigonometry Table

Trigonometric Ratios of Complementary Angles

sin (90° – A) = cos A,

cos (90° – A) = sin A,

tan (90° – A) = cot A,

cot (90° – A) = tan A,

sec (90° – A) = cosec A,

cosec (90° – A) = sec A

sin 2 A + cos 2 A = 1,

sec 2 A – tan 2 A = 1 for 0° ≤ A < 90°,

cosec 2 A = 1 + cot 2 A for 0° < A ≤ 90°

Also, access the following resources for NCERT Class 10 Chapter 8 Trigonometry, at BYJU’S: 

  • NCERT Introduction to Trigonometry Class 10 Notes
  • Introduction to Trigonometry Class 10 Important Questions
  • NCERT Exemplar Solutions Class 10 Introduction to Trigonometry
  • RD Sharma Solutions Introduction to Trigonometry Class 10

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

This chapter is the continuation of the previous chapter; here, the students will study the applications of trigonometry . It is used in geography, navigation, construction of maps, and determining the position of an island in relation to the longitudes and latitudes. In this chapter, students will see how trigonometry is used for finding the heights and distances of various objects without actually measuring them. They will get introduced to the term line of sight, angle of elevation, and angle of depression.

Topics Covered in Class 10 Maths Chapter 9 Some Applications of Trigonometry:

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

Important Points –

The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.

The angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level, i.e. the case when we raise our head to look at the object.

The angle of depression of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level, i.e. the case when we lower our head to look at the point being viewed.

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You would need to know the following:

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

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

(iii) The height AE of the student.

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

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

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

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

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

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

case study questions class 10 maths with solutions pdf

Also, access the following resources for NCERT Class 10 Chapter 9, Some Applications of Trigonometry, at BYJU’S: 

  • NCERT Some Applications of Trigonometry Class 10 Notes
  • Some Applications of Trigonometry Class 10 Important Questions
  • NCERT Exemplar Solutions Class 10 Some Applications of Trigonometry
  • RD Sharma Solutions Some Applications of Trigonometry Class 10

NCERT Solutions for Class 10 Maths Chapter 10 Circles

In earlier classes, students have studied about a circle and various terms related to a circle, such as a chord, segment, arc, etc. In this chapter, students will study the different situations that arise when a circle and a line are given in a plane. So, they will get thorough with the concept of Tangent to a Circle and Number of Tangents from a Point on a Circle.

Topics Covered in Class 10 Maths Chapter 10 Circles:

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

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

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

Number of Tangents from a Point on a Circle

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

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

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

Also, access the following resources for NCERT Class 10 Chapter 10 Circles at BYJU’S: 

  • NCERT Circles Class 10 Notes
  • Circles Class 10 Important Questions
  • NCERT Exemplar Solutions Class 10 Circles
  • RD Sharma Solutions Circles Class 10

NCERT Solutions for Class 10 Maths Chapter 11 Constructions

This chapter consists of a total of 2 exercises. Whatever students have learned about construction in earlier classes will also help them. In Exercise 11.1, students will study how to divide a line segment, whereas in Exercise 11.2, they will study the construction of tangents to a circle. Methods and steps for construction are explained, and also some examples are additionally given to make it clearer to the students.

Topics Covered in Class 10 Maths Chapter 11 Constructions :

1. Division of a line segment in a given ratio (internally). 2. Tangent to a circle from a point outside it. 3. Construction of a triangle similar to a given triangle.

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

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

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

Also, access the following resources for NCERT Class 10 Chapter 11 Constructions, at BYJU’S:

  • NCERT Constructions Class 10 Notes
  • Constructions Class 10 Important Questions
  • NCERT Exemplar Solutions Class 10 Constructions
  • RD Sharma Solutions Constructions Class 10

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

This chapter begins with the concepts of the perimeter and area of a circle. Using this concept, the chapter further explains how to find the area of sector and segment of a circular region. Moreover, students will get clarity on finding  the areas of some combinations of plane figures involving circles or their parts.

Topics Covered in Class 10 Maths Chapter 12 Areas Related to Circles :

Area of sectors and segments of a circle. Problems based on areas and perimeter/circumference of the above-said plane figures. (In calculating the area of segment of a circle, problems should be restricted to the central angle of 60°, 90° and 120° only.

circumference = 2πr

area of the circle = πr 2

Area of the sector of angle θ = (θ/360) × π r 2

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

case study questions class 10 maths with solutions pdf

Also access the following resources for NCERT Class 10 Chapter 12 Areas Related to Circles at BYJU’S: 

  • NCERT Areas Related to Circles Class 10 Notes
  • Areas Related to Circles Class 10 Important Questions
  • NCERT Exemplar Solutions Class 10 Areas Related to Circles
  • RD Sharma Solutions Areas Related to Circles Class 10

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

In Chapter 13, there are a total of 5 exercises. The first exercise consists of questions based on finding the surface area of an object formed by combining any two of the basic solids, i.e. cuboid, cone, cylinder , sphere and hemisphere. In exercise 13.2, questions are based on finding the volume of objects formed by combining any two of a cuboid, cone, cylinder, sphere and hemisphere. Exercise 13.3 deals with the questions in which a solid is converted from one shape to another. Exercise 13.4 is based on finding the volume, curved surface area and total surface area of a frustum of a cone. The last exercise is optional and has high-level questions based on all the topics of this chapter.

