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Class 11 maths case study based questions chapter 1 sets term 1 with answer key.

Class 11 Maths Case Study Based Questions Chapter 1 SETS Term 1 with Answer Key

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Class 11 Maths Sample Papers, NCERT Solutions | Mock Tests

Designed for the toppers, the course content of CBSE Class 11 Maths like Sample Papers, NCERT Solutions, Notes, and Important Questions can be availed as PDF on myCBSEguide.

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Regarded as a scoring subject, Mathematics is equally important, especially when it comes to the senior secondary level. One can master this subject with little effort. All they need to do is to apply the flow of reasons while proving a result or solving a problem. To attain this level of competence you need good practice. For having the good practice you need to have quality course material. You can get the best resources for CBSE class 11 Mathematics on myCBSEguide  as we gave a huge question bank with a variety of questions.  Download the latest Sample Papers for CBSE Class 11 Mathematics, chapter-related Revision Notes, NCERT solution, and test papers all in PDF files.

CBSE Class 11 Mathematics Resources

Trusted by millions of teachers and students alike, myCBSEguide is a one-stop solution for quality course content for CBSE subjects. Students must put some extra effort to excel in Mathematics at the senior secondary level, as it will be working as the foundation of their future careers and profession. We provide a wide range of products with the help of which you can prepare for senior secondary Mathematics on myCBSEguide beginning from the syllabus to the model test papers. There are online tests, mock tests, learning videos, revision notes, NCERT solutions, and some important questions for class 11 Mathematics.

Class 11 Mathematics Syllabus

The syllabus is regularly updated based on the latest development. Students of senior secondary level, i.e., Class 11 Mathematics are on the threshold of higher academics. The marks they score here will play a decisive role in choosing their career options. Therefore, the syllabus of class 11 Maths includes every such topic that helps the students to develop a positive attitude to think, analyze and articulate logically. Given below are the name and the weightage of chapters of Class 11 Mathematics.

The prescribed books for class 11 Mathematics are:

  • Mathematics Textbook for Class XI, NCERT Publications
  • Mathematics Lab Manual class XI, published by NCERT

To know the chapter and topic-related details check out our detailed blog on the  Class 11 Mathematics syllabus .

Class 11 Mathematics Notes and NCERT Solutions

All CBSE students should practice NCERT textbook solutions because most of the time the questions asked in the final board examination are based on them. As we know that the CBSE encourages following  NCERT  textbooks because they cover almost all possible topics of any central examination. Some of the topics of class 11 Mathematics are:

  • Binomial Theorem Miscellaneous
  • Complex Numbers and Quadratic Equations Miscellaneous
  • Conic Sections Miscellaneous
  • Limits and Derivatives Miscellaneous

To get the complete notes based on the exercise check out  Class 11 Mathematics NCERT Solutions . 

Although Mathematics is not a theory subject, an explanation of each chapter is needed. One cannot understand the chapter if they are not aware of the subject-specific terms and jargon along with the explanation of theorems. You can find a step-by-step explanation of each example sum of a particular topic of class 11 Mathematics. Do check our  Revision Notes for Class 11 Mathematics  and download them in PDF.

CBSE Class 11 Mathematics Case Study Questions

Case study questions are the latest type of questions included in the CBSE question paper. This change is to promote competency-based learning and motivate topics from real-life and other subject areas, greater emphasis has been laid on the application of various concepts. The class 11 Mathematics case study questions look forward to acquainting students with different aspects of Mathematics used in daily life. Being the newest question format, it is difficult to get an assured quality of CBQs in the market or over the internet. Check our  Class 11 Maths case study questions  to know the actual standard of the questions. These case-based questions have sub-questions which can be objective or subjective type depending on the CBSE sample question paper. To get these questions get a subscription to our  student dashboard.

CBSE Class 11 Mathematics Sample Papers

A student who aims to get good grades must solve sample papers religiously. Based on the official sample papers of the CBSE, myCBSEguide prepares around ten sample papers in each subject. Knowing the blueprint and MS can help the students to write their papers confidently. Even the school-level examinations follow the CBSE pattern, therefore it is advised to solve full-length class 11 Mathematic model test papers. Get the app to download the latest  Class 11 Maths Sample Papers 2023 . 

