case study based on real numbers class 10

Privacy Policy
Terms and Conditions

Web Stories

Tuesday, September 21, 2021

Case study based questions class 10 chapter 1 real numbers cbse board term 1 with answer key.

Hello students, Welcome to Maths Easy Institute.

Please do not enter any spam link in the comment box.

Warning: Do Not Copy!

Blog Archives

Best Books for IIT JEE
Best Colleges Of India
class 10 Case Study Based questions
Class 10 Maths MCQ
Class 11 Maths Case Study Questions
Class 11 Maths MCQ
Class 12 Math Case Study questions
Class 12 Maths MCQ
JEE MAIN MCQ
Maths Strategy JEE
News for Students

Blog Archive

► April (3)
► March (2)
► February (1)
► January (5)
► December (9)
► November (5)
► October (6)
Class 10 Maths Case Study Based Questions Chapter ...
Case Study Based Questions Class 10 Chapter 1 Real...
[Video] Indian Statistical (ISI) Institute Admissi...
[Video] Last 10 days MATHS Strategy for JEE MAIN G...
► April (4)
► March (3)
► October (2)
► September (7)
► August (2)
► July (4)

Class 10 Maths Case Study Questions of Chapter 1 Real Numbers

Post author: studyrate
Post published:
Post category: class 10th
Post comments: 0 Comments

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

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

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

Real Numbers Case Study Questions With Answers

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

Case Study/Passage-Based Questions

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

Answer: (d) no value of n

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

Answer: (c) for all n > 1

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

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

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

Answer: (a) always true

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

Answer: (d) 8

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

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

Answer: (b) LCM = pq2 x HCF

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

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

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

Answer: (d) 17

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

Answer: (b) 12599

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

Answer: (a) 3

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

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

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

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

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

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

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

Extra questions of class 10 maths chapter 12 areas related to circles pdf download.

Class 10 Maths Introduction to Trigonometry Handwritten Notes by Toppers – Download PDF

Mcq class 10 english from the diary of anne frank questions with answers english chapter 4, leave a reply cancel reply.

Save my name, email, and website in this browser for the next time I comment.

Gurukul of Excellence

Classes for Physics, Chemistry and Mathematics by IITians

Join our Telegram Channel for Free PDF Download

Case Study Questions for Class 10 Maths Chapter 1 Real Numbers

Last modified on: 9 months ago
Reading Time: 7 Minutes

Question 1:

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

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

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

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

Question 2:

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.

(i) What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B? (a) 144 (b) 128 (c) 288 (d) 272

(ii) If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32 , 36) is (a) 2 (b) 4 (c) 6 (d) 8

(iii) 36 can be expressed as a product of its primes as (a) (b) (c) (d)

(iv) 7 is a (a) Prime number (b) Composite number (c) Neither prime nor composite (d) None of the above

(v) If p and q are positive integers such that p = a and q= b, where a , b are prime numbers, then the LCM (p, q) is (a) ab (b) a 2 b 2 (c) a 3 b 2 (d) a 3 b 3

✨ Free Quizzes, Test Series and Learning Videos for CBSE Class 10 Maths

Download CBSE Books

Exam Special Series:

Sample Question Paper for CBSE Class 10 Science (for 2024)
Sample Question Paper for CBSE Class 10 Maths (for 2024)
CBSE Most Repeated Questions for Class 10 Science Board Exams
CBSE Important Diagram Based Questions Class 10 Physics Board Exams
CBSE Important Numericals Class 10 Physics Board Exams
CBSE Practical Based Questions for Class 10 Science Board Exams
CBSE Important “Differentiate Between” Based Questions Class 10 Social Science
Sample Question Papers for CBSE Class 12 Physics (for 2024)
Sample Question Papers for CBSE Class 12 Chemistry (for 2024)
Sample Question Papers for CBSE Class 12 Maths (for 2024)
Sample Question Papers for CBSE Class 12 Biology (for 2024)
CBSE Important Diagrams & Graphs Asked in Board Exams Class 12 Physics
Master Organic Conversions CBSE Class 12 Chemistry Board Exams
CBSE Important Numericals Class 12 Physics Board Exams
CBSE Important Definitions Class 12 Physics Board Exams
CBSE Important Laws & Principles Class 12 Physics Board Exams
10 Years CBSE Class 12 Chemistry Previous Year-Wise Solved Papers (2023-2024)
10 Years CBSE Class 12 Physics Previous Year-Wise Solved Papers (2023-2024)
10 Years CBSE Class 12 Maths Previous Year-Wise Solved Papers (2023-2024)
10 Years CBSE Class 12 Biology Previous Year-Wise Solved Papers (2023-2024)
ICSE Important Numericals Class 10 Physics BOARD Exams (215 Numericals)
ICSE Important Figure Based Questions Class 10 Physics BOARD Exams (230 Questions)
ICSE Mole Concept and Stoichiometry Numericals Class 10 Chemistry (65 Numericals)
ICSE Reasoning Based Questions Class 10 Chemistry BOARD Exams (150 Qs)
ICSE Important Functions and Locations Based Questions Class 10 Biology
ICSE Reasoning Based Questions Class 10 Biology BOARD Exams (100 Qs)

✨ Join our Online JEE Test Series for 499/- Only (Web + App) for 1 Year

✨ Join our Online NEET Test Series for 499/- Only for 1 Year

Discover more from Gurukul of Excellence

Subscribe now to keep reading and get access to the full archive.

Type your email…

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

$case study based on real numbers class 10$

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

$case study based on real numbers class 10$

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

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.

Test Generator

Create question paper PDF and online tests with your own name & logo in minutes.

Question Bank, Mock Tests, Exam Papers, NCERT Solutions, Sample Papers, Notes

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
CBSE Practice Papers 2023
Class 10 Maths Sample Papers 2024
Competency Based Learning in CBSE Schools

Save my name, email, and website in this browser for the next time I comment.

Class 10 Maths Chapter 1 Case Based Questions - Real Numbers

Case study – 1.

Q1: What is the minimum distance each should walk so that they can cover the distance in complete steps? (a) 120 m 40 cm (b) 122 m 40 cm (c) 12 m 4 cm (d) None of these Ans: (b) Explanation: The process of solving this problem involves finding the least common multiple (LCM) of the three given measurements. The LCM of a set of numbers is the smallest number that is a multiple of each of the numbers in the set. Here are the steps to find the LCM of 80 cm, 85 cm, and 90 cm: Step 1: Prime factorization The first step is to find the prime factors of each number.

For 80, the prime factors are 2, 2, 2, 2, and 5 (or 2⁴ х 5)
For 85, the prime factors are 5 and 17
For 90, the prime factors are 2, 3, 3, and 5 (or 2 х 3² х 5)

Step 2: Find the LCM Now, we find the LCM by taking the highest power of each prime factor from all the numbers.

The highest power of 2 is 2⁴ from 80
The highest power of 3 is 3² from 90
The highest power of 5 is 5 from 80 or 90
The highest power of 17 is 17 from 85

So, the LCM is 2⁴ х 3² х 5 х 17 = 12240 Step 3: Convert cm to m Finally, we convert the LCM from centimeters to meters. Since 1 meter is 100 cm, we divide 12240 by 100 to get 122.4 meters, which can also be written as 122 meters and 40 cm. Therefore, the minimum distance each should walk so that they can cover the distance in complete steps is 122 meters and 40 cm. This corresponds to option (b). Q2: What is the minimum number of steps taken by any of the three friends, when they meet again? (a) 120 (b) 125 (c) 130 (d) 136 Ans: (d) Explanation: To solve this problem, we need to find the least common multiple (LCM) of the step sizes of the three friends: 80 cm, 85 cm, and 90 cm. The LCM will give us the smallest distance that all three friends can walk together, taking whole steps. Here is the step-by-step process: Step 1: Prime Factorization We start by breaking down each number into its prime factors.

80 = 2 x 2 x 2 x 2 x 5 = 2⁴ x 5
85 = 5 x 17
90 = 2 x 3 x 3 x 5 = 2 x 3² x 5

Step 2: Find the LCM The LCM is found by taking the highest power of all the prime numbers that appear in the prime factorization of any of the numbers. LCM = 2⁴ x 3² x 5 x 17 = 12240 cm This means that the three friends will meet again after walking a distance of 12240 cm. Step 3: Determine the Minimum Steps Among the three friends, Angelina has the longest step size (90 cm). Therefore, she will take the smallest number of steps to cover the distance of 12240 cm. Number of steps taken by Angelina = Total distance / Step size = 12240 cm / 90 cm = 136 steps Hence, the correct answer is (d) 136 steps. Q3: The HCF of 80, 85, and 90 is (a) 5 (b) 10 (c) 12 (d) 18 Ans: (a) Explanation: The Highest Common Factor (HCF) of a set of numbers is the largest number that divides evenly into all the numbers in the set. In this case, we are looking for the HCF of 80, 85, and 90. The first step is to determine the prime factors of each of the numbers. Prime factors are the factors of a number that are prime numbers. 1. For 80, the prime factors are 2 and 5. We obtain this by dividing 80 by the smallest prime number (2) as many times as possible until we are left with a prime number. This gives us 2 x 2 x 2 x 2 x 5 = 2⁴ x 5. 2. For 85, the prime factors are 5 and 17. We obtain this by dividing 85 by the smallest prime number (2) as many times as possible until we are left with a prime number. This gives us 5 x 17. 3. For 90, the prime factors are 2, 3, and 5. We obtain this by dividing 90 by the smallest prime number (2) as many times as possible, then doing the same with the next smallest prime number (3) until we are left with a prime number. This gives us 2 x 3 x 3 x 5 = 2 x 3² x 5. Now that we have the prime factors of each number, we can determine the HCF by finding the largest number that is a factor of all three numbers. In this case, the only common factor among 80, 85, and 90 is 5. Therefore, the HCF of 80, 85, and 90 is 5, which corresponds to answer choice (a). Q4: The product of HCF and LCM of 80, 85, and 90 is (a) 60400 (b) 61000 (c) 61200 (d) 65500 Ans: (c) Explanation: The problem requires us to find the product of the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of the numbers 80, 85, and 90. Step 1: To find the HCF and LCM, we first need to find the prime factors of the three numbers. For 80, the prime factors are 2 x 2 x 2 x 2 x 5 (or 2 4 x 5). For 85, the prime factors are 5 x 17. For 90, the prime factors are 2 x 3 x 3 x 5 (or 2 x 3 2 x 5). Step 2: To find the HCF, we look for common prime factors. The only common factor among all three numbers is 5. So, HCF = 5. Step 3: For the LCM, we take the highest power of all the prime numbers in the factorization of each number. So, LCM = 2 2 x 3 2 x 5 x 17 = 12240. Step 4: Finally, we need to find the product of the HCF and LCM. This is done by multiplying the HCF (5) with the LCM (12240), which gives us 61200. So, the product of the HCF and LCM of 80, 85, and 90 is 61200. Therefore, the correct answer is option (C). Q5: 90 can be expressed as a product of its primes as (a) 2 х 3² х 5² (b) 2 х 3³ х 5 (c) 2² х 3² х 5 (d) 2 х 3² х 5 Ans: (d) Explanation: The question asks us to express 90 as a product of its prime factors. Prime factors are the factors of a number that are prime numbers. A prime number is a number that only has two factors: 1 and itself. Here are the steps to find the prime factors of 90: Step 1: Start by dividing the number 90 with the smallest prime number, which is 2. 90 is divisible by 2. So, divide 90 by 2. You get 45. Step 2: Now, try dividing 45 by 2. It can't be divided evenly. So, we move to the next prime number, which is 3. 45 divided by 3 gives 15. Step 3: Try dividing 15 by 3. It can't be divided evenly. So, we move to the next prime number, which is 5. 15 divided by 5 gives 3. Step 4: Now, we are left with 3. 3 is a prime number itself, so we stop here. So, the prime factors of 90 are 2, 3, 3, and 5. We can write this as 2 x 3² x 5, which matches option (d). Therefore, the correct answer is (d).