Topics Covered in Class 10 Maths Chapter 13 Surface Areas and Volumes:

Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

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

Diameter of sphere = 2r

Surface area of sphere = 4 π r 2

Volume of Sphere = 4/3 π r 3

Curved surface area of Cylinder = 2 πrh

Area of two circular bases = 2 πr 2

Total surface area of Cylinder = Circumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr 2

Volume of Cylinder = π r 2  h

Slant height of cone = l = √(r 2  + h 2 )

Curved surface area of cone = πrl

Total surface area of cone = πr (l + r)

Volume of cone = ⅓ π r 2  h

Perimeter of cuboid = 4(l + b +h)

Length of the longest diagonal of a cuboid = √(l 2  + b 2  + h 2 )

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

Volume of Cuboid = l × b × h

Also, access the following resources for NCERT Class 10 Chapter 13 Surface Areas and Volumes, at BYJU’S: 

  • NCERT Surface Areas and Volumes Class 10 Notes
  • Surface Areas and Volumes Class 10 Important Questions
  • NCERT Exemplar Solutions Class 10 Surface Areas and Volumes
  • RD Sharma Solutions Surface Areas and Volumes Class 10

NCERT Solutions for Class 10 Maths Chapter 14 Statistics

Here, students will learn the numerical representation of ungrouped data to grouped data and find the Mean, Mode and Median. Also, the concept of cumulative frequency, cumulative frequency distribution and how to draw cumulative frequency curves will be explained.

Topics Covered in Class 10 Maths Chapter 14 Statistics :

Mean, median and mode of grouped data (bimodal situation to be avoided).

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

  • Direct Method: x̅ = \(\begin{array}{l}\frac{\sum_{i=1}^{n}f_i x_i}{\sum_{i=1}^{n}f_i}\end{array} \) , where ∑f i x i is the sum of observations from value i = 1 to n And ∑f i is the number of observations from value i = 1 to n
  • Assumed mean method : x̅ = \(\begin{array}{l}a+\frac{\sum_{i=1}^{n}f_i d_i}{\sum_{i=1}^{n}f_i}\end{array} \)
  • Step deviation method : x̅ = \(\begin{array}{l}a+\frac{\sum_{i=1}^{n}f_i u_i}{\sum_{i=1}^{n}f_i}\times h\end{array} \)

The mode of grouped data:

Mode = \(\begin{array}{l}l+\frac{f_1 – f_0}{2f_1 – f_0 – f_2} \times h\end{array} \)

The median for a grouped data:

Median = \(\begin{array}{l}l+\frac{\frac{n}{2} – cf}{f} \times h\end{array} \)

Also, access the following resources for NCERT Class 10 Chapter 14 Statistics, at BYJU’S: 

  • NCERT Statistics Class 10 Notes
  • Statistics Class 10 Important Questions
  • NCERT Exemplar Solutions Class 10 Statistics
  • RD Sharma Solutions Statistics Class 10

NCERT Solutions for Class 10 Maths Chapter 15 Probability

The last chapter deals with Probability. The chapter starts with the theoretical approach of probability. Subsequently, the chapter explains the difference between  experimental probability and theoretical probability. There are various examples given to  explain it in a n effective way . So, before going through the exercise problems, students must solve the examples of CBSE Maths first.

Topics Covered in Class 10 Maths Chapter 15 Probability:

Classical definition of probability. Simple problems on finding the probability of an event.

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

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

  • The probability of a sure event (or certain event) is 1.
  • The probability of an impossible event is 0.
  • The probability of an event E is a number P(E) such that 0 ≤ P (E) ≤ 1
  • An event having only one outcome is called an elementary event. The sum of the probabilities of all the elementary events of an experiment is 1.

Also, access the following resources for NCERT Class 10 Chapter 15 Probability, at BYJU’S: 

  • NCERT Probability Class 10 Notes
  • Probability Class 10 Important Questions
  • NCERT Exemplar Solutions Class 10 Probability
  • RD Sharma Solutions Probability Class 10

NCERT Solutions for Class 10 Maths PDF in English Medium, as well as Hindi Medium (हिंदी मीडियम) for the academic year 2023-24, are followed by not only CBSE but also UP Board, Uttarakhand board and all other boards following NCERT Textbooks.

