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## CBSE Class 10 Maths Case Study

CBSE Board has introduced the case study questions for the ongoing academic session 2021-22. The board will ask the paper on the basis of a different exam pattern which has been introduced this year where 50% syllabus is occupied for MCQ for Term 1 exam. Selfstudys has provided below the chapter-wise questions for CBSE Class 10 Maths. Students must solve these case study based problems as soon as they are done with their syllabus.

These case studies are in the form of Multiple Choice Questions where students need to answer them as asked in the exam. The MCQs are not that difficult but having a deep and thorough understanding of NCERT Maths textbooks are required to answer these. Furthermore, we have provided the PDF File of CBSE Class 10 maths case study 2021-2022.

## Class 10 Maths (Formula, Case Based, MCQ, Assertion Reason Question with Solutions)

In order to score good marks in the term 1 exam students must be aware of the Important formulas, Case Based Questions, MCQ and Assertion Reasons with solutions. Solving these types of questions is important because the board will ask them in the Term 1 exam as per the changed exam pattern of CBSE Class 10th.

Important formulas should be necessarily learned by the students because the case studies are solved with the help of important formulas. Apart from that there are assertion reason based questions that are important too.

Assertion Reasoning is a kind of question in which one statement (Assertion) is given and its reason is given (Explanation of statement). Students need to decide whether both the statement and reason are correct or not. If both are correct then they have to decide whether the given reason supports the statement or not. In such ways, assertion reasoning questions are being solved. However, for doing so and getting rid of confusions while solving. Students are advised to practice these as much as possible.

For doing so we have given the PDF that has a bunch of MCQs questions based on case based, assertion, important formulas, etc. All the Multiple Choice problems are given with detailed explanations.

## CBSE Class 10th Case study Questions

Recently CBSE Board has the exam pattern and included case study questions to make the final paper a little easier. However, Many students are nervous after hearing about the case based questions. They should not be nervous because case study are easy and given in the board papers to ease the Class 10th board exam papers. However to answer them a thorough understanding of the basic concepts are important. For which students can refer to the NCERT textbook.

Basically, case study are the types of questions which are developed from the given data. In these types of problems, a paragraph or passage is given followed by the 5 questions that are given to answer . These types of problems are generally easy to answer because the data are given in the passage and students have to just analyse and find those data to answer the questions.

## CBSE Class 10th Assertion Reasoning Questions

These types of questions are solved by reading the statement, and given reason. Sometimes these types of problems can make students confused. To understand the assertion and reason, students need to know that there will be one statement that is known as assertion and another one will be the reason, which is supposed to be the reason for the given statement. However, it is students duty to determine whether the statement and reason are correct or not. If both are correct then it becomes important to check, does reason support the statement?

Moreover, to solve the problem they need to look at the given options and then answer them.

## CBSE Class 10 Maths Case Based MCQ

CBSE Class 10 Maths Case Based MCQ are either Multiple Choice Questions or assertion reasons. To solve such types of problems it is ideal to use elimination methods. Doing so will save time and answering the questions will be much easier. Students preparing for the board exams should definitely solve these types of problems on a daily basis.

Also, the CBSE Class 10 Maths MCQ Based Questions are provided to us to download in PDF file format. All are developed as per the latest syllabus of CBSE Class Xth.

## Class 10th Mathematics Multiple Choice Questions

Class 10 Mathematics Multiple Choice Questions for all the chapters helps students to quickly revise their learnings, and complete their syllabus multiple times. MCQs are in the form of objective types of questions whose 4 different options are given and one of them is a true answer to that problem. Such types of problems also aid in self assessment.

Case Study Based Questions of class 10th Maths are in the form of passage. In these types of questions the paragraphs are given and students need to find out the given data from the paragraph to answer the questions. The problems are generally in Multiple Choice Questions.

The Best Class 10 Maths Case Study Questions are available on Selfstudys.com. Click here to download for free.

To solve Class 10 Maths Case Studies Questions you need to read the passage and questions very carefully. Once you are done with reading you can begin to solve the questions one by one. While solving the problems you have to look at the data and clues mentioned in the passage.

In Class 10 Mathematics the assertion and reasoning questions are a kind of Multiple Choice Questions where a statement is given and a reason is given for that individual statement. Now, to answer the questions you need to verify the statement (assertion) and reason too. If both are true then the last step is to see whether the given reason support=rts the statement or not.

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## myCBSEguide

- Mathematics
- Case Study Class 10...

## Case Study Class 10 Maths Questions

Table of Contents

## myCBSEguide App

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

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

- 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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## Related Posts

- CBSE Class 10 Maths Sample Paper 2020-21
- Class 12 Maths Case Study Questions
- CBSE Reduced Syllabus Class 10 (2020-21)
- Class 10 Maths Basic Sample Paper 2024
- How to Revise CBSE Class 10 Maths in 3 Days
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- Competency Based Learning in CBSE Schools

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## Case Study Questions Class 10 Maths with Solutions PDF Download

case study questions class 10 maths pdf, case study questions class 10 maths with solutions, case study questions class 10 maths cbse chapter wise pdf download, how to solve case-based question in maths.

- First of all, a student needs to read the complete passage thoroughly. Then start solving the question
- After reading the question try to understand from which topics the question is asked. and try to remember all the concepts of that topic.
- Sometimes the question is very tricky and you will find it very difficult to understand. In that case, Read the question and passage again and again.
- After solving the answer check your answer with the options given.
- Remember, write only answering your answer book

## Link to Download Case-Study Questions of class 10

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## Set-1 | Padbandh MCQ Questions Class 10 - CBSE 2022

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## CBSE 10th Standard Maths Subject Case Study Questions With Solution 2021 Part - II

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

(ii) Proportional expense for each person is

(iii) The fixed (or constant) expense for the party is

(iv) If there would be 15 guests at the lunch party, then what amount Mr Jindal has to pay?

(v) The system of linear equations representing both the situations will have

(ii) Represent the situation faced by Suman, algebraically

(iii) The price of one Physics book is

(iv) The price of one Mathematics book is

(v) The system of linear equations represented by above situation, has

(ii) Represent algebraically the situation of day- II.

(iii) The linear equation represented by day-I, intersect the x axis at

(iv) The linear equation represented by day-II, intersect the y-axis at

(v) Linear equations represented by day-I and day -II situations, are

Amit is preparing for his upcoming semester exam. For this, he has to practice the chapter of Quadratic Equations. So he started with factorization method. Let two linear factors of \(a x^{2}+b x+c \text { be }(p x+q) \text { and }(r x+s)\) \(\therefore a x^{2}+b x+c=(p x+q)(r x+s)=p r x^{2}+(p s+q r) x+q s .\) Now, factorize each of the following quadratic equations and find the roots. (i) 6x 2 + x - 2 = 0

(ii) 2x 2 -+ x - 300 = 0

(iii) x 2 - 8x + 16 = 0

(iv) 6x 2 - 13x + 5 = 0

(v) 100x 2 - 20x + 1 = 0

(ii) Difference of pairs of shoes in 17 th row and 10 th row is

(iii) On next day, she arranges x pairs of shoes in 15 rows, then x =

(iv) Find the pairs of shoes in 30 th row.