Case Study – 2

Q1: What will be the value of x? (a) 15005 (b) 13915 (c) 56920 (d) 17429 Ans: (b) Explanation: The factor tree is a method used to break down any given number into its prime factors. In this case, we don't have the factor tree visually, but the question suggests that 'x' can be obtained by multiplying the numbers 5 and 2783. Step-by-step process: Step 1: Identify the numbers given. Here, we have 5 and 2783. Step 2: Multiply the given numbers. In this case, x = 5 * 2783 Step 3: Perform the multiplication. 5 * 2783 = 13915 So, by using these steps, we find that the value of 'x' is 13915. Therefore, the correct option is (b) 13915. Q2: What will be the value of y? (a) 23 (b) 22 (c) 11 (d) 19 Ans: (c) Explanation: The given factor tree shows how a number is broken down into its prime factors. The number at the top of the tree is the original number and the numbers at the bottom are all prime factors. In the question, we are not given the specific factor tree, but we are asked to find the value of 'y' given that Y = 2783/253. To solve this, we need to perform the division operation: 2783 divided by 253 equals to 11. Hence, the correct answer is option (c), i.e., y = 11. Q3: What will be the value of z? (a) 22 (b) 23 (c) 17 (d) 19 Ans: (b) Explanation: The given factor tree is not explicitly provided here, but from the available solution, we can assume that the number 253 is divided by 11 on the factor tree to obtain the value of z. The process for solving the problem is as follows: Step 1: Identify the numbers given in the factor tree. Here, it's 253 divided by 11 to get 'z'. Step 2: Divide the larger number (253) by the smaller number (11). 253 ÷ 11 = 23 So, z = 23. Therefore, the correct answer is (b) 23. In conclusion, a factor tree is a tool that breaks down any number into its prime factors. In this case, it helped to find the value of z by dividing 253 by 11. Q4: According to Fundamental Theorem of Arithmetic 13915 is a (a) Composite number (b) Prime number (c) Neither prime nor composite (d) Even number Ans: (a) Explanation: The Fundamental Theorem of Arithmetic states that every integer greater than 1 is either a prime number, or can be represented as a unique product of prime numbers. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, the first six prime numbers are 2, 3, 5, 7, 11, and 13. A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words, a composite number is any positive integer greater than one that is not a prime number. Now, let's consider the number 13915. We are given that 13915 can be written as the product of primes: 13915 = 5 х 11 х 11 х 23 = 5 х 11² х 23. Here, we can see that 13915 has more divisors than just 1 and itself (which are 5, 11 and 23). This means that 13915 is not a prime number. Also, as 13915 can be expressed as a product of prime numbers, it is not a number that falls into the category of 'neither prime nor composite'. As for being an even number, we know that an even number is any integer that can be divided by 2. In the case of 13915, it is not divisible by 2, so it is not an even number. Therefore, by process of elimination and based on the definitions, we can conclude that 13915 is a composite number (option a). Q5: The prime factorisation of 13915 is (a) 5 х 11³ х 13² (b) 5 х 11³ х 23² (c) 5 х 11² х 23 (d) 5 х 11² х 13² Ans: (c) Explanation: The prime factorisation of a number is the representation of that number as the product of its prime factors. Here's how you would calculate the prime factorisation of 13915 step-by-step:

First, find the smallest prime number that divides 13915. This will be 5, because 13915 is not divisible by 2 (it's not an even number), nor by 3 (the sum of its digits is not divisible by 3). So, you can start with 5.
Divide 13915 by 5, which gives you 2783.
Now, repeat the process with 2783. The smallest prime number that divides 2783 is 11. Divide 2783 by 11 to get 253.
Repeat the process with 253. It's not divisible by 2, 3, 5, or 7, but it is divisible by 11. Dividing by 11 gives you 23.
23 is a prime number itself, so that's the end of the process.

Therefore, the prime factorisation of 13915 is 5 x 11 x 11 x 23, or 5 x 11² x 23, which matches option (c).

Case Study – 3

Q1: What is the maximum capacity of a container which can measure the petrol of either tanker in exact number of time? (a) 150 litres (b) 160 litres (c) 170 litres (d) 180 litres Ans: (c) Explanation: The question is asking for the highest common factor (HCF) of 850 and 680. The HCF is the largest number that can evenly divide both numbers. Step 1: Find the prime factors of both numbers. Prime factors of 850 = 2 х 5 х 5 х 17 = 2 х 5² х 17 Prime factors of 680 = 2 х 2 х 2 х 5 х 17 = 2³ х 5 х 17 Step 2: Identify the common prime factors. The common prime factors of 850 and 680 are 2, 5, and 17. Step 3: Multiply the common prime factors to get the HCF. HCF of 850 and 680 = 2 х 5 х 17 = 170 Therefore, the maximum capacity of a container that can measure the petrol of either tanker an exact number of times is 170 litres, which corresponds to option (c). Q2: If the product of two positive integers is equal to the product of their HCF and LCM is true then, the LCM (850, 680) is (a) 3100 (b) 3200 (c) 3300 (d) 3400 Ans: (d) Explanation: The question is asking for the least common multiple (LCM) of 850 and 680. The LCM is the smallest number that is a multiple of both numbers. Step 1: We already have the prime factors of both numbers from the previous question, and the HCF. Prime factors of 850 = 2 х 5 х 5 х 17 = 2 х 5² х 17 Prime factors of 680 = 2 х 2 х 2 х 5 х 17 = 2³ х 5 х 17 HCF of 850 and 680 = 2 х 5 х 17 = 170 Step 2: Use the formula for finding the LCM when the HCF is known. LCM (850, 680) = (850 х 680) / HCF Step 3: Substitute the values into the formula. LCM (850, 680) = (850 х 680) / 170 = 3400 Therefore, the LCM of 850 and 680 is 3400, which corresponds to option (d). Q3: 680 can be expressed as a product of its primes as (a) 2² х 5 х 17 (b) 2¹ х 5 х 17 (c) 2³ х 5 х 17 (d) 2³ х 5 х 17⁰ Ans: (c) Explanation: To solve this problem, you need to understand what prime factorization is. Prime factorization is the process of breaking down a number into its smallest prime factors. Let's try to factorize the number 680. First, we need to find a prime number that can divide 680. The smallest prime number is 2, and it can divide 680, so we use it as our first factor. 680 ÷ 2 = 340 Now we continue the process with 340. Again, it can be divided by 2, so we use 2 as our next factor. 340 ÷ 2 = 170 We repeat the process with 170. It can be divided by 2, so we use 2 as our next factor. 170 ÷ 2 = 85 Now, 85 cannot be divided by 2, so we move to the next prime number, which is 3. However, 85 cannot be divided by 3 either. We continue this process until we find a prime number that can divide 85, which is 5. 85 ÷ 5 = 17 Finally, we have 17, which is a prime number itself, so our factorization process stops here. Therefore, the prime factorization of 680 is 2 × 2 × 2 × 5 × 17, or in the exponential form, it is 2³ × 5 × 17. Hence, option (c) is correct. Q4: 2 х 3 х 5 х 11 х 17 + 11 is a (a) Prime number (b) Composite number (d) Neither prime nor composite (d) None of the above Ans: (b) Explanation: The provided answer appears to be incorrect. The number 11 is indeed a prime number, not a composite number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, if a number is prime, it can only be divided without a remainder by 1 and itself. The number 11 meets this criteria, as it can only be divided evenly by 1 and 11. On the other hand, a composite number is a positive integer that has at least one positive divisor other than one or itself. In other words, it has more than two distinct divisors. Here, the number 11 does not have more than two distinct divisors. Thus, the number 11 is a prime number. Therefore, the correct answer is (a) Prime number. Q5: If p and q are positive integers such that p = a³b² and q = a²b³, where a, b are prime numbers, then the LCM (p, q) is (a) ab (b) a³b³ (c) a³b⁵ (d) a⁵b³ Ans: (b) Explanation: To find the least common multiple (LCM) of two numbers, we need to consider the highest powers of all the factors in the numbers. In this case, we are given that p = a³b² and q = a²b³, where a and b are prime numbers. The factors of p are a and b, with a having a power of 3 and b having a power of 2. The factors of q are also a and b, but here a has a power of 2 and b has a power of 3. When finding the LCM, we need to take the highest powers of these common factors. So, we take a to the power of 3 (since 3 is higher than 2) and b to the power of 3 (since 3 is higher than 2). Hence, the LCM of p and q is a³b³. Therefore, the correct option is (b) a³b³.

Case Study – 4

A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English, and Mathematics are 60, 84, and 108 respectively.