Sample papers are also helpful for periodic assessment too. This is because a sample paper has an assortment of questions. A standard sample paper has all types of questions such as very short answer (VSA), short answer (SA) and, long answer (LA) to effectively assess the knowledge, understanding, application, skills, analysis, evaluation and, synthesis. We can say that ideally, a sample paper matches the modalities of a proper pen-paper test.

CBSE Class 11 Maths Test Papers & Important Questions

Memorizing the rules and formulas is one thing and applying them is another. Good coordination between the two can make wonders. This can be achieved by enthusiastic practice. You can get the Test paper set for Class 11 Mathematics, which you can practice according to the level of your preparation. This helps in segmented learning. Test papers are good ways to learn and test simultaneously. The class 11 mathematics test papers have all types of questions. Besides, we make efforts to chalk out the most important questions from every chapter so that our students do not miss out on crucial information. Class 11 Mathematics important questions are available on myCBSEguide.

You can find such valuable study material for other CBSE subjects in our  CBSE module .

Class 11 Mathematics Case Study Questions

If you’re seeking a comprehensive and dependable study resource with Class 11 mathematics case study questions for CBSE, myCBSEguide is the place to be. It has a wide range of study notes, case study questions, previous year question papers, and practice questions to help you ace your examinations. Furthermore, it …

CBSE Class 11 Mathematics Syllabus 2022-23

CBSE Class 11 Mathematics Syllabus 2022-23 includes Sets and Functions, Coordinate Geometry, Statistics and Probability, Calculus etc for the session 2022 – 2023. Here is the detailed syllabus. To download class 11 Mathematics CBSE latest sample question papers for the 2023 exams, please install the myCBSEguide App which is the …

CBSE Term-1 MCQ Sample Papers 2021-22

CBSE will ask only MCQs in Term-1 Examination this year. The board will hold this first term exam in Nov-Dec 2021. As CBSE has already cleared that 1st term exam will carry 90 minutes, now it’s time to start preparation. Students can download CBSE Term-1 MCQ Sample Papers from myCBSEguide …

CBSE to Conduct Two Term Exams in 2021-22

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

CBSE Class-11 New Stream Selection Rules

The New Education Policy-2020 has suggested eliminating rigid stream selection rules. We know that there are three streams in class 11 and the choices to select subjects are limited. Students have to select subjects within the stream only. Thus, if you are taking Science Stream, you have no option to …

CBSE Reduced Syllabus by 30% for Session 2020-21

CBSE, New Delhi has reduced the syllabus for classes 9 to 12 by 30%. The CBSE Revised Syllabus 2020-21 is available in CBSE official website and myCBSEguide mobile app. Here is the complete circular regarding CBSE Revised Syllabus 2020-21: CBSE Reduced the Syllabus The prevailing health emergency in the country …

Multiple Choice Questions for CBSE Class 10 and 12

The new curriculum issued by CBSE, New Delhi includes objective type questions along with Multiple Choice Questions (MCQ). Now CBSE will ask around 20% questions based on objective type questions. myCBSEguide App has more than one lakh MCQ from class 3 to 12 in almost all major subjects. MCQ questions …

CBSE Online MCQ Quiz Maker

The ultimate quiz builder helps CBSE schools and teachers, create MCQ quiz online and share the same with their students. Now schools and coaching institutes can create and share MCQ quiz online with their own Name and Logo. The students will attempt the quiz and teachers will get the result …

Create CBSE Question Papers Online

Creating question papers online is easy. You can create question papers online with your name and logo in minutes. So, why to waste time consulting many books and finding suitable questions. Just log in to myCBSEguide Test Generator here and create question papers online. Follow 3 simple steps: Select your …

CBSE Syllabus for Class 11 Mathematics 2019-20

CBSE Syllabus for Class 11 Mathematics 2019-20 contains all the topics of this session. myCBSEguide provides you latest Syllabus for Class 11 Mathematics. Mathematics is the study of numbers, shape, and patterns. Mathematics is not only important for success in life, but it is all around us. Mathematics is the …

case study questions for class 11 maths

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Maths And Physics With Pandey Sir