(v) The total number of pairs of shoes in 5 th and 8 th row is

(ii) The number on first card is

(iii) What is the number on the 19 th card?

(iv) What is the number on the 23 rd card?

(v) The sum of numbers on the first 15 cards is

A sequence is an ordered list of numbers. A sequence of numbers such that the difference between the consecutive terms is constant is said to be an arithmetic progression (A.P.). On the basis of above information, answer the following questions. (i) Which of the following sequence is an A.P.?

(ii) If x, y and z are in A.P., then

(iii) If a 1 a 2 , a 3 ..... , a n are in A.P., then which of the following is true?

(iv) If the n th term (n > 1) of an A.P. is smaller than the first term, then nature of its common difference (d) is

(v) Which of the following is incorrect about A.P.?

(ii) Find the radius of the core.

(iii) S 2 =

(iv) What is the diameter of roll when one tissue sheet is rolled over it?

(v) Find the thickness of each tissue sheet

(ii) Distance travelled by aeroplane towards west after \(1 \frac{1}{2}\) hr is

(iii) In the given figure, \(\angle\) POQ is

(iv) Distance between aeroplanes after \(1 \frac{1}{2}\) hr is

(v) Area of \(\Delta\) POQ is

(ii) The value of x is

(iii) The value of PR is

(iv) The value of RQ is

(v) How much distance will be saved in reaching city Q after the construction of highway?

(ii) Length of BC =

(iii) Length of AD =

(iv) Length of ED =

(v) Length of AE =

(ii) The value of x + y is

(iii) Which of the following is true?

(iv) The ratio in which B divides AC is

(v) Which of the following equations is satisfied by the given points?

(ii) The value of x is equal to

(iii) If M is any point exactly in between city A and city B, then coordinates of M are

(iv) The ratio in which A divides the line segment joining the points O and M is

(v) If the person analyse the petrol at the point M(the mid point of AB), then what should be his decision?

(ii) The centre of circle is the

(iii) The radius of the circle is

(iv) The area of the circle is

(v) If \(\left(1, \frac{\sqrt{7}}{3}\right)\) is one of the ends of a diameter, then its other end is

(ii) The distance between A and Cis

(iii) If it is assumed that both buses have same speed, then by which bus do you want to travel from A to B?

(iv) If the fare for first bus is Rs10/km, then what will be the fare for total journey by that bus?

(v) If the fare for second bus is Rs 15/km, then what will be the fare to reach to the destination by this bus?

## *****************************************

Cbse 10th standard maths subject case study questions with solution 2021 part - ii answer keys.

(i) (a): 1 st situation can be represented as x + 7y = 650 ...(i) and 2 nd situation can be represented as x + 11y = 970 ...(ii) (ii) (b): Subtracting equations (i) from (ii), we get \(4 y=320 \Rightarrow y=80\) \(\therefore\) Proportional expense for each person is Rs 80. (iii) (c): Puttingy = 80 in equation (i), we get x + 7 x 80 = 650 \(\Rightarrow\) x = 650 - 560 = 90 \(\therefore\) Fixed expense for the party is Rs 90 (iv) (d): If there will be 15 guests, then amount that Mr Jindal has to pay = Rs (90 + 15 x 80) = Rs 1290 (v) (a): We have a 1 = 1, b 1 = 7, c 1 = -650 and \(a_{2}=1, b_{2}=11, c_{2}=-970 \) \(\therefore \frac{a_{1}}{a_{2}}=1, \frac{b_{1}}{b_{2}}=\frac{7}{11}, \frac{c_{1}}{c_{2}}=\frac{-650}{-970}=\frac{65}{97}\) \(\text { Here, } \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}\) Thus, system of linear equations has unique solution.

(i) (a): Situation faced by Sudhir can be represented algebraically as 2x + 3y = 850 (ii) (b): Situation faced by Suman can be represented algebraically as 3x + 2y = 900 (iii) (c) : We have 2x + 3y = 850 .........(i) and 3x + 2y = 900 .........(ii) Multiplying (i) by 3 and (ii) by 2 and subtracting, we get 5y = 750 \(\Rightarrow\) Y = 150 Thus, price of one Physics book is Rs 150. (iv) (d): From equation (i) we have, 2x + 3 x 150 = 850 \(\Rightarrow\) 2x = 850 - 450 = 400 \(\Rightarrow\) x = 200 Hence, cost of one Mathematics book = Rs 200 (v) (a): From above, we have \(a_{1} =2, b_{1}=3, c_{1}=-850 \) \(\text { and } a_{2} =3, b_{2}=2, c_{2}=-900\) \(\therefore \quad \frac{a_{1}}{a_{2}}=\frac{2}{3}, \frac{b_{1}}{b_{2}}=\frac{3}{2}, \frac{c_{1}}{c_{2}}=\frac{-850}{-900}=\frac{17}{18} \Rightarrow \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}\) Thus system of linear equations has unique solution.

(i) (b): Algebraic representation of situation of day-I is 2x + y = 1600. (ii) (a): Algebraic representation of situation of day- II is 4x + 2y = 3000 \(\Rightarrow\) 2x + y = 1500. (iii) (c) : At x-axis, y = 0 \(\therefore\) At y = 0, 2x + y = 1600 becomes 2x = 1600 \(\Rightarrow\) x = 800 \(\therefore\) Linear equation represented by day- I intersect the x-axis at (800, 0). (iv) (d) : At y-axis, x = 0 \(\therefore\) 2x + Y = 1500 \(\Rightarrow\) y = 1500 \(\therefore\) Linear equation represented by day-II intersect the y-axis at (0, 1500). (v) (b): We have, 2x + y = 1600 and 2x + y = 1500 Since \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}} \text { i.e., } \frac{1}{1}=\frac{1}{1} \neq \frac{16}{15}\) \(\therefore\) System of equations have no solution. \(\therefore\) Lines are parallel.