Q1: In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are (a) 14 (b) 12 (c) 16 (d) 18 Ans: (b) Explanation: In order to find the maximum number of participants that can be accommodated in each room, we need to find the Highest Common Factor (HCF) of the number of participants in each subject. The HCF of a set of numbers is the largest number that divides each of them without leaving a remainder. It can be found by listing all the factors of each number and finding the largest one that they have in common. Here are the factors of each number:

Factors of 60: 2 x 2 x 3 x 5 = 2² x 3 x 5
Factors of 84: 2 x 2 x 3 x 7 = 2² x 3 x 7
Factors of 108: 2 x 2 x 3 x 3 x 3 = 2² x 3³

The HCF of 60, 84, and 108 is 2² x 3 = 12. Therefore, the maximum number of participants that can be accommodated in each room is 12, which corresponds to the option (b). Q2: What is the minimum number of rooms required during the event? (a) 11 (b) 31 (c) 41 (d) 21 Ans: (d) Explanation: The question requires us to calculate the minimum number of rooms required for the seminar. This can be done by finding the highest common factor (HCF) of the number of participants in each subject. The HCF tells us the maximum number of participants that can be accommodated in each room such that all rooms have the same number of participants. Let's start by finding the prime factorization of the numbers. For 60, the prime factors are 2, 2, 3, and 5 (2² х 3 х 5). For 84, the prime factors are 2, 2, 3, and 7 (2² х 3 х 7). For 108, the prime factors are 2, 2, 3, 3, and 3 (2² х 3³). Now, the HCF is found by multiplying the lowest power of the common prime factors. In this case, the common prime factors are 2 and 3. The lowest power of 2 is 2 (as in 2²), and the lowest power of 3 is 1 (as in 3). So, the HCF is 2² х 3 = 12. Now, to find the number of rooms required for each subject, we divide the number of participants by the HCF. For Hindi, we need 60/12 = 5 rooms. For English, we need 84/12 = 7 rooms. For Mathematics, we need 108/12 = 9 rooms. Adding these together, the total number of rooms required is 5 + 7 + 9 = 21 rooms. Therefore, the answer is (d) 21. Q3: The LCM of 60, 84, and 108 is (a) 3780 (b) 3680 (c) 4780 (d) 4680 Ans: (a) Explanation: The problem revolves around finding the Least Common Multiple (LCM) of three numbers: 60, 84, and 108. To find the LCM of these numbers, we first need to find their prime factors. Here's how:

The prime factors of 60 are 2, 2, 3, and 5 (since 2*2*3*5 = 60). We can write it as 2² * 3 * 5.
The prime factors of 84 are 2, 2, 3, and 7 (since 2*2*3*7 = 84). We can write it as 2² * 3 * 7.
The prime factors of 108 are 2, 2, 3, 3, and 3 (since 2*2*3*3*3 = 108). We can write it as 2² * 3³.

Now, to find the LCM, we take the highest power of all the prime factors obtained from these numbers. If a prime factor is not present in one number but is present in another, we take the factor from the number where it is present.

We have the factor 2 in all three numbers, and the highest power is 2². So, we take 2².
We have the factor 3 in all three numbers, and the highest power is 3³. So, we take 3³.
We have the factor 5 only in 60. So, we take 5.
We have the factor 7 only in 84. So, we take 7.

Q4: The product of HCF and LCM of 60, 84, and 108 is (a) 55360 (b) 35360 (c) 45500 (d) 45360 Ans: (d) Explanation: The first step to solving this problem is understanding what HCF (Highest Common Factor) and LCM (Least Common Multiple) are. The HCF is the highest number that can divide two or more numbers without leaving a remainder. The LCM is the smallest number that is a multiple of two or more numbers. To find the HCF and LCM, we first need to find the prime factors of each number. For 60, the prime factors are 2, 2, 3, and 5 (or 2², 3, 5). For 84, the prime factors are 2, 2, 3, and 7 (or 2², 3, 7). For 108, the prime factors are 2, 2, 3, 3, and 3 (or 2², 3³). The HCF of these three numbers is found by taking the highest common factor of all three numbers, which is 2² (or 4) and 3. Multiplying these together gives us an HCF of 12. The LCM is found by taking the highest power of all the prime factors present in the numbers. This gives us 2², 3³, 5, and 7. Multiplying these together gives us an LCM of 3780. Finally, to find the product of the HCF and LCM, we multiply 12 and 3780 together, which gives us 45360. Hence, the correct answer is (d) 45360. Q5: 108 can be expressed as a product of its primes as (a) 2³ х 3² (b) 2³ х 3³ (c) 2² х 3² (d) 2² х 3³ Ans: (d) Explanation: The process of finding the answer is called prime factorization. Step 1: Start with the smallest prime number, which is 2. Check if 108 is divisible by 2. If it is, then write down 2 as a factor and divide 108 by 2. Step 2: You get 54 as the quotient. Now, repeat the process with 54. Is it divisible by 2? Yes, it is. So, write down 2 as a factor again and divide 54 by 2. Step 3: You now have a quotient of 27. Repeat the process. Is 27 divisible by 2? No, it's not. So, move on to the next prime number, which is 3. Step 4: Is 27 divisible by 3? Yes, it is. So, write down 3 as a factor and divide 27 by 3. Step 5: You get a quotient of 9. Repeat the process. Is 9 divisible by 3? Yes, it is. So, write down 3 as a factor again and divide 9 by 3. Step 6: You now have a quotient of 3. Repeat the process. Is 3 divisible by 3? Yes, it is. So, write down 3 as a factor again and divide 3 by 3. Step 7: You now have a quotient of 1. When you reach 1, you can stop the process. Step 8: Now, count the number of times each prime number appears in your list of factors. You have two 2s and three 3s. Step 9: Write down your answer as the product of the prime numbers, each raised to the power of its count. So, 108 = 2² х 3³. That's how you get the answer (d) 2² х 3³.

Case Study – 5

Q1: What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B? (a)144 (b) 128 (c) 288 (d) 272 Ans: (c) Explanation: The question requires finding the minimum number of books that can be equally distributed among the students of either section A or section B. This is essentially finding the least common multiple (LCM) of the number of students in both sections. Step 1: Find the prime factors of both 32 and 36. Prime factors of 32 are 2 x 2 x 2 x 2 x 2 = 2^5 Prime factors of 36 are 2 x 2 x 3 x 3 = 2^2 x 3^2 Step 2: Find the LCM of 32 and 36. For finding the LCM, we take the highest power of each prime factor that appears in the factorization of either 32 or 36. Here, for 2, the highest power is 5 (from 32) and for 3, it is 2 (from 36). So, LCM of 32 and 36 = 2^5 x 3^2 = 32 x 9 = 288. Hence, you would need a minimum of 288 books so that they can be equally distributed among the students of either section A or section B. So, the correct option is (C). Q2: If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32, 36) is (a) 2 (b) 4 (c) 6 (d) 8 Ans: (b) Explanation: To arrive at the solution, we need to understand two key concepts - Highest Common Factor (HCF) and Lowest Common Multiple (LCM). The HCF of two numbers is the highest number that can divide both of them without leaving a remainder. On the other hand, LCM of two numbers is the smallest number that can be divided by both of them without leaving a remainder. Let's break down the problem into steps: Step 1: Find the factors of the given numbers 32 and 36. Factors of 32: 2*2*2*2*2 = 2⁵ Factors of 36: 2*2*3*3 = 2²*3² Step 2: Find the LCM of 32 and 36. The LCM is found by multiplying the highest power of all the factors that appear in either number. Here we have 2⁵ from 32 and 2²*3² from 36. The higher power of 2 is 2⁵ from 32 and the higher power of 3 is 3² from 36. So, LCM = 2⁵*3² = 32*9 = 288 Step 3: Find the HCF of 32 and 36. The product of two integers (32 and 36) is equal to the product of their HCF and LCM. So, we can find the HCF by dividing the product of the two numbers by their LCM. HCF = (32*36) / LCM = (32*36) / 288 = 4 Therefore, the HCF of 32 and 36 is 4. Hence, the correct option is (b) 4. Q3: 36 can be expressed as a product of its primes as (a) 2² х 3² (b) 2¹ х 3³ (c) 2³ х 3¹ (d) 2⁰ х 3⁰ Ans: (a) Explanation: Prime factorization is the process of breaking down a number into its smallest prime factors. A prime number is a number that has only two distinct positive divisors: 1 and itself. For example, the first six prime numbers are 2, 3, 5, 7, 11, and 13. To express 36 as a product of its primes, we follow these steps: Step 1: Begin by dividing the number 36 with the smallest prime number, i.e., 2. 36 divided by 2 is 18. Step 2: Now divide 18 by 2 to get 9. Step 3: As 9 cannot be divided by 2, we move to the next prime number, which is 3. 9 divided by 3 is 3. Step 4: Finally, divide 3 by 3 to get 1. Now we stop because we have reached 1. The prime factors of 36 are therefore 2, 2, 3, and 3. We write this as 2² х 3². So, the answer is (a) 2² х 3². Q4: 7 х 11 х 13 х 15 + 15 is a (a) Prime number (b) Composite number (d) Neither prime nor composite (d) None of the above Ans: (b) Explanation: The question is asking to determine the type of number 15 is, when it's part of the given multiplication equation. Step 1: Let's understand the definitions first. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, and 13. A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words, a composite number is any positive integer greater than one that is not a prime number. Step 2: Now, consider the number 15. We can see that 15 is not a prime number because it has more than two factors, which are 1, 3, 5, and 15. Step 3: Therefore, 15 is a composite number. Hence, the correct option is (B). Q5: If p and q are positive integers such that p = ab² and q = a²b, where a, b are prime numbers, then the LCM (p, q) is (a) ab (b) a²b² (c) a³b² (d) a³b³ Ans: (b) Explanation: Let's break down the solution to understand it better. Firstly, we are given two positive integers, p and q which are represented as p = ab² and q = a²b, where a and b are prime numbers. The LCM (Least Common Multiple) is the smallest number that is a multiple of both numbers. In other words, it is the smallest number that both numbers can divide into evenly. When finding the LCM of two numbers represented as the product of prime numbers raised to some powers (as in this case), the LCM is simply the product of these primes each raised to the highest power that appears in either number. In this case, the prime number 'a' is raised to the first power in p and to the second power in q. Thus, in the LCM, 'a' is raised to the highest power of these, which is 2. Similarly, the prime number 'b' is raised to the second power in p and to the first power in q. In the LCM, 'b' is raised to the highest power of these, which is 2. Hence, the LCM of p and q is a²b² which corresponds to option (b). So, the correct answer is option (b) a²b².

Top Courses for Class 10

Video lectures, mock tests for examination, objective type questions, past year papers, important questions, extra questions, previous year questions with solutions, sample paper, practice quizzes, semester notes, viva questions, study material, shortcuts and tricks.

Case Based Questions: Real Numbers Free PDF Download

Importance of case based questions: real numbers, case based questions: real numbers notes, case based questions: real numbers class 10, study case based questions: real numbers on the app, welcome back, create your account for free.

case study based on real numbers class 10

Forgot Password

Unattempted tests, change country, practice & revise.