CBSE Class 10 Maths Chapter-wise Marks Weightage for 2023-24

 internal assessment class 10, benefits of ncert solutions class 10 maths:.

The Class 10 NCERT Solutions of Maths given here in PDFs have several benefits, which include:

  • The solutions given here are very easy-to-understand.
  • Solutions are provided in steps for better understanding.
  • Diagrams are given to help the students to visualise the solutions.
  • All the questions from each chapter are covered.

Students are advised to prepare all the chapters covered in the solution modules, which will eventually help them to gain a deeper knowledge of concepts. For effective preparations, it is essential for students to understand all the steps provided in the solutions.

How are CBSE Class 10 Maths Solutions of NCERT Helpful for the Board Exams?

CBSE Class 10 Maths is an important subject for students. Here, we have provided complete assistance to students for their preparation. Class 10 is the first benchmark for any student that will reflect in future records of achievement. CBSE always prescribes the NCERT books for exam preparation.

Exam preparation is a rigorous process that requires an overall understanding of individual chapters. This process demands hard work towards studies and an effective approach to getting through the solutions. This significant role is played by NCERT 10 Class Maths Solutions to equip students in preparation for competitive entrance exams. NCERT books are best known for putting forth the concepts in a simple way for better understanding. NCERT Class 10 Books for Mathematics are written in the most lucid and clear manner that helps to break the complex problems in the most efficient way.

Keep visiting to get complete chapter-wise NCERT Solutions for Class 10 Maths PDF free download for all the classes. Students can also find the NCERT Solutions for Class 10 Science , at BYJU’S. Students can download BYJU’S App to get a personalised learning experience and prepare for the exams more effectively.

Frequently Asked Questions on NCERT Solutions for Class 10 Maths

How to grasp the important concepts covered in the ncert solutions for class 10 maths , will the ncert solutions for class 10 maths help me to solve problems easily, where will i get the ncert solutions for class 10 maths pdf, are the ncert solutions for class 10 maths useful for the students under the cbse board, how to get an idea about the important concepts in the ncert solutions for class 10 maths , is byju’s ncert solutions for class 10 maths important, is the ncert solutions for class 10 maths the best reference guide for cbse students.

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HBSE Class 10 Maths Sample Paper 2024 PDF with Solutions_00.1

HBSE Class 10 Maths Sample Paper 2024 PDF with Solutions

The HBSE Class 10 Maths Sample Paper 2024 with solutions is given here. Download & Solve the Haryana Board Class Maths Sample Paper 2024 PDF, Get Answer Key PDF, Know HBSE 10th Maths Paper Pattern

HBSE Class 10 Maths Sample Paper 2024 PDF with Solutions_20.1

Table of Contents

The Board of School Education, Haryana (BSEH/HBSE) is conducting the HBSE 10th Maths Board Paper 2024 on the 12th of March 2024. The Haryana Board of School Education (HBSE) is conducting the Class 10th Maths paper 2024 in a single shift across all the exam centres. To score good marks in the Class 10 Mathematics board exam, students must solve the sample papers and the previous year’s papers. For this, we are providing students with the HBSE Class 10 Maths Sample Paper 2024 PDF with solutions. Students can also download the previous years’ papers here.

HBSE Class 10 Maths Sample Paper 2024

The HBSE Class 10 Maths Sample Paper 2024 has been released by the Haryana Board. The sample papers for both the standard and basic mathematics has been released in a single sample paper comprising 4 sets. The math sample paper contains questions from the official syllabus notified by BSEH. The HBSE Class 10 Sample papers also goes by the name of model paper or practice papers.

The HBSE Class sample paper 2024 questions are formulated by the board experts who also set the board exam paper for the Mathematics subject. Hence, the questions present in the practice paper have higher chances of repetition in the actual board paper. That is why it is crucial for students to go through the Mathematics model paper 2024 to boost their preparation level.

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Haryana Board Class 10 Maths Sample Paper 2024 Highlights

The Haryana Board Class 10 Maths sample paper 2024 consists of different types of questions, ranging from objective type questions to long descriptive questions. The examination is held for a total of 3 hours in offline mode. Students are not given any extra time to read the questions. The highlights of the Haryana Board Class 10 Maths model paper 2024 is given below.

Check: Haryana Board Class 10, 12 Date Sheet 2024

HBSE Class 10 Maths Paper 2024 Design

The Haryana Board releases the HBSE Class 10 Maths Paper 2024 after the conclusion of the exam. But, the question paper design for the Mathematics paper of the Haryana Board has been released. Students should carefully observe the Maths Paper Design for both the standard and basic question paper below.