(i) (b): We have \(6 x^{2}+x-2=0\) \(\Rightarrow \quad 6 x^{2}-3 x+4 x-2=0 \) \(\Rightarrow \quad(3 x+2)(2 x-1)=0 \) \(\Rightarrow \quad x=\frac{1}{2}, \frac{-2}{3}\) (ii) (c): \(2 x^{2}+x-300=0\) \(\Rightarrow \quad 2 x^{2}-24 x+25 x-300=0 \) \(\Rightarrow \quad(x-12)(2 x+25)=0 \) \(\Rightarrow \quad x=12, \frac{-25}{2}\) (iii) (d): \(x^{2}-8 x+16=0\) \(\Rightarrow(x-4)^{2}=0 \Rightarrow(x-4)(x-4)=0 \Rightarrow x=4,4\) (iv) (d): \(6 x^{2}-13 x+5=0\) \(\Rightarrow \quad 6 x^{2}-3 x-10 x+5=0 \) \(\Rightarrow \quad(2 x-1)(3 x-5)=0 \) \(\Rightarrow \quad x=\frac{1}{2}, \frac{5}{3}\) (v) (a): \(100 x^{2}-20 x+1=0\) \(\Rightarrow(10 x-1)^{2}=0 \Rightarrow x=\frac{1}{10}, \frac{1}{10}\)

Number of pairs of shoes in 1 st , 2 nd , 3 rd row, ... are 3,5,7, ... So, it forms an A.P. with first term a = 3, d = 5 - 3 = 2 (i) (d): Let n be the number of rows required. \(\therefore S_{n}=120 \) \(\Rightarrow \quad \frac{n}{2}[2(3)+(n-1) 2]=120 \) \(\Rightarrow \quad n^{2}+2 n-120=0 \Rightarrow n^{2}+12 n-10 n-120=0\) \(\Rightarrow \quad(n+12)(n-10)=0 \Rightarrow n=10\) So, 10 rows required to put 120 pairs. (ii) (b): No. of pairs in 1ih row = t 17 = 3 + 16(2) = 35 No. of pairs in 10th row = t 10 = 3 + 9(2) = 21 \(\therefore\) Required difference = 35 - 21 = 14 (iii) (c) : Here n = 15 \(\therefore\) t 15 = 3 + 14(2) = 3 + 28 = 31 (iv) (a): No. of pairs in 30 th row = t 30 = 3 +29(2) = 61 (v) (c): No. of pairs in 5 th row = t 5 = 3 + 4(2) = 11 No. of pairs in 8 th row = t 8 = 3 + 7(2) = 17 \(\therefore\) Required sum = 11 + 17 = 28

Let the numbers on the cards be a, a + d, a + Zd, ... According to question, We have (a + 5d) + (a + 13d) = -76 \(\Rightarrow\) 2a+18d = -76 \(\Rightarrow\) a + 9d= -38 ... (1) And (a + 7d) + (a + 15d) = -96 \(\Rightarrow\) 2a + 22d = -96 \(\Rightarrow\) a + 11d = -48 ...(2) From (1) and (2), we get 2d= -10 \(\Rightarrow\) d= -5 From (1), a + 9(-5) = -38 \(\Rightarrow\) a = 7 (i) (b): The difference between the numbers on any two consecutive cards = common difference of the A.P.=-5 (ii) (d): Number on first card = a = 7 (iii) (b): Number on 19th card = a + 18d = 7 + 18(-5) = -83 (iv) (a): Number on 23rd card = a + 22d = 7 + 22( -5) = -103 (v) (d): \(S_{15}=\frac{15}{2}[2(7)+14(-5)]=-420\)

(i) (c) (ii) (c) (iii) (d) (iv) (b) (v) (c)

Here S n = 0.1n 2 + 7.9n (i) (c): S n -1 = 0.1(n - 1) 2 + 7.9(n - 1) = 0.1n 2 + 7.7n - 7.8 (ii) (b): S 1 = t 1 = a = 0.1(1) 2 + 7.9(1) = 8 cm = Diameter of core So, radius of the core = 4 cm (iii) (a): S 2 = 0.1(2) 2 + 7.9(2) = 16.2 (iv) (d): Required diameter = t 2 = S 2 - S 1 = 16.2 - 8 = 8.2 cm (v) (c): As d = t 2 - t 1 = 8.2 - 8 = 0.2 cm So, thickness of tissue = 0.2 \(\div\) 2 = 0.1 cm = 1 mm

(i) (a): Speed = 1200 km/hr \(\text { Time }=1 \frac{1}{2} \mathrm{hr}=\frac{3}{2} \mathrm{hr}\) \(\therefore\) Required distance = Speed x Time \(=1200 \times \frac{3}{2}=1800 \mathrm{~km}\) (ii) (c): Speed = 1500 km/hr Time = \(\frac{3}{2}\) hr. \(\therefore\) Required distance = Speed x Time \(=1500 \times \frac{3}{2}=2250 \mathrm{~km}\) (iii) (b): Clearly, directions are always perpendicular to each other. \(\therefore \quad \angle P O Q=90^{\circ}\) (iv) (a): Distance between aeroplanes after \(1\frac{1}{2}\) hour \(\begin{array}{l} =\sqrt{(1800)^{2}+(2250)^{2}}=\sqrt{3240000+5062500} \\ =\sqrt{8302500}=450 \sqrt{41} \mathrm{~km} \end{array}\) (v) (d): Area of \(\Delta\) POQ= \(\frac{1}{2}\) x base x height \(=\frac{1}{2} \times 2250 \times 1800=2250 \times 900=2025000 \mathrm{~km}^{2}\)

(i) (b) (ii) (c): Using Pythagoras theorem, we have PQ 2 = PR 2 + RQ 2 \(\Rightarrow(26)^{2}=(2 x)^{2}+(2(x+7))^{2} \Rightarrow 676=4 x^{2}+4(x+7)^{2} \) \(\Rightarrow 169=x^{2}+x^{2}+49+14 x \Rightarrow x^{2}+7 x-60=0\) \(\Rightarrow x^{2}+12 x-5 x-60=0 \) \(\Rightarrow x(x+12)-5(x+12)=0 \Rightarrow(x-5)(x+12)=0 \) \(\Rightarrow x=5, x=-12\) \(\therefore \quad x=5\) [Since length can't be negative] (iii) (a) : PR = 2x = 2 x 5 = 10 km (iv) (b): RQ= 2(x + 7) = 2(5 + 7) = 24 km (v) (d): Since, PR + RQ = 10 + 24 = 34 km Saved distance = 34 - 26 = 8 km