CBSE Expert

CBSE Class 10 Maths: Case Study Questions of Chapter 1 Real Numbers PDF Download

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

Real Numbers Case Study Questions With answers

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

Case Study/Passage-Based Questions

Question 1:

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

Answer: (d) no value of n

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

Answer: (c) for all n > 1

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

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

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

Answer: (a) always true

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

Answer: (d) 8

Question 2:

Answer: (b) LCM = pq2 x HCF

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

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

Answer: (d) 17

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

Answer: (b) 12599

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

Answer: (a) 3

Download India's best Exam Preparation App Now.

Key Features

Revision Notes
Important Questions
Previous Years Questions
Case-Based Questions
Assertion and Reason Questions

No thanks, I’m not interested!

CBSE Case Study Questions for Class 10 Maths Real Numbers Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 10 Maths Real Numbers in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 10 Maths Real Numbers PDF

Mcq set 1 -, mcq set 2 -, checkout our case study questions for other chapters.

Chapter 2: Polynomials Case Study Questions
Chapter 3: Pair of Linear Equations in Two Variables Case Study Questions
Chapter 4: Quadratic Equation Case Study Questions
Chapter 5: Arithmetic Progressions Case Study Questions

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

Contact Form

Andhra Pradesh
Chhattisgarh
West Bengal
Madhya Pradesh
Maharashtra
Jammu & Kashmir
NCERT Books 2022-23
NCERT Solutions
NCERT Notes
NCERT Exemplar Books
NCERT Exemplar Solution
States UT Book
School Kits & Lab Manual
NCERT Books 2021-22
NCERT Books 2020-21
NCERT Book 2019-2020
NCERT Book 2015-2016
RD Sharma Solution
TS Grewal Solution
TR Jain Solution
Selina Solution
Frank Solution
ML Aggarwal Solution
Lakhmir Singh and Manjit Kaur Solution
I.E.Irodov solutions
ICSE - Goyal Brothers Park
ICSE - Dorothy M. Noronhe
Sandeep Garg Textbook Solution
Micheal Vaz Solution
S.S. Krotov Solution
Evergreen Science
KC Sinha Solution
ICSE - ISC Jayanti Sengupta, Oxford
ICSE Focus on History
ICSE GeoGraphy Voyage
ICSE Hindi Solution
ICSE Treasure Trove Solution
Thomas & Finney Solution
SL Loney Solution
SB Mathur Solution
P Bahadur Solution
Narendra Awasthi Solution
MS Chauhan Solution
LA Sena Solution
Integral Calculus Amit Agarwal Solution
IA Maron Solution
Hall & Knight Solution
Errorless Solution
Pradeep's KL Gogia Solution
OP Tandon Solutions
Sample Papers
Previous Year Question Paper
Value Based Questions
CBSE Syllabus
CBSE MCQs PDF
Assertion & Reason
New Revision Notes
Revision Notes
HOTS Question
Marks Wise Question
Toppers Answer Sheets
Exam Paper Aalysis
Concept Map
CBSE Text Book
Additional Practice Questions
Vocational Book
CBSE - Concept
KVS NCERT CBSE Worksheets
Formula Class Wise
Formula Chapter Wise
JEE Crash Course
JEE Previous Year Paper
Important Info
JEE Mock Test
JEE Sample Papers
SRM-JEEE Mock Test
VITEEE Mock Test
BITSAT Mock Test
Manipal Engineering Mock Test
AP EAMCET Previous Year Paper
COMEDK Previous Year Paper
GUJCET Previous Year Paper
KCET Previous Year Paper
KEAM Previous Year Paper
Manipal Previous Year Paper
MHT CET Previous Year Paper
WBJEE Previous Year Paper
AMU Previous Year Paper
TS EAMCET Previous Year Paper
SRM-JEEE Previous Year Paper
VITEEE Previous Year Paper
BITSAT Previous Year Paper
UPSEE Previous Year Paper
CGPET Previous Year Paper
CUSAT Previous Year Paper
AEEE Previous Year Paper
Crash Course
Previous Year Paper
NCERT Based Short Notes
NCERT Based Tests
NEET Sample Paper
Previous Year Papers
Quantitative Aptitude
Numerical Aptitude Data Interpretation
General Knowledge
Mathematics
Agriculture
Accountancy
Business Studies
Political science
Enviromental Studies
Mass Media Communication
Teaching Aptitude
NAVODAYA VIDYALAYA
SAINIK SCHOOL (AISSEE)
Mechanical Engineering
Electrical Engineering
Electronics & Communication Engineering
Civil Engineering
Computer Science Engineering
CBSE Board News
Scholarship Olympiad
School Admissions
Entrance Exams
All Board Updates
Miscellaneous
State Wise Books
Engineering Exam

STATE WISE BOOKS
ENGINEERING EXAM
SCHOLARSHIP OLYMPIAD
STATE BOOKS

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.

CBSE Class 10 Exams Finish, When Can You Expect Results? Details Here

CBSE Board Class 10 Information Technology Answer Key 2024 and Question Papers, Download PDF All SETs

CBSE Board Class 10 Computer Applications Answer Key 2024 and Question Papers, Download PDF All SETs

CBSE Class 10 Information Technology Exam 2024 : Most Important Questions Answers for Last-Minute Revision

CBSE Class 10 Computer Applications Exam 2024 : Most Important Questions Answers for Last-Minute Revision

CBSE Board Class 10 Maths Answer Key 2024 and Question Papers, Download PDF All SETs

NCERT Solutions for Class 12 Maths
NCERT Solutions for Class 10 Maths
CBSE Syllabus 2023-24
Social Media Channels
Login Customize Your Notification Preferences

Second click on the toggle icon

Provide prime members with unlimited access to all study materials in PDF format.

Allow prime members to attempt MCQ tests multiple times to enhance their learning and understanding.

Provide prime users with access to exclusive PDF study materials that are not available to regular users.

New QB365-SLMS
NEET Materials
JEE Materials
Banking first yr Materials
TNPSC Materials
DIPLOMA COURSE Materials
5th Standard Materials
12th Standard Materials
11th Standard Materials
10th Standard Materials
9th Standard Materials
8th Standard Materials
7th Standard Materials
6th Standard Materials
12th Standard CBSE Materials
11th Standard CBSE Materials
10th Standard CBSE Materials
9th Standard CBSE Materials
8th Standard CBSE Materials
7th Standard CBSE Materials
6th Standard CBSE Materials
Tamilnadu Stateboard
Scholarship Exams
Scholarships

Class 10th Maths - Real Number Case Study Questions and Answers 2022 - 2023

By QB365 on 09 Sep, 2022

QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 10th Maths Subject - Real Number, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

QB365 - Question Bank Software

Real number case study questions with answer key.

10th Standard CBSE

Final Semester - June 2015

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

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

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

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

Real numbers are extremely useful in everyday life. That is probably one of the main reasons we all learn how to count and add and subtract from a very young age. Real numbers help us to count and to measure out quantities of different items in various fields like retail, buying, catering, publishing etc. Every normal person uses real numbers in his daily life. After knowing the importance of real numbers, try and improve your knowledge about them by answering the following questions on real life based situations. (i) Three people go for a morning walk together from the same place. Their steps measure 80 cm, 85 cm, and 90 cm respectively. What is the minimum distance travelled when they meet at first time after starting the walk assuming that their walking speed is same?

(ii) In a school Independence Day parade, a group of 594 students need to march behind a band of 189 members. The two groups have to march in the same number of columns. What is the maximum number of columns in which they can march?

(iii) Two tankers contain 768litres and 420 litres of fuel respectively. Find the maximum capacity of the container which can measure the fuel of either tanker exactly.

(iv) The dimensions of a room are 8 m 25 cm, 6 m 75 crn and 4 m 50 cm. Find the length of the largest measuring rod which can measure the dimensions of room exactly.

(v) Pens are sold in pack of 8 and notepads are sold in pack of 12. Find the least number of pack of each type that one should buy so that there are equal number of pens and notepads

In a classroom activity on real numbers, the students have to pick a number card from a pile and frame question on it if it is not a rational number for the rest of the class. The number cards picked up by first 5 students and their questions on the numbers for the rest of the class are as shown below. Answer them. (i) Suraj picked up $\sqrt{8}$ and his question was - Which of the following is true about $\sqrt{8}$ ?

(ii) Shreya picked up 'BONUS' and her question was - Which of the following is not irrational?

(iii) Ananya picked up $\sqrt{5}$ -. $\sqrt{10}$ and her question was - $\sqrt{5}$ -. $\sqrt{10}$ _________is number.

(iv) Suman picked up $\frac{1}{\sqrt{5}}$ and her question was - $\frac{1}{\sqrt{5}}$ is __________ number.

(v) Preethi picked up $\sqrt{6}$ and her question was - Which of the following is not irrational?

Decimal form of rational numbers can be classified into two types. (i) Let x be a rational number whose decimal expansion terminates. Then x can be expressed in the form $\frac{p}{\sqrt{q}}$ where p and q are co-prime and the prime faetorisation of q is of the form 2 n ·5 m , where n, mare non-negative integers and vice-versa. (ii) Let x = $\frac{p}{\sqrt{q}}$ be a rational number, such that the prime faetorisation of q is not of the form 2 n 5 m , where n and m are non-negative integers. Then x has a non-terminating repeating decimal expansion. (i) Which of the following rational numbers have a terminating decimal expansion?

(ii) 23/(2 3 x 5 2 ) =

(iii) 441/(2 2 x 5 7 x 7 2 ) is a_________decimal.

(iv) For which of the following value(s) of p, 251/(2 3 x p 2 ) is a non-terminating recurring decimal?

(v) 241/(2 5 x 5 3 ) is a _________decimal.

HCF and LCM are widely used in number system especially in real numbers in finding relationship between different numbers and their general forms. Also, product of two positive integers is equal to the product of their HCF and LCM. Based on the above information answer the following questions. (i) If two positive integers x and yare expressible in terms of primes as x = p2q3 and y = p3 q, then which of the following is true?

(ii) A boy with collection of marbles realizes that if he makes a group of 5 or 6 marbles, there are always two marbles left, then which of the following is correct if the number of marbles is p?

(iii) Find the largest possible positive integer that will divide 398, 436 and 542 leaving remainder 7, 11, 15 respectively.

(iv) Find the least positive integer which on adding 1 is exactly divisible by 126 and 600.

(v) If A, Band C are three rational numbers such that 85C - 340A :::109, 425A + 85B = 146, then the sum of A, B and C is divisible by

(ii) Find the LCM of 60, 84 and 108.

(iii) Find the HCF of 60, 84 and 108.

(iv) Find the minimum number of rooms required, if in each room, the same number of participants are to be seated and all of them being in the same subject.

(v) Based on the above (iv) conditions, find the minimum number of rooms required for all the participants and officials.