HBSE Class 10 Maths Sample Paper 2024 PDF with Solutions_30.1

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Haryana Board Class 10th Mathematics Paper 2024 Pattern

The class 10 Mathematics question paper 2024 of the Haryana Board follows the pattern of the model question paper. The HBSE class 10th Maths question paper 2024 consists of five different sections. The Mathematics question paper includes Section A, Section B, Section C, Section D, and Section E. The detailed exam pattern is given below.

  • There are one-mark questions in Section A ranging from 1 to 20. Multiple-choice questions (MCQs) range from 1 to 18, with one-word answers Questions 19 and 20 are Assertion-Reasoning based; fill in the blank, True/False.
  • Very Short Answer Type (VSA) questions with two marks apiece, ranging from 21 to 25, make up Section-B.
  • Short-answer (SA) style questions with three marks apiece, ranging from 26 to 31, make up Section-C.
  • Long-Answer (LA) type questions with five marks each, ranging from 32 to 35, are found in Section-D.
  • In Section-E, questions 36 through 38 are four-mark questions based on case studies. Every case study question has an internal choice option worth two marks.
  • Every question is compulsory in the paper. Nonetheless, two questions in Section B, two questions in Section C, two questions in Section D, and three questions in Section E all allow for internal choice.

Class 10 Maths Model Questions 2024 Haryana Board

The Haryana Board Class 10 Model questions that are important for the Maths board exam is given below. Along with the questions, answers to the grammar-based questions and objective questions is also provided.

Q. Two APs have the same common difference. The first term of one of theseis-2 and that of the other is -6.Then the difference between their 5th terms is

(a) 2       (b) -2       (c)4       (d)-4

Q. The point which lies on the perpendicular bisector of the line segment joining the points A(-2,-5) and B(2,5) is

(a) (0,0)     (b) (0,2)     (c) (2,0)     (d)(-2,0)

Q. .If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80° ,then ∠POA is equal to

(a) 50°     (b) 60°    (c) 70°     (d)80°

Q. The common point of a tangent to a circle and the circle is called____________

Q. The value of tanA is always less than 1. (True /False)

Q. If ∆ABC is right angled at C , then the value of cos(A+B) is ______________

Q. In a circle of diameter 70 cm, if an arc subtends an angle of 60° at the centre, then length of arc ______________

Q. The radii of two cylinders are in the ratio 5:7 and their heights are intheratio3:5, then the ratio of their curved surface area is :

(a) 3:7     (b)7:3     (c)4:7     (d)7:4

Q. If the mean and the median of a data are 12 and 15 respectively, then its mode is (a) 13.5     (b)21     (c) 6     (d)14

Q. For which value(s)of k will the pair of equations kx +3y = k-3 12x + ky =k have no solution?

Q. Two concentric circles are of radii 5cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Q. A car has two wipers which do not overlap. Each wiper has a blade of length 25cm sweeping through an angle of 115°.Find the total area cleaned at each sweep of the blades.

Q. The difference between two numbers is 26 and one number is three times the other. Find them

Q. A ladder 15m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, find the height of the wall.

HBSE Class 10 Maths Sample Paper 2024 PDF with Solutions_60.1

Math Sample Paper 2024 Class 10 PDF Download HBSE

The Math Class 10th Sample Paper 2024 of the Haryana Board is provided below. Students should solve the questions provided in the model paper to get good marks in the exam. The sample papers for all the four codes is given below.

Haryana Board Class 10 Maths Sample Paper Set D

Haryana Board Class 10 Maths Sample Paper Set C

Haryana Board Class 10 Maths Sample Paper Set B

Haryana Board Class 10 Maths Sample Paper Set A

HBSE Class 10 Maths Sample Paper 2024 Solutions

The solutions for the Haryana Board Class 10 Maths sample paper 2024 given above has also been provided by us in the PDF form. Students are advised to first solve the sample papers on their own and then check the solutions given in the answer key. In this way, they will be able to improve their conceptual clarity.

HBSE Class 10 Maths Sample Paper Answer Key 2024 Set D

HBSE Class 10 Maths Sample Paper Answer Key 2024 Set C

HBSE Class 10 Maths Sample Paper Answer Key 2024 Set B

HBSE Class 10 Maths Sample Paper Answer Key 2024 Set A

HBSE Class 10 Maths Sample Paper 2024 PDF with Solutions_70.1

HBSE 10th Class Mathematics Previous Year Question Papers

The pattern and nature of the HBSE 10th Mathematics Paper 2024 will be identical to the previous year papers. That is why, we are also offering students with the HBSE Class 10 Mathematics previous year papers pdf below in the article. The Haryana Board previous year question papers are the best resource for practicing before the exam. The previous year papers of the HBSE 10th class Mathematics is given herein.