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CBSE Class 11 Term-1 Maths 2021-22: Topic-Wise MCQs, Case-Based & Assertion/Reason

CBSE Class 11 Term-1 Maths 2021-22: Topic-Wise MCQs, Case-Based & Assertion/Reason

Cbse class 11 maths MCQs term1

In this Post I Have Provided Mathematics  Class 11 Chapter-Wise MCQs, Case-Based Question And Assertion/Reason For Term-1 Session 2021-22 With Solutions. CBSE has Recently Included These Types Of MCQs  And Assertion/Reason For Term-1 Exam 2020.   Every Student Knows these types of Questions Are Very Important For Their Term-1 Examination.

Any student who want to download these MCQs, then they have to click on given respective download links and it will be automatically download in your Google Drive.

CBSE Class 11th  Physics  Term-1 2021-22: Topic-Wise MCQs, Case-Based & Assertion/Reason

For Downlod   Click Here

Given Below Are The Class 11 Mathematics Chapter Name with Respective Download Links Containing Study Material:

CBSE Sample Papers For Class 11 Mathematics

CBSE sample paper for class  11th Maths  is an important tools to analyse itself. Before going to final examinations every student try to solve different types of sample question paper. It will enhance your knowledge and also provide to increase mental ability. Sample question paper are the best resources for the student to prepare for their Board examinations.

These sample question papers are very helpful to the student to get an entire experience before attempting the Board examinations papers. If students solve different types of sample question papers then they get the good confidence about the appropriate answer and they make good score in their Board examinations.

As every student know CBSE always change their exam pattern and also the model paper for their Board examinations that is why it is very important to all the student to understand the Model paper pattern before going to the final examinations.

In this articles I have provided different types of question papers on the basis of CBSE latest exam pattern which will definitely help to the student for the good preparation for their examinations.

In every year before the Board examination, CBSE provide model test paper to the student, on the basis of these model test papers I have prepared sample question papers for class  11th Maths  which will help to the student to understand the concept of model test paper and also it will help to the student for good preparation for their board examination.

CBSE Sample Paper:

Maths And Physics With Pandey Sir  is a website which provide free study material and notes to every students who are preparing for their Board examinations. By going in Level Section you can select CBSE sample papers. In this section, I have provided CBSE sample paper for class 9th to 12th.

Also if you are preparing for any competitive exams, they can find out study material and important notes in Level Section. In this website I have also provided most important MCQs questions, Assertion/Reason based questions and case study based questions for Board examinations or any other competitive examinations.

Benefits Of Solving CBSE Sample Papers for Examination:

Time Management:-

With the help of CBSE sample question papers you can make a proper strategy for their examinations also by practicing sample question papers you can manage your time during the Board examinations.

Examination Strategy:-

After practicing different types of sample question papers you can understand on which section you have spend more time and which section is easy and which section is hard. In this way you can make a proper examination strategy.

Self Evaluation:-

Self evaluation is very important to every student because with the help of self evaluation, student can understand their weak and strong point, which is very important for any Board examinations. After practicing more and more simple paper you can evaluate himself.

To Identify Silly Mistakes:-

As every student know there are many questions in their question paper which are very easy  but student make mistakes in this types of question. By solving different types of sample question papers you can reduce their silly mistakes.

Advantages Of CBSE Sample Question Papers:

* To get a good exam ideas about your examination paper patterns

* Student can easily access to the question papers

* It is very helpful to know about the mark distribution system.

* Helpful in self evaluation

* To know about the pattern of CBSE

* Help to adjust a proper time management

* Available in PDF format

* Chapter wise CBSE sample papers

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* CBSE sample paper class 12

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* CBSE sample paper class 11

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case study questions for class 11 maths

Class 11th Applied Mathematics - Descriptive Statistics 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 11 Applied Mathematics Subject - Descriptive Statistics, 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

Descriptive statistics case study questions with answer key.

11th Standard CBSE

Final Semester - June 2015

Applied Mathematics

case study questions for class 11 maths

(ii) What is the central angle formed by the region represented by Italy i.e. , 30.3%

(iii) What is the total population in Germany is 5,54,40,000, then how many persons are infected by Corona Virus ?