(b) Find the total number of stacks formed.

(d) If the thickness of each English book is 3 cm, then the height of each stack of English books is

(e) If each Hindi book weighs 1.5 kg, then find the weight of books in a stack of Hindi books.

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

Real number case study questions with answer key answer keys.

(i) (d) : For a number to end in zero it must be divisible by 5, but 4 n = 22 n is never divisible by 5. So, 4 n never ends in zero for any value of n. (ii) (c) : We know that product of two rational numbers is also a rational number. So, a 2 = a x a = rational number a 3 = a 2 x a = rational number a 4 = a 3 x a = rational number ................................................ ............................................... a n = a n-1 x a = rational number. (iii) (d): Let x = 2m + 1 and y = 2k + 1 Then x 2 + y 2 = (2m + 1) 2 + (2k + 1) 2 = 4m 2 + 4m + 1 + 4k 2 + 4k + 1 = 4(m 2 + k 2 + m + k) + 2 So, it is even but not divisible by 4. (iv) (a): Let three consecutive positive integers be n, n + 1 and n + 2. We know that when a number is divided by 3, the remainder obtained is either 0 or 1 or 2. So, n = 3p or 3p + lor 3p + 2, where p is some integer. If n = 3p, then n is divisible by 3. If n = 3p + 1, then n + 2 = 3p + 1 + 2 = 3p + 3 = 3(p + 1) is divisible by 3. If n = 3p + 2, then n + 1 = 3p + 2 + 1 = 3p + 3 = 3(p + 1) is divisible by 3. So, we can say that one of the numbers among n, n + 1 and n + 2 Wi always divisible by 3. (v) (d): Any odd number is of the form of (2k +1), where k is any integer. So, n 2 - 1 = (2k + 1)2 -1 = 4k 2 + 4k For k = 1, 4k 2 + 4k = 8, which is divisible by 8. Similarly, for k = 2, 4k 2 + 4k = 24, which is divisible by 8. And for k = 3, 4k 2 + 4k = 48, which is also divisible by 8. So, 4k 2 + 4k is divisible by 8 for all integers k, i.e., n 2 - 1 is divisible by 8 for all odd values of n.

(i) (b): Here 80 = 2 4 x 5, 85 = 17 x 5 and 90 = 2 x 3 2 x 5 L.C.M of 80, 85 and 90 = 2 4 x 3 x 3 x 5 x 17 = 12240 Hence, the minimum distance each should walk when they at first time is 12240 cm. (ii) (c): Here 594 = 2 x 3 3 x 11 and 189 = 3 3 x 7 HCF of 594 and 189 = 3 3 = 27 Hence, the maximum number of columns in which they can march is 27. (iii) (c) : Here 768 = 2 8 x 3 and 420 = 2 2 x 3 x 5 x 7 HCF of 768 and 420 = 2 2 x 3 = 12 So, the container which can measure fuel of either tanker exactly must be of 12litres. (iv) (b): Here, Length = 825 ern, Breadth = 675 cm and Height = 450 cm Also, 825 = 5 x 5 x 3 x 11 , 675 = 5 x 5 x 3 x 3 x 3 and 450 = 2 x 3 x 3 x 5 x 5 HCF = 5 x 5 x 3 = 75 Therefore, the length of the longest rod which can measure the three dimensions of the room exactly is 75cm. (v) (a): LCM of 8 and 12 is 24. $\therefore $ The least number of pack of pens = 24/8 = 3 $\therefore $ The least number of pack of note pads = 24/12 = 2

(i) (b): Here $\sqrt{8}$ = 2 $\sqrt{2}$ = product of rational and irrational numbers = irrational number (ii) (c): Here, $\sqrt{9}$ = 3 So, 2 + 2 $\sqrt{9}$ = 2 + 6 = 8 , which is not irrational. (iii) (b): Here. $\sqrt{15}$ and $\sqrt{10}$ are both irrational and difference of two irrational numbers is also irrational. (iv) (c): As $\sqrt{5}$ is irrational, so its reciprocal is also irrational. (v) (d): We know that $\sqrt{6}$ is irrational. So, 15 + 3. $\sqrt{6}$ is irrational. Similarly, $\sqrt{24}$ - 9 = 2. $\sqrt{6}$ - 9 is irrational. And 5 $\sqrt{150}$ = 5 x 5. $\sqrt{6}$ = 25 $\sqrt{6}$ is irrational.

(i) (c): Here, the simplest form of given options are 125/441 = 5 3 /(3 2 x 7 2 ), 77/210 = 11/(2 x 3 x 5), 15/1600 = 3/(2 6 x 5) Out of all the given options, the denominator of option (c) alone has only 2 and 5 as factors. So, it is a terminating decimal. (ii) (b): 23/(2 3 x 5 2 ) = 23/200 = 0.115 (iii) (a): 441/(2 2 x 5 7 x 7 2 ) = 9/(2 2 x 5 7 ), which is a terminating decimal. (iv) (d): The fraction form of a non-terminating recurring decimal will have at least one prime number other than 2 and 5 as its factors in denominator. So, p can take either of 3, 7 or 15. (v) (a): Here denominator has only two prime factors i.e., 2 and 5 and hence it is a terminating decimal.

(i) (b): LCM of x and y = p 3 q 3 and HCF of x and y = p 2 q Also, LCM = pq 2 x HCF. (ii) (d): Number of marbles = 5m + 2 or 6n + 2. Thus, number of marbles, p = (multiple of 5 x 6) + 2 = 30k + 2 = 2(15k + 1) = which is an even number but not prime (iii) (d): Here, required numbers = HCF (398 - 7, 436 - 11,542 -15) = HCF (391,425,527) = 17 (iv) (b): LCMof126and600 = 2 x 3 x 21 x 100= 12600 The least positive integer which on adding 1 is exactly divisible by 126 and 600 = 12600 - 1 = 12599 (v) (a): Here 8SC - 340A = 109 and 425A + 85B = 146 On adding them, we get 85A + 85B + 85C = 255 ~ A + B + C = 3, which is divisible by 3.

(i) (d): Total number of participants = 60 + 84 + 108 = 252 (ii) (d): 60 = 22 x 3 x 5 84 = 22 x 3 x 7 108 = 22 x 33 LCM(60, 84, 108) = 22 x 33 x 5 x 7 = 3780 (iii) (a): 60 = 22 x 3 x 5 84 = 22 x 3 x 7 108 = 22 x 33 HCF(60, 84, 108) = 22 x 3 = 12 (iv) (c): Minimum number of rooms required for all the participants = 252/12 = 21 (v) (d): Minimum number of rooms required for all = 21 + 1 = 22

(a) (ii) 96 = 2 5 x 3 240 = 2 4 x3 x5 (b) (iii) Total number of books = 96 +240+336=672 Number of books in each stack = 48 $\therefore$ Number of stacks formed -= $\frac{672}{48}=14$ (c) (i) Number of mathmatics books = 336 Number of stacks of mathematics books formed = $\frac{336}{48}$ = 7 (d) (iv) Number of books in each stack of english books = 48 Thickness of each english book = 3 cm $\therefore$ Height of each stack of english books = (48X3) cm = 144cm (e) (iii) Number of books in a stack of hindi books = 48 Weight of each hindi book = 1.5kg $\therefore$ The weight of books in a stack of hindi books = (48X1.5)kg = 72kg

Related 10th Standard CBSE Maths Materials

10th standard cbse syllabus & materials, cbse 10th social science the making of a global world chapter case study question with answers, cbse 10th social science nationalism in india chapter case study question with answers, cbse 10th social science the rise of nationalism in europe chapter case study question with answers, cbse 10th science metals and non metals chapter case study question with answers, cbse 10th science acids, bases and salts chapter case study question with answers, cbse 10th science chemical reactions and equations chapter case study question with answers, class 10th science - our environment case study questions and answers 2022 - 2023, class 10th science - magnetic effects of electric current case study questions and answers 2022 - 2023, class 10th science - electricity case study questions and answers 2022 - 2023, class 10th science - human eye and the colourful world case study questions and answers 2022 - 2023, class 10th science - light reflection and refraction case study questions and answers 2022 - 2023, class 10th science - heredity and evolution case study questions and answers 2022 - 2023, class 10th science - how do organisms reproduce case study questions and answers 2022 - 2023, class 10th science - life processes case study questions and answers 2022 - 2023, class 10th science - periodic classification of elements case study questions and answers 2022 - 2023.

Class VI to XII

Tn state board / cbse, 3000+ q&a's per subject, score high marks.

10th Standard CBSE Study Materials

10th Standard CBSE Subjects

Bihar Board

SRM University

NBSE Result 2024
MP Board 10th Result 2024
MP Board 12th Result 2024
TS Board Results 2024
NBSE Board Result 2024
UK Board Result 2024
Karnataka Board Result
Shiv Khera Special
Education News
Web Stories
Current Affairs
नए भारत का नया उत्तर प्रदेश
School & Boards
College Admission
Govt Jobs Alert & Prep
GK & Aptitude
CBSE Class 10 Study Material

CBSE Class 10 Maths Case Study Questions for Chapter 2 - Polynomials (Published by CBSE)

Check the case study questions published by cbse for class 10 maths chapter 2 - polynomials. these questions are important for the preparation of cbse class 10 maths exam 2021-22..

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 released a question bank to help the students get familiarised with the case study questions. We have provided here the case study questions for CBSE Class 10 Maths Chapter 2 - Polynomials. All the questions have sub-questions of MCQ type. You can find the answer (correct option) written against each question. Practice all the case study based questions right after you finish with the chapter - Polynomials. This will help you prepare for your Maths exam easily and effectively.

Case Study Questions for Class 10 Maths Chapter 2 - Polynomials

CASE STUDY 1:

The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.

1. In the standard form of quadratic polynomial, ax 2 + bx + c, a, b and c are

a) All are Polynomials.

b) All are rational numbers.

c) ‘a’ is a non zero real number and b and c are any Polynomials.

d) All are integers.

Answers: c) ‘a’ is a non zero real number and b and c are any Polynomials.

2. If the roots of the quadratic polynomial are equal, where the discriminant D = b 2 – 4ac, then

a) D > 0

b) D < 0

c) D ≥ 0

Answers: d) D = 0

3. If α and 1/α are the zeroes of the quadratic polynomial 2x2 – x + 8k, then k is

c) –1/4

Answers: b) 1/4

4. The graph of x 2 +1 = 0

a) Intersects x‐axis at two distinct points.

b)Touches x‐axis at a point.

c) Neither touches nor intersects x‐axis.

d)Either touches or intersects x‐ axis.

Answers: c) Neither touches nor intersects x‐axis.