HBSE Class 10 Maths Question Paper 2022 Part II

HBSE Class 10 Maths Question Paper 2022 Part 1

Haryana Board Class 10 Math Question Paper 2023

Maths Answer Key 2024 HBSE Class 10

The Answer key for the questions asked in the Maths board paper of class 10 will be provided below by our experts. Students should make sure to check their answers against the answer key provided below. The expert answer key contains 100% accurate answers for all the questions. The answer key will be updated shortly after the conclusion of the exam.

HBSE Class 10 Maths Sample Paper 2024 PDF with Solutions_80.1

HBSE 10th Maths Board Paper PDF 2024

The HBSE 10th Maths Board Paper 2024 PDF will be provided below after the conclusion of the exam. Students can use this exam paper to check the answers. The question paper will also be beneficial for the students going to take the board exam next year.

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How many sections are there in the Haryana Board Class 10 Maths paper 2024?

The Haryana Board Class 10 Mathematics paper has a total of five sections.

Which section consists objective questions in the HBSE 10th Maths paper?

The section A of the HBSE Maths paper consists of objective questions.

How many questions are there in the Haryana Board 10th Mathematics paper?

The Haryana Board 10th class Mathematics exam paper has a total of 38 questions.

Where can I download the Haryana Board 10th sample papers 2024?

Students can download the Haryana Board 10th sample papers 2024 PDF along with the answer key from the article above.

Is there any negative marking in the HBSE 10th Mathematics paper?

No, there is no negative marking in the Mathematics exam of the HBSE Class 10.

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CBSE Class 12 Physics Exam 2024 Question Paper and Answer Key

CBSE Class 12 Physics Exam 2024 Question Paper and Answer Key

Table of Contents

The CBSE Class 12 Physics examination, held on March 4th, 2024, has concluded, and students who appeared for the exam can now access the answer key for all sets. The answer key for CBSE Class 12 Physics Exam 2024 is now available on this platform for students to review and assess their performance.

Class 12 Physics Answer Key 2024:

Cbse class 12 physics answer key 2024 set 1 question, question paper code: 55/4/1.

Q1. Two charges + q each are kept ‘2a’ distance apart. A third charge – 2q is placed midway between them. The potential energy of the system is- Answer: (C) -7q2 /8πε0a

Q2. Two identical small conducting balls and B 2 are given -7 pC and + 4 B 1 pC charges respectively. They are brought in contact with a third identical ball B 3 and then separated. If the final charge on each ball is -2 pC, the initial charge on B 3 was Answer: B) – 3 pC

Q3. The quantum nature of light explains the observations on the photoelectric effect as- Answer: (B) the maximum kinetic energy of photoelectrons depends only on the frequency of incident radiation.

Q4. The radius (r n ) of nth orbit in Bohr model of hydrogen atom varies with n Answer: (C) r n & n²

Q5. A straight wire is kept horizontally along east-west direction. If a steady current flows in wire from east to west, the magnetic field at a point above the wire will point towards Answer: (C) North

Q6. The magnetic susceptibility for a diamagnetic material is Answer: (A) small and negative

Q7. A galvanometer of resistance 100 ohm is converted into an ammeter of range (0-1 A) using a resistance of 0.1 ohm. The ammeter will show full scale deflection for a current of about Answer: (D) 0.1 A

Q8. A circular loop A of radius R carries a current L. Another circular loop B of radius r (= R/20) placed concentrically in the plane of A. The magnetic flux linked with loop B is proportional to Answer: (C) R2/3

Q9. Figure shows the variation of inductive reactance X₁ of two ideal inductors of inductance L 1 and L 2 with angular frequency w. The value of Answer: (C) 3

Q10. The phase difference between electric field E and magnetic field B in an electromagnetic wave propagating along z-axis is Answer: (A) Zero

Q11. A coil of N turns is placed in a magnetic field such that B is perpendicular to the plane of the coal R changes with time as B=B 0 cos (2 πt/T ) where ‘T’ is time period. The magnitude of emf induced in the coil will be maximum at Answer: (C) t = n T/2

Q12. In Balmer series of hydrogen atom, as the wavelength of spectral lines decreases, they appear-

Answer: (B) further apart and stronger in intensity.

Q13. Assertion (A): Electrons are ejected from the surface of zinc when it is irradiated by yellow light. Reason (R): Energy associated with a photon of yellow light is more than the work function of zinc.

Answer:(C) If Assertion (A) is true and Reason (R) is false.

Q14. Assertion (A): The temperature coefficient of resistance is positive for metals and negative for p-type semiconductors. Reason (R): The charge carriers in metals are negatively charged, whereas the majority charge carriers in p-type semiconductors are positively charged.

Answer: (A) If both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Q15. Assertion (A): When electrons drift in a conductor, it does not mean that all free electrons in the conductor are moving in the same direction. Reason (R): The drift velocity is superposed over large random velocities of electrons.