(i) (b): If \(\Delta\) AED and \(\Delta\) BEC, are similar by SAS similarity rule, then their corresponding proportional sides are \(\frac{B E}{A E}=\frac{C E}{D E}\) (ii) (c): By Pythagoras theorem, we have \(\begin{array}{l} B C=\sqrt{C E^{2}+E B^{2}}=\sqrt{4^{2}+3^{2}}=\sqrt{16+9} \\ =\sqrt{25}=5 \mathrm{~cm} \end{array}\) (iii) (a): Since \(\Delta\) ADE and \(\Delta\) BCE are similar. \(\therefore \quad \frac{\text { Perimeter of } \triangle A D E}{\text { Perimeter of } \Delta B C E}=\frac{A D}{B C} \) \(\Rightarrow \frac{2}{3}=\frac{A D}{5} \Rightarrow A D=\frac{5 \times 2}{3}=\frac{10}{3} \mathrm{~cm}\) (iv) (b): \(\frac{\text { Perimeter of } \triangle A D E}{\text { Perimeter of } \Delta B C E}=\frac{E D}{C E} \) \(\Rightarrow \frac{2}{3}=\frac{E D}{4} \Rightarrow E D=\frac{4 \times 2}{3}=\frac{8}{3} \mathrm{~cm}\) (v) (d) : \(\frac{\text { Perimeter of } \Delta A D E}{\text { Perimeter of } \Delta B C E}=\frac{A E}{B E} \Rightarrow \frac{2}{3} B E=A E\) \(\Rightarrow A E=\frac{2}{3} \sqrt{B C^{2}-C E^{2}} \) \(\text { Also, in } \triangle A E D, A E=\sqrt{A D^{2}-D E^{2}}\)

(i) (a): We have, OA = 2 \(\sqrt{2}\) km \(\Rightarrow \sqrt{2^{2}+y^{2}}=2 \sqrt{2} \) \(\Rightarrow 4+y^{2}=8 \Rightarrow y^{2}=4 \) \(\Rightarrow y=2 \quad(\because y=-2 \text { is not possible })\) (ii) (c): We have OB = 8 \(\sqrt{2}\) \(\Rightarrow \sqrt{x^{2}+8^{2}}=8 \sqrt{2} \) \(\Rightarrow x^{2}+64=128 \Rightarrow x^{2}=64 \) \(\Rightarrow x=8 \quad(\because x=-8 \text { is not possible })\) (iii) (c) : Coordinates of A and Bare (2, 2) and (8, 8) respectively, therefore coordinates of point M are \(\left(\frac{2+8}{2}, \frac{2+8}{2}\right)\) i.e .,(5.5) (iv) (d): Let A divides OM in the ratio k: 1.Then \(2=\frac{5 k+0}{k+1} \Rightarrow 2 \mathrm{k}+2=5 k \Rightarrow 3 k=2 \Rightarrow k=\frac{2}{3}\) \(\therefore\) Required ratio = 2 : 3 (v) (b): Since M is the mid-point of A and B therefore AM = MB. Hence, he should try his luck moving towards B.

(i) (c): Required coordinates are \(\left(0, \frac{4}{3}\right)\) (ii) (c) (iii) (a): Radius = Distance between (0,0) and \(\left(\frac{4}{3}, 0\right)\) \(=\sqrt{\left(\frac{4}{3}\right)^{2}+0^{2}}=\frac{4}{3} \text { units }\) (iv) (b): Area of circle = \(\pi\) (radius) 2 \(=\pi\left(\frac{4}{3}\right)^{2}=\frac{16}{9} \pi \text { sq. units }\) (v) (d): Let the coordinates of the other end be (x,y). Then (0,0) will bethe mid-point of \(\left(1, \frac{\sqrt{7}}{3}\right)\) and (x, y). \(\therefore\left(\frac{1+x}{2}, \frac{\frac{\sqrt{7}}{3}+y}{2}\right)=(0,0) \) \(\Rightarrow \frac{1+x}{2}=0 \text { and } \frac{\frac{\sqrt{7}}{3}+y}{2}=0 \) \(\Rightarrow x=-1 \text { and } y=-\frac{\sqrt{7}}{3}\) Thus, the coordinates of other end be \(\left(-1, \frac{-\sqrt{7}}{3}\right)\)

Coordinates of A, Band Care (-2, -3), (2, 3) and (3,2). (i) (d): Required distance \(=\sqrt{(2+2)^{2}+(3+3)^{2}}\) \(=\sqrt{4^{2}+6^{2}}=\sqrt{16+36}=2 \sqrt{13} \mathrm{~km} \approx 7.2 \mathrm{~km}\) (ii) (d): Required distance \(=\sqrt{(3+2)^{2}+(2+3)^{2}}\) \(=\sqrt{5^{2}+5^{2}}=5 \sqrt{2} \mathrm{~km}\) (iii) (b): Distance between Band C \(=\sqrt{(3-2)^{2}+(2-3)^{2}}=\sqrt{1+1}=\sqrt{2} \mathrm{~km}\) Thus, distance travelled by first bus to reach to B \(=A C+C B=5 \sqrt{2}+\sqrt{2}=6 \sqrt{2} \mathrm{~km} \approx 8.48 \mathrm{~km}\) and distance travelled by second bus to reach to B \(=A B=2 \sqrt{13} \mathrm{~km} \approx 7.2 \mathrm{~km}\) \(\therefore\) Distance of first bus is greater than distance of the second bus, therefore second bus should be chosen. (iv) (d): Distance travelled by first bus = 8.48 km \(\therefore\) Total fare = 8.48 x 10 = Rs 84.80 (v) (b): Distance travelled by second bus = 7. 2 km \(\therefore\) Total fare = 7.2 x 15 = Rs 108

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## Case Study Based Questions – Class 10 Maths

CBSE has recently added Case Study Based Questions or CSQ in Maths, Science and Social Science. You can visit this article to get to practice the official Sample Papers released by CBSE by clicking over here . Also do join out telegram channel to get all the updates and to participate in Quiz by clicking here.

## What is Case Study Based Questions or CSQ?

Case Study Based or CSQ are typically questions in which the paragraph or passage is given and you simply have to answer them. This questions are not very tough to solve and are introduced so that you score better marks as schools and tuition are kept closed due to the COVID Pandemic. As a result, this had to be introduced. This is resulting to us, by having 34 MCQ which is really very good for scoring 100/100 in CBSE.

## How to start preparing for CSQ’s?

To start preparing for CSQ you will need to learn all the chapters very thoroughly especially all the chapters of Geometry. CSQ from Maths can include a mixture of many chapters thus preparing all the concepts is must. They will surely be helpful. After completing all your syllabus you will need to practice a lot. So scroll below to find more than 15 Case study based question.

## Is it Easy, Hard or Moderate?

This questions are very simple if practiced at least 20-25 questions than you can easily score lot of good marks or you can score full in Maths!! Practice all the questions below.

## How much time to give to each CSQ?

You will be getting 4 Case Study Question’s each would be having 5 sub questions out of which you have to just do 4 questions. So find the shortest and most theoretical question as theoretical questions doesn’t required much solving and it will not even take 1 min to solve. Each question should not take more than 6 min, resulting to only 24 min for 16 questions which is enough. Solving as many CSQ helps in better understanding and reducing the time for each question.