(iv) What is the central angle formed by the region represented by Germany i.e., 10.2%

(v) If other region is having total population 1,50,00,000, then what is the population infected in Finland ?

case study questions for class 11 maths

(ii) What is the difference between the highest production item and the lowest production item ?

(iii) Ratio of production of Bananas and Potatoes is

(iv) If production of Pineapple and apples are equal and the sum of their production is equal to thrice the production of Pears, then which of the following equation represent this:

(v) Which two items have same production during the year?

case study questions for class 11 maths

(ii) Mean of the given data is

(iii) What is the mean deviation about the median of the given scores ?

(iv) If the scores 38 and 34 are replaced by 68 and 74 what will be the mean of the data ?

(v) Difference between maximum value of data and minimum vale of data is called

case study questions for class 11 maths

(ii) What is the variance of the given data ?

(iii) Relation between Variance and Standard Deviation is

(iv) What is the Standard Deviation of the data ?

(v) Mean of first 20 natural numbers is

case study questions for class 11 maths

(i) The value  \(\Sigma d\)   is 

(ii) What is the value  \(\Sigma d^{2}\)  is 

(iii) What is the value of n 2 in the given data?

(iv) What is rank correlation of the given data?

(v) What does very low value of the rank correlation in the above answer indicates?

In class of Statistics, teacher was discussing the concept of Measures of Correlation, in which he was discussing about Karl Pearson’s Coefficient of Correlation. During his class, he discussed the following few points on this: This is the best method for finding correlation between two variables provided the relationship between the two variables is linear. This method is also known as product-moment correlation coefficient. Pearson's correlation coefficient may be defined as the ratio of covariance between the two variables to the product of the standard deviations of the two variables. If the two variables are denoted by x and y and of the corresponding bivariates data are ( x i , y i) for i = 1, 2, 3, ...., n, then the coefficent of correlation between x and y due to Karl Pearson, is given by: r = r xy  \(\text { or } \quad r_{x y}=\frac{\operatorname{Cov}(x, y)}{\sqrt{\operatorname{Var} x} \cdot \sqrt{\operatorname{Var} y}}\)   =  \(\frac{\operatorname{Cov}(x, y)}{\sigma_{x} \cdot \sigma_{y}}\)   where,    \(\operatorname{Cov}(x, y)=\frac{\Sigma(x-\bar{x})(y-\bar{y})}{N}\)   =  \(\frac{\Sigma x y}{N}-\bar{x} \cdot \bar{y}\)   =  \(\sigma_{x}=\sqrt{\frac{\Sigma(x-\bar{x})^{2}}{N}}=\sqrt{\frac{\Sigma x^{2}}{N}-x^{-2}}\)   =  \(\sigma_{y}=\sqrt{\frac{\Sigma(y-\bar{y})^{2}}{N}}=\sqrt{\frac{\Sigma y^{2}}{N}-y^{-2}}\)   \(\text { If } x-\bar{x}, y-\bar{y}\)  are small fractions, we use  \(r=\frac{\Sigma(x-\bar{x})(y-\bar{y})}{\sqrt{\sum(x-\bar{x})^{2}} \sqrt{\Sigma(y-\bar{y})^{2}}}\)  

If x, y are small numbers, we use  \(r=\frac{\Sigma x y-\frac{1}{N} \Sigma x \Sigma y}{\sqrt{\Sigma x^{2}-\frac{1}{N}(\Sigma x)^{2}} \sqrt{\sum y^{2}-\frac{1}{N}(\Sigma y)^{2}}}\)   For example: Find Karl Pearson's coefficient of correlation between X and Y for the following :

Following problem was given to students on the same concept: On the basis of the above information, answer the following questions: (i) Pearson’s correlation coefficient may be defined as the ratio of covariance between the two variables to the

(ii) What is the value  \(\Sigma x y\)   in this data:

(iii) What is the value \(\Sigma x^{2}\) ? 

(iv) What is the value of  \(\Sigma y^{2}\)   ?

(v) What is the value of Karl Pearson’s Coefficient of Correlation between x and y?

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

Descriptive statistics case study questions with answer key answer keys.