5. If the sum of the roots is –p and product of the roots is –1/p, then the quadratic polynomial is

a) k(–px 2 + x/p + 1)

b) k(px 2 – x/p – 1)

c) k(x 2 + px – 1/p)

d) k(x 2 – px + 1/p)

Answers: c) k(x 2 + px – 1/p)

CASE STUDY 2:

An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.

1. The shape of the poses shown is

d) Parabola

Answer: d) Parabola

2. The graph of parabola opens downwards, if _______

a) a ≥ 0

c) a < 0

d) a > 0

Answer: c) a < 0

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

Answer: c) 2

4. The two zeroes in the above shown graph are

Answer: b) -2, 4

CASE STUDY 3:

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 indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.

1. The shape of the path traced shown is

2. The graph of parabola opens upwards, if _______

b) a < 0

c) a > 0

d) 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) x 3 + 2x 2 – 5x – 6

Also Check:

CBSE Case Study Questions for Class 10 Maths - All Chapters

Tips to Solve Case Study Based Questions Accurately

Get here latest School , CBSE and Govt Jobs notification in English and Hindi for Sarkari Naukari and Sarkari Result . Download the Jagran Josh Sarkari Naukri App . Check Board Result 2024 for Class 10 and Class 12 like CBSE Board Result , UP Board Result , Bihar Board Result , MP Board Result , Rajasthan Board Result and Other States Boards.

Nagaland Board Result 2024
Nagaland Board HSLC Result 2024
NBSE HSLC, HSSLC Result 2024
Nagaland Board HSSLC Result 2024
nbsenl.edu.in NBSE Result 2024
NBSE Toppers List 2024
एमपी बोर्ड 10 वीं टॉपर लिस्ट 2024
AP SSC Results 2024 Manabadi by Jagran Josh
AP SSC Topper List 2024
CBSE Study Material
CBSE Class 10

Latest Education News

International Dance Day 2024: 45+ Quotes, Wishes, Messages And Captions to Share with Dance Lover Friends

Picture Puzzle IQ Test: Find the mistake in the office desk picture in 5 seconds!

Brain Teaser IQ Test: Find six hidden words in the birthday party picture in 15 seconds!

Optical Illusion IQ Test: You Are A Visual Ninja If You Can Spot A Carrot In 8 Seconds!

Today’s School Assembly Headlines (29 April): Lok Sabha Election 2024 Phase 2, SCO Defence Ministers Meeting 2024, Thomas and Uber Cup 2024 and Other News in English

CGBSE Board Result 2024: Chhattisgarh Class 10, 12 Result Date, Time, Latest News And Official Website at cgbse.nic.in

CGBSE 12th Result 2024: Chhattisgarh Board 12 रिजल्ट Date, Latest News And Official Website at cgbse.nic.in

CGBSE 10th Result 2024: Chhattisgarh Board 10 रिजल्ट Date, Time, Latest News And Official Website at cgbse.nic.in

Highest Run Chases in IPL: आईपीएल इतिहास के सबसे बड़े सफल रन चेज़ कौन-से है? देखें पूरी लिस्ट

HPBOSE 12th Result 2024 Live Updates: Himachal Pradesh Class 12 Inter Results at hpbose.org, Check Online by Roll Number

UK Board Result 2024: Uttrakhand Board UBSE Class 10, 12 Result Date And Time at uaresults.nic.in

UK Board Result 2024 Class 10: Uttrakhand Board Class 10th Result Date And Time at ubse.uk.gov.in

UK Board Result 2024 Class 12: Uttrakhand Board Class 12th Result Date And Time at ubse.uk.gov.in

HPBOSE 12th Result 2024: HP Board Class 12 Result Date And Time At hpbose.org

HPBOSE Result 2024: HP Board Class 10, 12 Result Date And Time At hpbose.org

IPL 2024 Stats: आईपीएल में किसने फेंकी थी पहली गेंद, किसने लिया था पहला विकेट और किसने जड़ा था पहला छक्का

IPL इतिहास में सबसे तेज़ 200 रन बनाने वाली 5 टीमें कौन-सी है?

IPL 2024 Live Streaming: मोबाइल या टीवी कहां और कैसे देखें आईपीएल का LIVE टेलीकास्ट?

IPL 2024 Full Schedule: आईपीएल 2024 का फुल शेड्यूल,आज किस टीम का है मैच जानें यहां

SSC GD Constable Result 2024 Live: जीडी कांस्टेबल रिजल्ट ssc.gov.in पर, यहां से डाउनलोड करें मेरिट लिस्ट

Important Questions for Class 10 Maths Chapter 1 Real Numbers

Chapter 1 real numbers important questions for cbse class 10 maths board exams.

Important Questions for Chapter 1 Real Numbers Class 10 Maths

Real numbers class 10 maths important questions very short answer (1 mark).

2. The decimal expansion of the rational number 43/2 4 5 3 will terminate after how many places of decimals?

2 × 7 2

Real Numbers Class 10 Maths Important Questions Short Answer-I (2 Marks)

18. Check whether 4 n can end with the digit 0 for any natural number n.

If the number 4 n for any n, were to end with the digit zero, then it would be divisible by 5 and 2.

That is, the prime factorization of 4 n would contain the prime 5 and 2. This is not possible because the only prime in the factorization of 4 n = 2 2n is 2. So, the uniqueness of the Fundamental Theorem of Arithmetic guarantees that there are no other primes in the factorization of 4 n . So, there is no natural number n for which 4 n ends with the digit zero. Hence 4 n cannot end with the digit zero.

19. Write the denominator of the rational number 257/500 in the form 2 m × 5 n , where m and n are non-negative integers. Hence write its decimal expansion without actual division.

500 = 25 × 20

= 52 × 5 × 4

= 53 × 22

Here, denominator is 500 which can be written as 22 × 53.

Now decimal expansion,

Real Numbers Class 10 Maths Important Questions Short Answer-II (3 Marks)

The required answer will be HCF of 144 and 90.

144 = 2 4 × 3 2

90 = 2 × 3 2 × 5

HCF (144, 90) = 2 × 3 2 = 18

Thus each stack would have 18 cartons.

Let p be a prime number and if possible, let √p be rational

where m and n are co-primes and n ≠0 .

Squaring on both sides, we get

or, pn 2 = m 2 ...(1)

Here p divides pn 2 . Thus p divides m 2 and in result p also divides m.

Let m = pq for some integer q and putting m = pq in eq. (1), we have

pn 2 = p 2 q 2

or, n 2 = pq 2

Here, p divides pq 2 . Thus p divides n 2 and in result p also divides n.

[∵ p is prime and p divides n 2 ⇒ p divides n]

Thus p is a common factor of m and n but this contradicts the fact that m and n are primes. The contradiction arises by assuming that √p is rational.

Hence, √p is irrational.

30. Amita, Sneha, and Raghav start preparing cards for all persons of an old age home. In order to complete one card, they take 10, 16 and 20 minutes respectively. If all of them started together, after what time will they start preparing a new card together? (2013)

To find the earliest (least) time, they will start preparing a new card together, we find the LCM of 10, 16 and 20. 10 = 2 × 5 16 = 24 20 = 22 × 5 LCM = 24 × 5 = 16 × 5 = 80 minutes They will start preparing a new card together after 80 minutes.

31. If two positive integers x and y are expressible in terms of primes as x = p 2 q 3 and y = p 3 q, what can you say about their LCM and HCF. Is LCM a multiple of HCF? Explain. (2014)

x = p 2 q 3 and y = p 3 q LCM = p 3 q 3 HCF = p 2 q …(i) Now, LCM = p 3 q 3 ⇒ LCM = pq 2 (p 2 q) ⇒ LCM = pq 2 (HCF) Yes, LCM is a multiple of HCF. Explanation: Let a = 12 = 2 2 × 3 b = 18 = 2 × 3 2 HCF = 2 × 3 = 6 …(ii) LCM = 2 2 × 3 2 = 36 LCM = 6 × 6 LCM = 6 (HCF) [From (ii)] Here LCM is 6 times HCF.

32. Show that any positive odd integer is of the form 4q + 1 or 4q + 3 where q is a positive integer. Solution Let a be a positive odd integer By Euclid’s Division algorithm: a = 4q + r …[where q, r are positive integers and 0 ≤ r < 4] a = 4q or 4q + 1 or 4q + 2 or 4q + 3 But 4q and 4q + 2 are both even a is of the form 4q + 1 or 4q + 3.

Real Numbers Class 10 Maths Important Questions Long Answer (4 Marks)

We have n 2 - n = n(n-1) Thus n 2 - n is product of two consecutive positive integers. Any positive integer is of the form 2q or 2q + 1, for some integer q. Case 1: n = 2q If n = 2q we have n(n-1) = 2q(2q-1) = 2m where m = q(2q-1) which is divisible by 2. Case 2: n = 2q+1 If n = 2q+1, we have n(n-1) = (2q+1) (2q+1-1) = 2q(2q+1) = 2m where m = q(2q+1) which is divisible by 2. Hence, n 2 - n is divisible by 2 for every positive integer n.

Real Numbers Class 10 Maths Case Based Questions

1. If p and q are positive integers such that p = ab2 and q = a2b, where a, b are prime numbers, then the LCM (p, q) is

Given, p = ab 2 = a × b × b

q = a 2 b = a × a × b

LCM of (p, q) = a 2 b 2

Prime factor 32 is 2×2×2×2×2

Prime factor 36 is 2×2×3×3

HCF is 2×2 = 4

HCF of 32 and 36 is 4.

3. 7 × 11 × 13 × 15 + 15 is a

A. Prime number B. Composite number C. Neither prime nor composite D. None of the above

B. Composite number

7 × 11 × 13 × 15 + 15 is composite number.

Take 15 common

15 ( 7 × 11 × 13 + 1)

So, given number has factor other than 1 and itself so it is a composite number.

4. What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B?

A. 144 B. 128 C. 288 D. 272

We have to find the LCM of 32 and 36.

LCM(32, 36) = 2 5 × 9 = 288

Hence, the minimum number of books required to distribute equally among students of section A and section B are 288.

B. Read the following text and answer the following questions on the basis of the same:

A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.

1. Find the sum of exponents of the prime factors of total number of plants.

A. 2 B. 3 C. 5 D. 6

Total number of plants = 135 + 225 = 360

The prime factors of 360 = 2 × 2 × 2 × 3 × 3 × 5

= 23 × 32 × 51

∴ Sum of exponents = 3 + 2 + 1 = 6.