Below are more than 15 examples of CSQ’s for Maths!

## 1st Case Study Based Question

Shankar is having a triangular open space in his plot. He divided the land into three parts by drawing boundaries PQ and RS which are parallel to BC. Other measurements are as shown in the figure.

- What is the area of this land? i) 120 m 2 ii) 60 m 2 iii) 20 m 2 iv) 30 m 2
- What is the length of PQ? i) 2.5 m ii) 5 m iii) 6 m iv) 8 m
- The length of RS is i) 5 m ii) 6 m iii) 8 m iv) 4 m
- Area of △APQ is i) 7.5 m 2 ii) 10 m 2 iii) 3.75 m 2 iv) 5 m 2
- What is the area of △ARS? i) 21.6 m 2 ii) 10 m 2 iii) 3.75 m 2 iv) 6 m 2

## 2nd Case Study Based Question

There is some fire incident in the house. The fireman is trying to enter the house from the window as the main door is locked. The window is 6 m above the ground. He places a ladder against the wall such that its foot is at a distance of 2.5 m from the wall and its top reaches the window.

- Here, be the ladder and be the wall with the window. i) CA, AB ii) AB, AC iii) AC, BC iv) AB, BC
- We will apply Pythagoras Theorem to find length of the ladder. It is: i) AB 2 = BC 2 – CA 2 ii) CA 2 = BC 2 + AB 2 iii) BC 2 = AB 2 + CA 2 iv) AB 2 = BC 2 + CA 2
- The length of the ladder is . i) 4.5 m ii) 2.5 m iii)6.5 m iv) 5.5 m
- What would be the length of the ladder if it is placed 6 m away from the wall and the window is 8 m above the ground? i) 12 m ii) 10 m iii) 14 m iv) 8 m
- How far should the ladder be placed if the fireman gets a 9 m long ladder? i) 6.7 m (approx.) ii) 7.7 m (approx.) iii) 5.7 m (approx.) iv) 4.7 m (approx.)

## 3rd Case Study Based Question

In the school garden Ajay(A), Brijesh(B), Chinki(C) and Deepak(D) planted their flower plants of Rose, Sunflower, Champa and Jasmine respectively as shown in the following figure. A fifth student Eshan wanted to plant her flower in this area. The teacher instructed Eshan to plant his flower plant at a point E such that CE: EB = 3 : 2.

- Find the coordinates of point E where Eshan has to plant his flower plant. i) (5, 6) ii) (6, 5) iii) (5, 5) iv) (6, 7)
- Find the area of △ECD. i) 9.5 square unit ii) 11.5 square unit iii) 10.5 square unit iv)12.5 square unit
- Find the distance between the plants of Ajay and Deepak. i) 8.60 unit ii) 6.60 unit iii) 5.60 unit iv) 7.60 unit
- The distance between A and B is: i) 5.5 units ii) 7 units iii) 6 units iv) 5 units
- The distance between C and D is: i) 5.5 units ii) 7 units iii) 6 units iv) 5 units

## 4rth Case Study Based Questions

SUN ROOM The diagrams show the plans for a sun room. It will be built onto the wall of a house. The four walls of the sunroom are square clear glass panels. The roof is made using

- Four clear glass panels, trapezium in shape, all the same size.
- One tinted glass panel, half a regular octagon in shape

- Find the mid-point of the segment joining the points J (6, 17) and I (9, 16).[Refer to Top View] i) ( 33/2 , 15/2 ) ii) ( 3/2 , 1/2 ) iii) ( 15/2 , 33/2 ) iv) ( 1/2 , 3/2 )
- The distance of the point P from the y-axis is; [Refer to Top View] i) 4 ii) 15 iii) 19 iv) 25
- The distance between the points A and S is: [Refer to Front View] i) 4 ii) 8 iii) 16 iv) 20
- Find the coordinates of the point which divides the line segment joining the points A and B in the ratio 1:3 internally. [Refer to Front View] i) (8.5, 2.0) ii) (2.0, 9.5) iii) (3.0, 7.5) iv) (2.0, 8.5)
- If a point (x,y) is equidistant from the Q(9,8) and S(17,8), then [Refer to Front View] i) x + y = 13 ii) x – 13 = 0 iii) y – 13 = 0 iv) x – y = 13

## 5th Case Study based Question

Education with vocational training is helpful in making a student self-reliant and to help and serve the society. Keeping this in view, a teacher made the following table giving the frequency distribution of a student undergoing vocational training from the training institute.

- Median class of above data: i) 20 – 24 ii) 20.5 – 24.5 iii) 19.5 – 24.5 iv) 24.5 – 29.5
- Calculate the median. i) 24.06 ii) 30.07 iii) 24.77 iv) 42.07
- The empirical relationship between mean, median, mode: i) Mode = 3 Median + 2 Mean ii) Mode = 3 Median – 2 Mean iii) Mode = 3 Mean + 2 Median iv) 3 Mode = Median – 2 Mean
- If mode = 80 and mean = 110, then find the median. i) 200 ii) 500 iii) 190 iv) 100
- The mode is the: i) middlemost frequent value ii) least frequent value iii) maximum frequent value iv) none of these

## 6th Case Study Based Question

Two brothers Ramesh and Pulkit were at home and have to reach School. Ramesh went to Library first to return a book and then reaches School directly whereas Pulkit went to Skate Park first to meet his friend and then reaches School directly.

- How far is School from their Home? i) 5 m ii) 3 m iii) 2 m iv) 4 m
- What is the extra distance travelled by Ramesh in reaching his School? i) 4.48 metres ii) 6.48 metres iii) 7.48 metres iv) 8.48 metres
- What is the extra distance travelled by Pulkit in reaching his School? (All distances are measured in metres as straight lines) i) 6.33 metres ii) 7.33 metres iii) 5.33 metres iv) 4.33 metres
- The location of the library is: i) (-1, 3) ii) (1, 3) iii) (3, 1) iv) (3, -1)
- The location of the Home is: i) (4, 2) ii) (1, 3) iii) (4, 5) iv) (5,4)

## 7th Case Study Based Question

The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmohar is planted on the boundary of the plot at a distance of 1m from each other. There is a triangular grassy lawn inside the plot as shown in Fig. The students have to sow seeds of flowering plants on the remaining area of the plot.

- Considering A as the origin, what are the coordinates of A? i) (0, 1) ii) (1, 0) iii) (0, 0) iv (-1, -1)
- What are the coordinates of P? i) (4, 6) ii) ( 6, 4) iii) (4, 5) iv) (5, 4)
- What are the coordinates of R? i) (6, 5) ii) (5, 6) iii) ( 6, 0) iv) (7, 4)
- What are the coordinates of D? i) (16, 0) ii) (0, 0) iii) (0, 16) iv) (16, 1)
- What are the coordinates of P if D is taken as the origin? i) (12, 2) ii) (-12, 6) iii) (12, 3) iv) (6, 10)

## 8th Case Study Based Question

There exist a tower near the house of Shankar. The top of the tower AB is tied with steel wire and on the ground, it is tied with string support. One day Shankar tried to measure the longest of the wire AC using Pythagoras theorem.