(i) (d):  45,45,000 Total population infected with Corona Virus \(=\frac{30.3}{100} \times 1,50,00,000\)   = 45,45,000 (ii) (d):  109.08° Central angle =  \(\frac{30.3}{100} \times 360^{\circ}\) = 109.08° (iii) (a):  56,54,880 Total population infected \(=\frac{10.2}{100} \times 55440000\) =  56,54,880 (iv) (c) :  37° Central angle  \(=\frac{10.2}{100} \times 360^{\circ}=36.7\) = 37° (v) (c):  6,30,000 Total population infected in Finland \(=\frac{4.2}{100} \times 1,50,00,000\) = 6,30,000

(i) (b):  potatoes Highest production item is potatoes i.e., 35,000 (ii) (d):  25000 Difference = 35000 – 10000 = 25000 (iii) (b): 5 : 7 \( \text { Ratio } =\frac{25000}{35000} \) \(=\frac{5}{7} \) = 5 : 7 (iv) (a): 2x = 3y Since production Pineapple and Apples are equal, let it be x and let production of Pears is y. Therefore,2x = 3y (v) (a):  Peas and Beans

(i) (c): 47 Arranging the data in ascending order = 34, 38, 42, 44, 46, 48, 54, 55, 63, 70 Median = A.M. of 5th and 6th observation \(=\frac{46+48}{2}=47\)   (ii) (b):   49.4 Sum of all the scores = 494 \(\text { Mean }=\frac{494}{10}=49.4\) (iii) (b):  8.6

\(\text { Mean Deviation }=\frac{1}{n} \times \sum\left|d_{i}\right|=\frac{86}{10}=8.6\) (iv) (d): 56.4 Sum of new scores = 564 New mean =  \(\frac{564}{10}=56.4\)   (v) (d):   range It is called range of the data.

(i) (a): 14 \(\text { Mean }=\frac{12+8+13+15+22}{5}\) = 14 (ii) (c): 21.1 Since, mean  \((\bar{x})\)  = 14

\( \operatorname{Var}(X) =\frac{1}{n} \sum\left(x_{i}-\bar{X}\right) \) \(=\frac{106}{5}=21.2\)   (iii) (b):   \(\text { Variance }=\sqrt{S . D}\)   (iv) (a): 4.604 \( \mathrm{S} . \mathrm{D} =\sqrt{\mathrm{Var}} \) \(=\sqrt{21.2}=4.604 \)   (v) (c): 10.5 Sum of first 20 natural numbers = S 20 \(=\frac{20}{2}[2 \times 1+(19) 1]\)   s 20 = 210 \(\text { Mean }=\frac{210}{20}\) = 10.5

(i) (a): 0

Therefore,  \(\Sigma d\)   = 0 (ii) (c): 166 \(\Sigma d^{2}\)   = 25 + 1 + 9 + 1 + 36 + 16 + 1 + 9 + 4 + 64 = 166 (iii) (d): 100 n 2 = 10 2 = 100 (iii) (d): –0.006 Rank correlation is given by: \(r_{s}=1-\frac{6 \Sigma d^{2}}{n\left(n^{2}-1\right)}\)   =  \(1-\frac{6 \times 166}{10\left(10^{2}-1\right)}\)   =  \(1-\frac{996}{990}\)   =  \(\frac{990-996}{990}\)   =  \(\frac{-6}{990}\)   =  –0.006 (v) (b): there is hardly any agreement between the ranks. The very low value (almost 0) indicates that there is hardly any agreement between the ranks.

(i) (b): product of the standard deviations (ii) (c): 80

(iii) (c): 55

(iv) (a): 220

(v) (b): –0.5

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CBSE Case Study Questions for Class 11 Maths Complex Numbers Free PDF

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Mere Bacchon, you must practice the CBSE Case Study Questions Class 11 Maths Complex 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 11 Maths Complex Numbers PDF

Checkout our case study questions for other chapters.

  • Chapter 3 Trigonometric Functions Case Study Questions
  • Chapter 4 Principle of Mathematical Induction Case Study Questions
  • Chapter 6 Linear Inequalities Case Study Questions
  • Chapter 7 Permutations and Combinations 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.