2. What is total numbers of row in which they can be planted

A. 3 B. 5 C. 8 D. 15

Number of rows of Rose plants = 135/45 = 3

Number of rows of marigold plants = 225/45 = 5

Total number of rows = 3 + 5 = 8

3. Find the sum of exponents of the prime factors of the maximum number of columns in which they can be planted.

We have proved that the maximum number of columns = 45

So, prime factors of 45

= 3 × 3 × 5 = 32 × 51

∴ Sum of exponents = 2 + 1 = 3.

More Study Materials for Class 10

Important Questions Class 10
NCERT Solutions Class 10 Maths
Important Questions Class 10 Maths
Study Materials for Class 10 Maths
Maths Formula Class 10
Solved MCQ Questions Class 10

Contact Form

Math Article
Real Numbers For Class 10

Real Numbers Class 10 Notes: Chapter 1

Cbse real numbers class 10 notes:- download pdf here, class 10 maths chapter 1 real number notes.

CBSE Class 10 Maths Chapter 1 Real Numbers Notes are provided here in detail. As we all know, any number, excluding complex numbers, is a real number. Positive and negative integers, irrational numbers, and fractions are all examples of real numbers. To put it another way, any number found in the real world is a real number. Numbers can be found all around us. Natural numbers are being used to count objects, integers are used to measure temperature, rational numbers are used to represent fractions, irrational numbers are used to calculate the square root of a number, etc. These various types of numbers form a collection of real numbers. Here, we are going to learn what a real number is, Euclid’s division algorithm, the fundamental theorem of arithmetic, methods of finding LCM and HCF and the complete explanation of rational and irrational numbers with examples.

Real Numbers

Positive integers, negative integers, irrational numbers, and fractions are all examples of real numbers. In other words, we can say that any number is a real number, except for complex numbers. Examples of real numbers include -1, ½, 1.75, √2, and so on. In general,

Real numbers constitute the union of all rational and irrational numbers.
Any real number can be plotted on the number line.

To know more about real numbers, visit here .

Students can refer to the short notes and MCQ questions along with a separate solution pdf of this chapter for quick revision from the links below.

Real Numbers Short Notes
Real Numbers MCQ Practice Questions
Real Numbers MCQ Practice Solutions

Euclid’s Division Lemma

Euclid’s Division Lemma states that given two integers a and b , there exists a unique pair of integers q and r such that a = b × q + r a n d 0 ≤ r < b .
This lemma is essentially equivalent to : dividend = divisor × quotient + remainder
In other words, for a given pair of dividend and divisor, the quotient and remainder obtained are going to be unique.

For more information on Euclid’s Division Lemma, watch the below video

To know more about Euclid’s Division Lemma, visit here .

Euclid’s Division Algorithm

Euclid’s Division Algorithm is a method used to find the H.C.F of two numbers, say a and b where a> b.
We apply Euclid’s Division Lemma to find two integers q and r such that a = b × q + r a n d 0 ≤ r < b .
If r = 0, the H.C.F is b; else, we apply Euclid’s division Lemma to b (the divisor) and r (the remainder) to get another pair of quotient and remainder.
The above method is repeated until a remainder of zero is obtained. The divisor in that step is the H.C.F. of the given set of numbers.

For more information on Euclid’s Division Algorithm, watch the below video

The Fundamental Theorem of Arithmetic

Prime Factorisation

Prime Factorisation is the method of expressing a natural number as a product of prime numbers.
Example: 36 = 2 × 2 × 3 × 3 is the prime factorisation of 36.

Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic states that the prime factorisation for a given number is unique if the arrangement of the prime factors is ignored.
Example: 36 = 2 × 2 × 3 × 3 OR, 36 = 2 × 3 × 2 × 3
Therefore, 36 is represented as a product of prime factors (Two 2s and two 3s) ignoring the arrangement of the factors.

To know more about the Fundamental Theorem of Arithmetic, visit here .

Method of Finding LCM

As we know, the smallest of the common multiples of two or more numbers is called the lowest common multiple (LCM). Example: To find the Least Common Multiple ( L.C.M ) of 36 and 56,

36 = 2 × 2 × 3 × 3 56 = 2 × 2 × 2 × 7
The common prime factors are 2 × 2
The uncommon prime factors are 3 × 3 for 36 and 2 × 7 for 56.
LCM of 36 and 56 = 2 × 2 × 3 × 3 × 2 × 7 which is 504

To know more about LCM, visit here .

Method of Finding HCF

We know that the greatest number that divides each of the given numbers without leaving any remainder is the highest common factor (HCF) of two or more given numbers. H.C.F can be found using two methods – Prime factorisation and Euclid’s division algorithm.

Given two numbers, we express both of them as products of their respective prime factors. Then, we select the prime factors that are common to both the numbers
Example – To find the H.C.F of 20 and 24 20 = 2 × 2 × 5 and 24 = 2 × 2 × 2 × 3
The factor common to 20 and 24 is 2 × 2 , which is 4, which in turn is the H.C.F of 20 and 24.
It is the repeated use of Euclid’s division lemma to find the H.C.F of two numbers.

The required HCF is 6 .

To know more about HCF, visit here .

For more information on HCF and LCM, watch the below video

To know more about the Properties of HCF and LCM, visit here .

Product of Two Numbers = HCF X LCM of the Two Numbers

For any two positive integers a and b, a × b = H . C . F × L . C . M .
Example – For 36 and 56, the H.C.F is 4 and the L.C.M is 504 36 × 56 = 2016 4 × 504 = 2016 Thus, 36 × 56 = 4 × 504
Let us consider another example: For 5 and 6, the H.C.F is 1 and the L.C.M is 30 5 × 6 = 30 1 × 30 =30 Thus, 5 × 6 = 1 × 30
The above relationship, however, doesn’t hold true for 3 or more numbers

To know the Relationship between LCM and HCF, visit here .

Applications of HCF & LCM in Real-World Problems

L.C.M can be used to find the points of common occurrence. For example,ringing of bells that ring with different frequencies, the time at which two persons running at different speeds meet, and so on.

For more information on Applications Of LCM, watch the below video

Revisiting Irrational Numbers

Irrational numbers.

Any number that cannot be expressed in the form of p/q (where p and q are integers and q ≠ 0 .) is an irrational number. Examples √2 , π , e and so on.

To know more about Irrational Numbers, visit here .

Number theory: Interesting results

If a number p (a prime number) divides a 2 , then p divides a. Example: 3 divides 6 2 i.e 36, which implies that 3 divides 6.
The sum or difference of a rational and an irrational number is irrational
The product and quotient of a non-zero rational and irrational number are irrational.
√p is irrational when ‘p’ is a prime. For example, 7 is a prime number, and √7 is irrational. The above statement can be proved by the method of “Proof by contradiction”.

To know more about Number theory, visit here .

Proof by Contradiction

In the method of contradiction, to check whether a statement is TRUE (i) We assume that the given statement is TRUE. (ii) We arrive at some result which contradicts our assumption, thereby proving the contrary. Eg: Prove that √7 is irrational. Assumption: √7 is rational. Since it is rational √7 can be expressed as √7 = a/b , where a and b are co-prime Integers, b ≠ 0. On squaring, a 2 /b 2 = 7 ⇒ a 2 = 7 b 2 . Hence, 7 divides a. Then, there exists a number c such that a=7c. Then, a 2 = 49 c 2 . Hence, 7 b 2 = 49 c 2 or b 2 = 7 c 2 . Hence 7 divides b. Since 7 is a common factor for both a and b, it contradicts our assumption that a and b are coprime integers. Hence, our initial assumption that √7 is rational is wrong. Therefore, √7 is irrational.

Revisiting Rational Numbers and Their Decimal Expansions

Rational numbers.

Rational numbers are numbers that can be written in the form p/q, where p and q are integers and q ≠ 0 . Examples -1/2 , 4/5, 1 , 0 , − 3 and so on.

To know more about Rational Numbers, visit here .

Terminating and Non-Terminating Decimals

Terminating decimals are decimals that end at a certain point. Example: 0.2, 2.56 and so on. Non-terminating decimals are decimals where the digits after the decimal point don’t terminate. Example: 0.333333….., 0.13135235343… Non-terminating decimals can be : a) Recurring – a part of the decimal repeats indefinitely (0 . 142857 142857 …. ) b) Non-recurring – no part of the decimal repeats indefinitely. Example: π = 3.1415926535…

To know more about terminating and non-terminating decimals, click here .

Check if a given rational number is terminating or not

If a/b is a rational number, then its decimal expansion would terminate if both of the following conditions are satisfied : a) The H.C.F of a and b is 1. b) b can be expressed as a prime factorisation of 2 and 5 i.e b = 2 m × 5 n where either m or n, or both can = 0. If the prime factorisation of b contains any number other than 2 or 5, then the decimal expansion of that number will be recurring

1/40 = 0.025 is a terminating decimal, as the H.C.F of 1 and 40 is 1, and the denominator (40) can be expressed as 2 3 × 5 1 .

3/7 = 0.428571 is a recurring decimal as the H.C.F of 3 and 7 is 1 and the denominator (7) is equal to 7 1

Real Numbers for Class 10 Solved Examples

Find the largest number that divides 70 and 125 leaving the remainder 5 and 8 respectively.

First, subtract the remainder from the number.

(i.e) 70-5 = 65

125-8 = 117.

Thus, we need to find the largest number that divides 65 and 117 and leaves the remainder 0.

To find the largest number, take the HCF of 65 and 117.

Finding HCF of 65 and 117.

65 = 5×13

117 = 3×3×13.

Hence, HCF (65, 117) = 13.

Therefore, the largest number that divides 70 and 125 leaving the remainder 5 and 8 respectively is 13.

Find the LCM of 306 and 657, given that HCF (306, 657) = 9.

Given that, HCF (306, 657) = 9.

We know that HCF × LCM = Product of Numbers

Hence, 9×LCM = 306×657

9×LCM = 201042

LCM = 201042/9

LCM = 22338.

Therefore, LCM of 306 and 657 is 22338.

Prove that 1/√2 is an irrational number.

To prove 1/√2 is an irrational number.

Now, let us take the opposite assumption.

(i.e) Take 1/√2 is a rational number.

We know that rational numbers are the numbers that can be written in the form of p/q, where q is not equal to 0. (p and q are two co-prime numbers)

Hence, 1/√2 = p/q.

Now, simplify the above equation by multiplying √2 on both sides.

1 = (p√2)/q

q = p√2

Hence, we get q/p = √2.

Here, p and q are integers, and hence q/p is a rational number.

But, √2 is an irrational number.

Hence, our assumption is wrong.

Therefore, 1/√2 is an irrational number.

Hence, proved.

Frequently Asked Questions on Class 10 Real Numbers

What is euclid’s division algorithm, what does real numbers for class 10 explains, is 10i a real number, what does the fundamental theory of arithmetic explain.