Q16. Assertion (A): In interference and diffraction of light, light energy reduces in one region producing a dark fringe. It increases in another region and produces a bright fringe. Reason (R): This happens because energy is not conserved in the phenomena of interference and diffraction.

Answer: (B) If both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)

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[Latest]Important Questions for Class 10 Maths CBSE Chapter Wise PDF

Available CBSE NCERT Chapter Wise Extra and Important Questions for Class 10 Maths with answers and solutions PDF will surely encourage students to secure graceful marks in the board examinations. Access the below links & practice well for your maths examination.

case study questions class 10 maths with solutions pdf

Class 10 Maths Important Questions with Answers PDF

Important Question of Maths Class 10 plays a vital role in scoring more marks in board exams. We have provided Important Extra questions for class 10 Mathematics & Class 10 Maths Board Important Questions with Answers.

  • Real Numbers Class 10 Important Questions
  • Polynomials Class 10 Important Questions
  • Pair of Linear Equations in Two Variables Class 10 Important Questions
  • Quadratic Equations Class 10 Important Questions
  • Arithmetic Progressions Class 10 Important Questions
  • Triangles Class 10 Important Questions
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  • Introduction to Trigonometry Class 10 Important Questions
  • Applications of Trigonometry Class 10 Important Questions
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  • Constructions Class 10 Important Questions
  • Areas Related to Circles Class 10 Important Questions
  • Surface Areas and Volumes Class 10 Important Questions
  • Statistics Class 10 Important Questions
  • Probability Class 10 Important Questions

Candidates who are studying under CBSE, UP, MP, Gujarat boards, and in search of NCERT Important Questions Class 10 Maths with Solutions.

We hope the given NCERT Important Questions for Class 10 Maths with Solutions Answers Chapter Wise Pdf free download of Mathematics will help you.

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CBSE Class 10 Social Science Answer Key 2024 (All Sets): Download PDF

img src="https://img.jagranjosh.com/images/2024/March/732024/sst_exam-answer-key-2024.jpg" width="1200" height="675" />

CBSE Class 10 Social Science  Answer Key 202 4 :  The CBSE Class 10th Social Science Exam was conducted today, March 7, 2024. The exam paper has been reviewed to be well-balanced and moderately easy. Now, most of the students must be eagerly awaiting the answers or solutions for today’s CBSE Class 10 Social Science exam as they seek to review and assess their performance.

So, to help all of them, we have presented below the answer key for today’s CBSE Class 10 Social Science Paper 2024. This answer key includes answers to all questions which have been meticulously crafted by the subject matter experts. In addition to the answer key, you can check the exam analysis and also download all sets of the question paper in PDF here.

CBSE Class 10  Social Science  Paper Analysis 2024: Student Feedback,  Difficulty Level; Watch Video!

CBSE Class 10  Social Science  Question Paper 2024 PDF (All Sets)

Watch Video for Students' Reactions on CBSE Class 10 Social Science Exam 2024

Cbse class 10 social science  answer key 202 4.

(Multiple Choice Questions)

1.From which of the following countries Giuseppe Garibaldi belonged to?

(a) Austria

Answer: (b) Italy

2.Two statements are given below. They are Assertion (A) and Reason (R).

Read both the statements and choose the correct option.

Assertion (A): The most serious source of nationalist tension in Europe after 1871 was Balkan.

Reason (R): A large part of the Balkan was under the control of Ottoman Empire.

(a) Both, (A) and (R) are true and (R) is the correct explanation of (A).

(b) Both, (A) and (R) are true but (R) is not the correct explanation of (A).

(c) (A) is true but (R) is false.

(d) (A) is false but (R) is true.

 Answer: (a) Both, (A) and (R) are true and (R) is the correct explanation of (A).

3.Arrange the following events in chronological order and choose the correct option from the following:

I.Treaty of Constantinople

II.Defeat of Napoleon

III.Unification of Italy

IV.Unification of Germany

(a) I, II, IV and III

(b) II, III, I and IV

(c) II, I, IV and III

(d) IV, I, III and II

 Answer: (c) II, I, IV and III

4.Which one of the following pairs regarding Indian nationalism is correctly matched?

          Leaders                   Contribution

(a) Sardar Patel    :  Hindustan Socialist Republican Army

(b) Bhagat Singh    :  Swaraj Party

(c) C.R. Das              :  Bardoli Satyagraha

(d) Jawahar Lal Nehru : Oudh Kisan Sabha

 Answer:(d) Jawahar Lal Nehru : Oudh Kisan Sabha 

5.Choose the correctly matched

(a) Ferrous - Natural Gas

(b) Non-Ferrous - Nickel

(c) Non-Metallic Minerals - Limestone

(d) Energy Minerals - Cobalt

 Answer: (c) Non-Metallic Minerals - Limestone

6.Read the given statements and choose the correct option with regard to Rabi cropping season from the following :

I.Rabi crops are sown in winter.