- In the figure, the length of wire AC is: (take BC = 60 ft) i) 75 ft ii) 100 ft iii) 120 ft iv) 90 ft
- What is the area of △ABC? i) 2400 ft 2 ii) 4800 ft 2 iii) 6000 ft 2 iv) 3000 ft 2
- What is the length of the wire PC? i) 20 ft ii) 30 ft iii) 25 ft iv) 40 ft
- What is the length of the hypotenuse in △ABC? i) 100 ft ii) 80 ft iii) 60 ft iv) 120 ft
- What is the area of a △POC? 100 ft 2 150 ft 2 200 ft 2 250 ft 2

## 9th Case Study Based Question

- SCALE FACTOR AND SIMILARITY SCALE FACTOR: A scale drawing of an object is the same shape as the object but a different size. The scale of a drawing is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio. SIMILAR FIGURES: The ratio of two corresponding sides in similar figures is called the scale factor. Hence, two shapes are Similar when one can become the other after a resize, flip, slide, or turn.

- A model of a boat is made on a scale of 1:4. The model is 120cm long. The full size of the boat has a width of 60cm. What is the width of the scale model? i) 20 cm ii) 25 cm iii) 15 cm iv) 240 cm
- What will affect the similarity of any two polygons? i) They are flipped horizontally ii) They are dilated by a scale factor iii) They are translated down iv) They are not the mirror image of one another
- If two similar triangles have a scale factor of a: b. Which statement regarding the two triangles is true? i) The ratio of their perimeters is 3a: b ii) Their altitudes have a ratio a: b iii) Their medians have a ratio a/2:b iv)Their angle bisector have a ration a 2 :b 2
- The shadow of a stick 5m long is 2m. At the same time, the shadow of a tree 12.5m high is: i) 3m ii)3.5m iii)4.5m iv)5m
- Below you see a student’s mathematical model of a farmhouse roof with measurements. The attic floor, ABCD in the model, is a square. The beams that support the roof are the edges of a rectangular prism, EFGHKLMN. E is the middle of AT, F is the middle of BT, G is the middle of CT, and H is the middle of DT. All the edges of the pyramid in the model have a length of 12 m.

What is the length of EF, where EF is one of the horizontal edges of the block? i) 24m ii) 3m iii) 6m iv) 10m

## 10th Case Study Based Question

An Aeroplan leaves an Airport and flies due north at 300 km/h. At the same time, another Aeroplan leaves the same Airport and flies due west at 400 km/h.

- Distance travelled by the first Airplane in 1.5 hours i) 450 km ii) 300 km iii) 150 km iv) 600 km
- Distance travelled by the second Airplane in 1.5 hours i) 450 km ii) 300 km iii) 150 km iv) 600 km
- Which of the following line segment shows the distance between both the airplane? i) OA ii) AB iii) OB iv) WB
- Which airplane travelled a long distance and by how many km? i) Second, 150 km ii) Second, 250 km iii) First, 150 km iv) First, 250 km
- How far apart the two airplanes would be after 1.5 hours? i) 600 km ii) 750 km iii) 300 km iv) 150 km

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## Class 10 Maths Case Study Questions PDF Download

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Are you looking for a reliable source to download Class 10 Maths case study questions in PDF format? Look no further! In this article, we will provide you with a comprehensive collection of case study questions specifically designed for Class 10 Maths Case Study Questions . Whether you are a student or a teacher, these case study questions will prove to be a valuable resource in your preparation or teaching process.

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

If you want to want to prepare all the tough, tricky & difficult questions for your upcoming exams, this is where you should hang out. CBSE Case Study Questions for Class 10 will provide you with detailed, latest, comprehensive & confidence-inspiring solutions to the maximum number of Case Study Questions covering all the topics from your NCERT Text Books !

Table of Contents

## CBSE 10th Maths: Case Study Questions With Answers

Students taking the 10th board examinations will see new kinds of case study questions in class. The board initially incorporated case study questions into the board exam. The chapter-by-chapter case study question and answers are available here.

## Chapterwise Case Study Questions for Class 10 Mathematics

Case study questions are an essential component of the Class 10 Mathematics curriculum. They provide students with real-world scenarios where they can apply mathematical concepts and problem-solving skills. By analyzing and solving these case study questions, students develop a deeper understanding of the subject and improve their critical thinking abilities.

The above Case studies for Class 10 Maths will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 10 Mathematics Case Studies have been developed by experienced teachers of schools.studyrate.in for the benefit of Class 10 students.

- Class 10th Science Case Study Questions

## Benefits of Case Study Questions for Class 10 Mathematics

Case study questions offer several benefits to both students and teachers. Here are some key advantages:

- Practical Application : Case study questions bridge the gap between theory and real-life situations, allowing students to apply mathematical concepts in practical scenarios.
- Analytical Thinking : By solving case study questions, students enhance their analytical thinking and problem-solving skills.
- Conceptual Clarity : Case study questions help reinforce the fundamental concepts of mathematics, leading to improved conceptual clarity.
- Exam Preparation : Practicing case study questions prepares students for their Class 10 Mathematics exams, as they become familiar with the question formats and types.
- Comprehensive Assessment : Teachers can use case study questions to assess students’ understanding of various mathematical concepts in a comprehensive manner.

## How to Use Case Study Questions Effectively

To make the most out of the case study questions, follow these effective strategies:

- Read the question carefully : Understand the given scenario and identify the mathematical concepts involved.
- Analyze the problem : Break down the problem into smaller parts and determine the approach to solve it.
- Apply relevant formulas and concepts : Utilize your knowledge of the subject to solve the case study question.
- Show your working : Clearly demonstrate the steps and calculations involved in reaching the solution.
- Check your answer : Always verify if your solution aligns with the given problem and recheck calculations for accuracy.

## Tips for Solving Case Study Questions

Here are some useful tips to excel in solving case study questions:

- Practice regularly : Regular practice will enhance your problem-solving skills and familiarity with different question formats.
- Understand the concepts: Ensure you have a strong foundation in the underlying mathematical concepts related to each chapter.
- Work on time management : Practice solving case study questions within a stipulated time to improve your speed and efficiency during exams.
- Seek clarification : If you encounter any doubts or difficulties, don’t hesitate to seek guidance from your teacher or peers.