Download BYJU’S – The Learning App and stay tuned with us to learn all Maths-related concepts easily by exploring more videos.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

Visit BYJU’S for all Maths related queries and study materials

Your result is as below

Request OTP on Voice Call

Register with BYJU'S & Download Free PDFs

COMMENTS

CBSE Class 10 Maths Case Study Questions for Class 10 Maths Chapter 1
4. 7 × 11 × 13 × 15 + 15 is a. a) Prime number. b) Composite number. c) Neither prime nor composite. d) None of the above. Answer: b) Composite number. 5. If p and q are positive integers such ...
Case Study Based Questions Class 10 Chapter 1 Real Numbers CBSE Board
In this post, you will get CASE Study Questions of Chapter 1 (Real Numbers) of Class 10th. These Case study Questions are based on the Latest Syllabus for 2020- 21 of the CBSE Board. Chapter 1 (Real numbers)
CBSE 10th Standard Maths Real Number Case Study Questions With Solution
CBSE 10th Standard Maths Subject Real Number Case Study Questions With Solution 2021 Answer Keys. Case Study Questions. (i) (d) : For a number to end in zero it must be divisible by 5, but 4 n = 22 n is never divisible by 5. So, 4 n never ends in zero for any value of n. (ii) (c) : We know that product of two rational numbers is also a rational ...
PDF Real Numbers- Case Study Case Study 1
c) 'a' is a non zero real number and b and c are any real numbers. 2. d) D=0 3. b) 4. c) Neither touches nor intersects x‐axis. 5. c) k ( ) CASE STUDY 2: An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise,
Class 10 Maths Case Study Questions of Chapter 1 Real Numbers
There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked. Real Numbers Case Study Questions With Answers. Here, we have provided case-based/passage-based questions for Class 10 Maths Chapter 1 Real Numbers
Case Study Questions for Class 10 Maths Chapter 1 Real Numbers
Case Study Questions for Class 10 Maths Chapter 1 Real Numbers. Question 1: HCF and LCM are widely used in number system especially in real numbers in finding relationship between different numbers and their general forms. Also, product of two positive integers is equal to the product of their HCF and LCM. Based on the above information answer ...
CBSE Class 10 Maths Case Study Questions PDF
Download Case Study Questions for Class 10 Mathematics to prepare for the upcoming CBSE Class 10 Final Exam of 2022-23. 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. ... Chapter-1 Real Numbers. Starting with an introduction to ...
CBSE Class 10 Maths Real Numbers Case Study Questions
Real Numbers Case Study Questions (CSQ's) Practice Tests. Timed Tests. Select the number of questions for the test: Select the number of questions for the test: TopperLearning provides a complete collection of case studies for CBSE Class 10 Maths Real Numbers chapter. Improve your understanding of biological concepts and develop problem ...
Case Study on Real Numbers Class 10 Maths PDF
Students looking for Case Study on Real Numbers Class 10 Maths can use this page to download the PDF file. The case study questions on Real Numbers are based on the CBSE Class 10 Maths Syllabus, and therefore, referring to the Real Numbers case study questions enable students to gain the appropriate knowledge and prepare better for the Class 10 ...
Class 10 Maths
This video explains the detailed solution and explanation of Case Study Based Questions related to Chapter 1 Real Numbers.This video will give you a better u... CBSE Exam, class 10
Case Study Class 10 Maths Questions
Case Study Class 10 Maths Questions subjective type are based on the new reduced syllabus for the session 2022-23 and new marking scheme 2023. ... Real Numbers Case Study Question; ... 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 ...
Class 10 Maths Chapter 1 Case Based Questions
The Case Based Questions: Real Numbers is an invaluable resource that delves deep into the core of the Class 10 exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
CBSE Class 10 Maths: Case Study Questions of Chapter 1 Real Numbers PDF
Here, we have provided case-based/passage-based questions for Class 10 Maths Chapter 1 Real Numbers. Case Study/Passage-Based Questions. Question 1: Srikanth has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions ...
CBSE Case Study Questions For Class 10 Maths Real Numbers Free PDF
Mere Bacchon, you must practice the CBSE Case Study Questions Class 10 Maths Real Numbers in order to fully complete your preparation.They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!. I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams.
Case Study Questions Class 10 Maths Chapter 1 Real Numbers
Case Study Questions Class 10 Maths Chapter 1 Real Numbers | Board Exams 2021Watch Other Playlist:CLASS 10 NCERT CHAPTERSChapter 2: https://bit.ly/3nLKczJCha...
NCERT Solutions for Class 10 Maths Chapter 1- Real Numbers
Key Features of NCERT Solutions for Class 10 Maths Chapter 1- Real Numbers. These NCERT Solutions help you solve and revise the updated CBSE syllabus of Class 10 for 2023-24. After going through the stepwise solutions given by our subject expert teachers, you will be able to score more marks.
CBSE Class 10 Maths Case Study : Case Study With Solutions
Furthermore, we have provided the PDF File of CBSE Class 10 maths case study 2021-2022. CBSE Class 10 Maths Chapter Wise Case Study. Maths Chapter 1 Real Number Case Study. Maths Chapter 2 Polynomial Case Study. Maths Chapter 3 Pair of Linear Equations in Two Variables Case Study. Maths Chapter 4 Quadratic Equations Case Study.
Chapter 1 Real Numbers Cased based Questions I Class 10 Maths I Case
Chapter 1 Real Numbers Cased based Questions I Class 10 Maths I Case study base I Ashish SirShort Tricks on Quadratic Equations https://youtu.be/zJR6qKh6X-8R...
Class 10th Maths
By QB365 on 09 Sep, 2022 . QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 10th Maths Subject - Real Number, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.
CBSE Class 10 Maths Questions Based on Case Study from Class 10 Maths
1. In the standard form of quadratic polynomial, ax2 + bx + c, a, b and c are. a) All are Polynomials. b) All are rational numbers. c) 'a' is a non zero real number and b and c are any ...
Important Questions for Class 10 Maths Chapter 1 Real Numbers
Real Numbers Class 10 Maths Important Questions Short Answer-II (3 Marks) 23. Prove that 3 + 2√3 is an irrational number. Solution. Let us assume to the contrary, that 3 + 2√3 is rational. So that we can find integers a and b (b ≠ 0). Such that 3 + 2√3 = ab, where a and b are coprime. Rearranging the equations, we get.
Real Numbers Class 10 Maths Chapter 1 Notes
CBSE Class 10 Maths Chapter 1 Real Numbers Notes are provided here in detail. As we all know, any number, excluding complex numbers, is a real number. Positive and negative integers, irrational numbers, and fractions are all examples of real numbers. To put it another way, any number found in the real world is a real number.
Class 10 : Real Numbers- Case Study Based Questions
Use Code PN10 to unlock the class. In this session, Prashant Sir will discuss on important concepts and will take practice through Polls on Real Numbers. This session will be helpful for aspirants preparing for CBSE class 10th exam. This session will be conducted in Hinglish and notes will provided in English.

Tuesday, September 21, 2021

Warning: Do Not Copy!

Blog Archive

Class 10 Maths Case Study Questions of Chapter 1 Real Numbers

Real Numbers Case Study Questions With Answers

You Might Also Like

Class 10 Maths Introduction to Trigonometry Handwritten Notes by Toppers – Download PDF

Case Study Questions for Class 10 Maths Chapter 1 Real Numbers

Download CBSE Books

Leave a Reply Cancel reply

Discover more from Gurukul of Excellence

Case Study Class 10 Maths Questions

myCBSEguide App

Format of Maths Case-Based Questions

Maths Case Study Question Paper 2023

Case Study Question in Mathematics

Case Study Question – 1

Case Study Question – 2

Case Study Question – 3

Case Study Question – 4

Case Study Question – 5

Case Study Question – 6

More Case Study Questions

How to Solve Case-Based Questions?

What are Class 10 competency-based questions?

Case Study Questions in Maths Question Paper

Case Studies on CBSE’s Official Website

10 Maths Case Studies in myCBSEguide App

Related Posts

Leave a Comment

Class 10 Maths Chapter 1 Case Based Questions - Real Numbers

Case Study – 2

Case Study – 3

Case Study – 4

Case Study – 5

Top Courses for Class 10

Case Based Questions: Real Numbers Free PDF Download

Forgot Password

CBSE Class 10 Maths: Case Study Questions of Chapter 1 Real Numbers PDF Download

Real Numbers Case Study Questions With answers

Leave a Comment Cancel reply

Download India's best Exam Preparation App Now.

CBSE Case Study Questions for Class 10 Maths Real Numbers Free PDF

CBSE Case Study Questions for Class 10 Maths Real Numbers PDF

How should I study for my upcoming exams?

Contact Form

CBSE Class 10 Maths Case Study

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

CBSE Class 10th Case study Questions

CBSE Class 10th Assertion Reasoning Questions

CBSE Class 10 Maths Case Based MCQ

Class 10th Mathematics Multiple Choice Questions

CBSE Class 10 Exams Finish, When Can You Expect Results? Details Here

CBSE Board Class 10 Information Technology Answer Key 2024 and Question Papers, Download PDF All SETs

CBSE Board Class 10 Computer Applications Answer Key 2024 and Question Papers, Download PDF All SETs

CBSE Class 10 Information Technology Exam 2024 : Most Important Questions Answers for Last-Minute Revision

CBSE Class 10 Computer Applications Exam 2024 : Most Important Questions Answers for Last-Minute Revision

CBSE Board Class 10 Maths Answer Key 2024 and Question Papers, Download PDF All SETs

Class 10th Maths - Real Number Case Study Questions and Answers 2022 - 2023

QB365 - Question Bank Software

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

Related 10th Standard CBSE Maths Materials

Class VI to XII

10th Standard CBSE Study Materials

10th Standard CBSE Subjects

SRM University

CBSE Class 10 Maths Case Study Questions for Chapter 2 - Polynomials (Published by CBSE)

Latest Education News

Important Questions for Class 10 Maths Chapter 1 Real Numbers

Important Questions for Chapter 1 Real Numbers Class 10 Maths

Real Numbers Class 10 Maths Important Questions Short Answer-I (2 Marks)

Real Numbers Class 10 Maths Important Questions Short Answer-II (3 Marks)

Real Numbers Class 10 Maths Important Questions Long Answer (4 Marks)

Real Numbers Class 10 Maths Case Based Questions

More Study Materials for Class 10

Contact Form

Real Numbers Class 10 Notes: Chapter 1

Real Numbers

Euclid’s Division Lemma

For more information on Euclid’s Division Lemma, watch the below video