II.Sown from October to December and harvested from April to June.

III.Important crops are Maize, Cotton, Jute.

IV.Punjab, Haryana, Uttar Pradesh are important for the production of wheat.

(a) I, III and IV

(b) II, Ill and IV

(c) I, II and IV

(d) I, II and III

Answer: (c) I, II and IV

7.Identify the soil with the help of following information.

  • It develops in areas with high temperature.
  • It is the result of intense leaching due to heavy rain.
  • Humus content is low.

(a) Arid soil

(b) Yellow soil

(c) Laterite soil

(d) Black soil

Answer: (c) Laterite soil

8.Which of the following term refers to the belief in and advocacy for the social, political and economic equality of women?

(a) Patriarchy

(b) Matriarchy

(c) Socialist

(d) Feminists

Answer: (d) Feminists

9.Read the given statements :

  • India has no official religion.
  • All the communities have freedom to profess and practice any religion in India.

Which one of the following constitutional term is used for the above statements ?

(a) Republic

(b) Secular

(c) Sovereign

(d) Socialist

Answer: (b) Secular

10.Match the Column I with Column II and choose the correct option :

Answer: Option (d)

11.Which of the following was the primary objective of Belgium to form the separate  government in Brussels?

(a) Promoting cultural events.

(b) Managing international relations.

(c) Enforcing local laws.

(d) Ensuring linguistic accommodation.

Answer: (d) Ensuring linguistic accommodation.

12.Which one of the following countries has two-party system?

(b) United Kingdom

(d) Pakistan

Answer:(b) United Kingdom

13.What role do 'checks and balances' play in a democratic country?

Choose the most suitable option from the following.

(a) To establish a direct form of government without representatives.

(b) To create a separation of powers to prevent from authoritarianism.

(c) To prevent any change to the Constitution.

(d) To ensure absolute power for one branch of government.

Answer: (b) To create a separation of powers to prevent from authoritarianism.

14.Suppose, the monthly income of the family members is as follows respectively :

  • Mother - Rs. 50,000/-
  • Father - Rs. 40,000/-
  • Son - Rs. 20,000/-
  • Daughter - Rs. 20,000/-

The average income of the family would be :

(a) Rs. 32,000/-

(b) Rs. 30,000/-

(c) Rs. 32,500/-

(d) Rs. 33,000/-

Answer:(c) Rs. 32,500/-

15.Which one of the following indices is given priority by the World Bank with respect to development?

(a) Infant Mortality Rate

(b) Equality

(c) Body Mass Index

(d) Per Capita Income

Answer: (d) Per Capita Income

16.Choose the correct option to fill in the blank.

Removing barriers or restrictions on business and trade set by the government is called as ____________.

(a) Disinvestment

(b) Special Economic Zones

(c) Liberalisation

(d) Foreign Direct Investment

Answer:  (c) Liberalisation

17. Which one of the following is an example of organized sector activities?

(a) A farmer irrigating his field.

(b) A handloom weaver working in her house.

(c) A headload worker carrying cement.

(d) A teacher taking classes in a government school.

Answer: (d) A teacher taking classes in a government school.

18.Which of the following are developmental goals of a prosperous farmer?

Choose the correct from the given options.

I.Better wages

II.Higher support prices for crops

III.Assured high family income

IV.More days for work

(a) Only I and II are correct.

(b) Only II and IV are correct.

(c) Only II and III are correct.

(d) Only I and IV are correct.

Answer: (c) Only II and III are correct.

19. Why do lenders often require collateral before lending loan? Choose the most suitable option from the following.

(a) To lower interest rates for borrowers.

(b) To establish personal relations.

(c) To increase their profit margins.

(d) To mitigate the risk of loan default.

Answer: (d) To mitigate the risk of loan default.

20. Look at the given picture carefully and infer the income of the bank.

Choose the correct option from the following.

(a) The difference between the amount deposited and borrowed by the bank to Reserve Bank of India.

(b) The difference of amount of interest between what is charged from borrowers and what is paid to depositors.

(c) The difference of interest rate between what is charged from borrowers and what is charged from depositor.

(d) The difference between the amount deposited by the depositor and borrowed by the borrower.

Answer: (b) The difference of amount of interest between what is charged from borrowers and what is paid to depositors.

Note* More answers are being updated. Keep refreshing this page for answers to the remaining questions.