Case study questions are an invaluable resource for Class 10 Mathematics students. They provide practical application opportunities and strengthen conceptual understanding. By utilizing the chapter-wise case study questions provided in this article, students can enhance their problem-solving skills, prepare effectively for exams, and develop a deeper appreciation for the subject.

## FAQs on Class 10 Maths Case Study Questions

Q1: can i download the class 10 maths case study questions in pdf format.

Yes, you can download the Class 10 Maths case study questions in PDF format from our site free of cost.

## Q2: Are the case study questions aligned with the latest curriculum?

Yes, the case study questions presented in this article are designed to align with the latest Class 10 Mathematics curriculum.

## Q3: How can case study questions improve my exam preparation?

Case study questions help you understand the practical application of mathematical concepts, enabling you to approach exam questions with greater confidence and clarity.

## Q5: Where can I find more resources for Class 10 Mathematics preparation?

Download more resources of Class 10th Maths from schools.studyrate.in, we offer additional resources and practice materials for Class 10 Mathematics.

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## CBSE Class 10 Maths: Case Study Questions of Chapter 2 Polynomials PDF Download

Case study Questions in the Class 10 Mathematics Chapter 2 are very important to solve for your exam. Class 10 Maths Chapter 2 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based questions for Class 10 Maths Chapter 2 Polynomials

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.

## Polynomials Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 10 Maths Chapter 2 Polynomials

Case Study/Passage-Based Questions

Question 1:

Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoors on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of a parabola representing quadratic polynomial.

1. The shape of the path traced shown is

d) Parabola

Answer: d) Parabola

2. The graph of parabola opens upwards, if _______

b) a < 0

c) a > 0

Answer: c) a > 0

3. Observe the following graph and answer

In the above graph, how many zeroes are there for the polynomial?

Answer: d) 3

4. The three zeroes in the above shown graph are

b) -2, 3, 1

c) -3, -1, 2

d) -2, -3, -1

Answer: c) -3, -1, 2

5. What will be the expression of the polynomial?

a) x 3 + 2x 2 – 5x – 6

b) x 3 + 2x 2 – 5x + 6

c) x 3 + 2x 2 + 5x – 6

d) x 3 + 2x 2 + 5x + 6

Answer: a) x3 + 2×2 – 5x – 6

Answer: (b) parabolic

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

Answer: (c) x2-36

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

Answer: (c) 0

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

Answer: (b) -2

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

Answer: (d) −53

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## NCERT Solutions for Class 10 Maths

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

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 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.

## 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

## 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 .

## 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.

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.

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

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

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## CBSE Class 10 Maths Practice Paper 2024 Solved: Download for Important Questions and Last Minute Revision

Cbse class 10 maths standard practice paper: check the class 10 maths practice paper to prepare important questions and help you in last minute revision for the upcoming cbse class 10 maths exam 2024. download the practice paper and solutions in pdf..

CBSE Class 10 Maths Standard Practice Paper PDF: CBSE Class 10 Maths Exam 2024 is scheduled for March 11, 2024. This is going to be one of the most crucial exams for class 10 students in deciding their overall performance in CBSE 10th class and their future educational pursuits. To perform well in this important exam, students are advised to thoroughly practice with the sample papers, previous years’ question papers and the practice papers. We have provided here the CBSE Class 10 Maths Standard Practice Paper which has been curated by subject experts analysing the previous years' question patterns and the latest CBSE syllabus. By solving this comprehensive practice paper, students can assess their preparedness for the CBSE Class 10 Maths Exam 2024 and enhance their problem-solving skills. Solutions to all questions are also provided here to facilitate a better understanding of the concepts and help students identify and rectify any errors in their answers. Download the practice paper and solutions in PDF here.

## CBSE Class 10 Maths Standard Practice Paper 2024

1. What is the degree of the constant polynomial?

(a) 2

(b) 1

(c) 0

(d) 4

Answer: (c) 0

2. Which of the following cannot be the probability of an event?

(a) 23

(b) –1.5

(c) 15

Answer: (b) –1.5

3. Which one of the following options is true?

y =3x+5 has:

(a) unique solution

(b) infinite solutions

(c) two solution

Answer: (b) infinite solutions

4. For what values of k will the following pair of linear equations have infinitely many solutions?

(i) kx + 3y – (k – 3) = 0

(ii) 12x + ky – k = 0

(a) -6

(b) 0

(c) 6

(d) All of these

Answer: (d) All of these

5. What is the common difference of following AP:

3, 3+√2, 3+2√2, 3+3√2, ...............

(a) 3

(b) 2

(c) √2

Answer: (c) √2

6. If Tn is the nth term of an AP and Tn = 2n -3 then what is the common difference of the A.P?

(a) -2

(b) 5

(c) 3

(d) 2

Answer: (d) 2

7. If TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠ PTQ is equal to:

(a) 60°

(b) 70°

(c) 80°

Answer: (b) 70°

8. Find the value of k for which the quadratic equation 2x 2 -kx+k=0 has equal roots.

(a) only 0

(b) only 8

(c) 0 and 8

(d) can’t find

Answer: (c) 0 and 8

9. What is the product of zeroes of the polynomial 2x 2 -7x+6?

(a) 12

(b) 9

(c) 3

Answer: (c) 3

10. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is :

(a)5 units

(b) 12 units

(c) 11 units

(d) (7 + 5) units

Answer: (b) 12 units

11. In a ∆ABC, If tan A = cot B, then A + B is equal to :

(a) 60°

(b) 120°

(c) 90°

Answer: (c) 90°

12. If sin A = 35 then cosA is equal to :

(a) 0

(b) 1

(c) 45

Answer: (c) 45

13. On comparing the ratios a1/a2, b1/b2 and c1/c2 find out whether the following pair of linear equations is consistent, or inconsistent.

2 x + 5 y - 5 = 0 and 4 x + 10 y + 7 = 0

(a) Consistent

(b) Inconsistent

(c) Nothing to say

Answer: (b) Inconsistent

14. If x= 1/√3 is a root of the equation Px 2 + (√3- √2)x -1=0 , then the value of P 2 +1 is :

(a) 6

(b) 6

(c) 7

Answer: (a) 6

15. In the given figure, PA and PB are tangents to the given circle such that PA = 5 cm and ∠APB = 60°. The length of chord AB is :

(a) 5√2 cm

(b) 5 cm

(c) 5√3 cm

Answer: (b) 5 cm

16. If two positive integers p and q can be expressed as p = ab 2 and q = a 3 b, where a, b being prime numbers, then LCM (p, q) is equal to:

(a) ab

(b) a 2 b 2

(c) a 3 b 2

(d) a 3 b 3

Answer: (c) a 3 b 2

17. Simplest rationalizing factor of √8 is:

(a) √8

(b) √2

(c) 3√2

Answer: (b) √2

18. If LCM of 12 and 42 is 10 m +4 then value of m is :

(a) 6

(b) 7

(c) 0

Answer: (d) 8

Direction: In the question number 19 and 20, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct option

19. Statement A (Assertion): Ravi goes 30 m due East and then 40 m due North. His distance from the starting point is 50 m.