Also Check: 

CBSE Class 10 Syllabus 2023-2024 (All Subjects)

CBSE  Class 10 Deleted Topics 2023-2024 (All Subjects)

CBSE Class 10 Sample Paper 2023-2024 (All Subjects)

CBSE Class 10 Practice Papers 2023-2024

CBSE Class 10 Important MCQs All Subjects 2023-2024

NCERT Solutions for Class 10 (All Subjects and Chapters)

CBSE Class 10 Social Science Answer Key 2024 (All Sets): Download PDF

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  • CBSE Class 10

CBSE Class 10 Science Question Paper 2024 PDF with Answer Key (All Sets)

Cbse class 10 science paper 2024: get free pdf download of all sets of the cbse class 10 science question paper 2024 here. also, get the link to download the cbse class 10 science answer key for all sets..

Gurmeet Kaur

CBSE Class 10 Science  Exam Pattern 2024:

The CBSE Class 10 Science question paper included 39 questions for 80 marks. The time allowed to write the paper was 3 hours. All questions were compulsory with some questions having internal choices.

  • Section A consisted  of 20 MCQs carrying 1 mark each.
  • S ection B consisted of  6 Very Short questions carrying 02 marks each.
  • S ection C consisted  of 7 Short Answer type questions carrying 03 marks each.
  • Section D consisted  of 3 Long Answer type questions carrying 05 marks each.
  • Section E consisted of  3 source-based/case-based units of assessment of 04 marks each with sub-parts.

CBSE Class 10 Science  Question Paper 2024  (Set 1)

case study questions class 10 maths with solutions pdf

CBSE Class 10 Science  Question Paper 2024 (Set 2)

case study questions class 10 maths with solutions pdf

CBSE Class 10 Science  Question Paper 2024 (Set 3)

case study questions class 10 maths with solutions pdf

CBSE Class 10 Science  Answer Key 2024  (All Sets)

To be updated

Also Check:

CBSE Class 10 Syllabus 2023-2024 (All Subjects)

CBSE  Class 10 Deleted Topics 2023-2024 (All Subjects)

CBSE Class 10 Sample Paper 2023-2024 (All Subjects)

CBSE Class 10 Practice Papers 2023-2024

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  1. Case Study Questions Class 10 Maths with Solutions PDF Download

    Case Study Questions Class 10 Maths PDF. In class 10 Board Exam 2021, You will find a new type of case-based questions. This is for the first time when you are going to face these type of questions in the board examination. CBSE has introduced these types of questions to better understand each chapter of class 10 maths.

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  13. CBSE Class 10 Maths: Case Study Questions of Chapter 2 Polynomials PDF

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  17. NCERT Solutions for Class 10 Maths Updated for 2023-24 Exams

    NCERT Solutions for Class 10 Maths Updated for 2023-24 Session - Free PDF Download. NCERT Solutions for Class 10 Maths for all the exercises from Chapters 1 to 15 are provided here.These NCERT Solutions are curated by our expert faculty to help students in their exam preparations. Students looking for the NCERT Solutions of Class 10 Maths can download all chapter-wise PDFs to find a better ...

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  19. CBSE Maths paper for 10th board exam 2024

    CBSE Maths Paper Class 10: The Central board of Secondary Education( CBSE) will conduct the Maths exam on March 11, 2024.Class 10th exams started on February 15, 2024, and will end on March 13, 2024. Students appearing for the CBSE maths exam must be aware of the question paper pattern and know the type of questions asked in the CBSE Board exam 2024.

  20. Class 12 Maths Answer Key 2024 for SET 1, 2, 3

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  22. HBSE Class 10 Maths Sample Paper 2024 PDF with Solutions

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  23. Class 10 Maths: Case Study Questions of Chapter 5 Arithmetic

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  24. Class 10 Maths: Case Study Questions of Chapter 4 Quadratic Equations PDF

    Now represent the following situations in the form of a quadratic equation. The sum of squares of two consecutive integers is 650. (a) x 2 + 2x - 650 = 0 (b) 2x 2 +2x - 649 = 0. (c) x 2 - 2x - 650 = 0 (d) 2x 2 + 6x - 550 = 0. Show Answer. The sum of two numbers is 15 and the sum of their reciprocals is 3/10. (a) x 2 + 10x - 150 = 0.

  25. CBSE Class 12 Physics Exam 2024 Question Paper and Answer Key

    Q1. Two charges + q each are kept '2a' distance apart. A third charge - 2q is placed midway between them. The potential energy of the system is-. Answer: (C) -7q2 /8πε0a. Q2. Two identical small conducting balls and B 2 are given -7 pC and + 4 B 1 pC charges respectively.

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

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  27. [Latest]Important Questions for Class 10 Maths CBSE Chapter Wise PDF

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  28. CBSE Class 10 Social Science Answer Key 2024 (All Sets): Download PDF

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  29. CBSE Class 10 Social Science Practice Paper 2024 with Solutions

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  30. CBSE Class 10 Science Question Paper 2024 PDF: Set 1, 2 and 3

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