Statement R( Reason): In right angled triangle ABC, right angled at B, AB 2 = BC 2 + AC 2

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

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

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

Answer: (c) Assertion (A) is true but reason (R) is false.

20. If Sn is the sum of the first n terms of an A.P., then its nth term an is given by an = S n – S n-1

Reason: The 10th term of the A.P. 5, 8, 11, 14, ………………. is 35.

Also Check:

CBSE Class 10 Maths Sample Paper for Board Exam 2024

CBSE Class 10 Maths Additional Questions by CBSE for Board Exam 2024

CBSE Class 10 Maths Important MCQs for All Chapters

CBSE Class 10 Maths Deleted Syllabus for Board Exam 2024

CBSE Class 10 Maths Mind Maps for Quick Revision of All Chapters

Revised NCERT Book for CBSE Class 10 Maths

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## CBSE Class 10 Maths 2 Marks Important Questions for 2024 Board Exam, Download Free PDF

img src="https://img.jagranjosh.com/images/2024/January/1712024/CBSE-Class-10-(1).jpg" width="1200" height="675" />

CBSE 10th Maths 2 Marks Questions : CBSE Class 10 Maths Exam is scheduled for March 11, 2024. In this article, we have provided chapter-wise PDFs of 2 marks important maths questions with solutions for Class 10.

These chapter-wise important questions and solutions have been developed by using a combination of the current academic year's marking scheme, previous-year exam questions, recent sample papers provided by the board, and the updated curriculum for the 2023–2024 academic year. As less than a month is left until the final examination, students are advised to not only revise important concepts but also solve a sufficient number of questions. Through practicing these questions, students will be able to develop an efficient time management strategy and score top marks in the examination.

## CBSE Class 10 Maths Question Paper Pattern

CBSE Class 10 Maths exam will be of three hours duration. Here, students can check the Class 10 maths question paper pattern and prepare for the final examination accordingly.

## List of Chapter-wise Important Questions of 2 Marks for Class 10th Maths with Solutions

Students appearing for the CBSE Class 10 mathematics board exam 2023–24 can download the PDFs of chapter-wise important 2-mark maths questions with solutions using the links given below in the table.

Also Check:

Note: PDF links for the remaining chapters will be available soon. Please continue to check for updates regarding important 2 marks questions for Class 10 Maths.

Also Read:

CBSE Date Sheet 2024 Class 10 PDF Download

NCERT Book for Class 10 Maths PDF (Revised)

NCERT Exemplar Solutions for Class 10 Maths (Chapter-Wise )

CBSE Class 10 Maths Complete Study Material

NCERT Solutions for Class 10 (2023-2024) All Subjects & Chapters, PDF Download

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CBSE Class 10 Maths Case Study CBSE Board has introduced the case study questions for the ongoing academic session 2021-22. The board will ask the paper on the basis of a different exam pattern which has been introduced this year where 50% syllabus is occupied for MCQ for Term 1 exam.

by experts Download Case Study Questions for Class 10 Mathematics to prepare for the upcoming CBSE Class 10 Final Exam. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 10 so that they can score 100% on Boards.

Case Study Class 10 Maths Questions March 22, 2023 by myCBSEguide Table of Contents myCBSEguide App 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. Install Now

CASE STUDY 1. To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.

CBSE Class 10 Maths Case Study Questions for Chapter Real Numbers The Central Board of Secondary Education has introduced the case study questions in class 10 exam pattern 2021-2022. The...

Important Case Study Questions from CBSE Class 10 Maths: CBSE Class 10 Maths board exam 2023 is on 21st March, 2023. With the exam approaching fast, CBSE Board exam candidates are...

There will be 5 case-based questions in class 10 mathematics. Each Question will have 5 MCQs based on the paragraph. Out of 5, you have to solve 4 MCQ questions. Case Study Questions Class 10 Maths CBSE Chapter Wise PDF Download How to Solve Case-Based Question in Maths?

10th Standard CBSE Maths Case study Questions CBSE 10th Standard Maths Subject Case Study Questions With Solution 2021 Part - II 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 .

CBSE Class 10 Maths Case Study Based Questions for Chapter 5 CBSE Class 10 Case Study Questions for Maths Chapter 5 - Arithmetic Progression are available here with answers. All...

CBSE's question bank on case study for Class 10 Maths Chapter 7 is available here. Practice this new type of questions to score good marks in your board exam. By Gurmeet Kaur Apr 19,...

CBSE Class 10 Maths paper in Board Exam 2022 will have some questions based on the case study. These questions are entirely new for the class 10 students. Therefore, the board has...

CASE STUDY 1: On a weekend Rani was playing cards with her family . The deck has 52 cards. If her brother drew one card. 1. Find the probability of getting a king of red colour. a) 1/26 b) 1/13...

10th Case Study Based Question. An Aeroplan leaves an Airport and flies due north at 300 km/h. At the same time, another Aeroplan leaves the same Airport and flies due west at 400 km/h. Distance travelled by the first Airplane in 1.5 hours. i) 450 km.

We have provided here the case study questions for CBSE Class 10 Maths Chapter 9 - Some Applications of Trigonometry. All these questions have been published by the Central Board of...

CBSE 10th Maths: Case Study Questions With Answers Students taking the 10th board examinations will see new kinds of case study questions in class. The board initially incorporated case study questions into the board exam. The chapter-by-chapter case study question and answers are available here.

2266 questions English 2085 questions SST 996 questions casestudyquestions.com Download case study question pdfs for CBSE Class 10th Maths, CBSE Class 10th English, CBSE Class 10th Sciece, CBSE Class 10th SST.

You can check your knowledge by solving case study-based questions for Class 10 Maths Chapter 2 Polynomials. 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 ...

CBSE Class 10 Boards 2024: Stay informed about CBSE Class 10 Boards 2024 with the latest updates and essential information. ... Case Based Questions, Source-based Integrated Questions or any other format. Composition of question paper for Board Examination 2024 (Theory) ... CBSE 10th Exam Pattern 2024: Mathematics (Basic) Sections in the ...

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

CBSE Class 10 Maths Standard Practice Paper PDF: CBSE Class 10 Maths Exam 2024 is scheduled for March 11, 2024. This is going to be one of the most crucial exams for class 10 students in deciding ...

CBSE 10th Maths 2 Marks Questions: CBSE Class 10 Maths Exam is scheduled for March 11, 2024. In this article, we have provided chapter-wise PDFs of 2 marks important maths questions with solutions ...