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  • Class 11 Maths
  • Chapter 16: Probability

Important Questions for Class 11 Maths Chapter 16 - Probability

Important questions for class 11 Maths Chapter 16 Probability are given here, which are taken from the previous year’s question paper. Go through all the problems provided here, which will help you to score good marks in Class 11 final examination. Before solving the problems, be thorough with the concepts covered in the chapter – Probability. All the important questions in chapter 16 probability are solved here in a step-by-step procedure. Students can prepare these questions for the upcoming examinations because most of the questions are asked from the previous year’s question papers. Also, get important questions for class 11 Maths for all the chapters at BYJU’S.

Class 11 Maths Chapter 16 – Probability covers important concepts, such as random experiment, algebra of events, events and types of events, axiomatic approach to the probability

Also, check:

  • Important 1 Mark Questions for CBSE Class 11 Maths
  • Important 4 Marks Questions for CBSE Class 11 Maths
  • Important 6 Marks Questions for CBSE Class 11 Maths

Important Questions for Class 11 Maths Chapter 16 Probability with Solutions

The most important questions for class 11 Maths Chapter 16 probability are provided with solutions. It includes MCQs, short type and long type answers. Practice these problems in a smart way a achieve good marks in the examination.

Question 1:

If P(A) is ⅗. Find P (not A)

Given that: P(A) = ⅗

To find P(not A) = 1 – P(A)

P (not A) = 1- ⅗

Therefore, P(not A) = ⅖.

Question 2:

Find the probability that when a hand of 7 cards are drawn from the well-shuffled deck of 52 cards, it contains

(i) all kings and (ii) 3 kings

(i) To find the probability that all the cards are kings:

If 7 cards are chosen from the pack of 52 cards

Then the total number of combinations possible is: 52 C 7

= 52!/ (7! 45!)

Assume that A be the event that all the kings are selected

We know that there are only 4 kings in the pack of 52 cards

Thus, if 7 cards are chosen, 4 kings are chosen out of 4, and 3 should be chosen from the 48 remaining cards.

Therefore, the total number of combinations is:

n(A) = 4 C 4 x 48 C 3

= 48!/3! 45!

Therefore, P(A) = n(A)/n(S)

Therefore, the probability of getting all the 7 cards are kings is 1/7735

(ii) To find the probability that 3 cards are kings:

Assume that B be the event that 3 kings are selected.

Thus, if 7 cards are chosen, 3 kings are chosen out of 4, and 4 cards should be chosen from the 48 remaining cards.

n(B) = 4 C 3 x 48 C 4

Therefore, P(B) = n(B)/n(S)

Therefore, the probability of getting 3 kings is 9/1547

Question 3:

An urn contains 6 balls of which two are red and four are black. Two balls

are drawn at random. The probability that they are of different colours is

(i)⅖ (ii)1/15 (iii)8/15 (iv)4/15

A correct answer is  an option (c)

Explanation:

Given that, the total number of balls = 6 balls

Let A and B be the red and black balls respectively,

The probability that two balls drawn, are different = P(the first ball drawn is red)(the second ball drawn is black)+ P(the first ball drawn is black)P(the second ball drawn is red)

= (2/6)(4/5) + (4/6)(2/5)

=(8/30)+ (8/30)

Question 4:

A couple has two children,

(i) Find the probability that both children are males if it is known that at least one of the children is male.

(ii) Find the probability that both children are females if it is known that the elder child is a female.

Let, the boy be denoted by b & girl be denoted by g

So, S = {(b, b) ,(b, g),(g, b), (g, g)}

To find probability that both children are males, if known that at least one of children is male

Let E : Both children are males F : At least one child is male

To find P(E|F)

E : Both children are males

E = {(b, b)}

F : At least one child is male

F = {(b, g), (g, b), (b, b)}

E ∩ F = {(b, b)}

P(E ∩ F ) = 1/4

P(E|F) = (𝑃(𝐸 ∩ 𝐹))/(𝑃(𝐹))

= (1/4)/(3/4)

∴ Required Probability is 𝟏/𝟑

S = {(b, b) ,(b, g),(g, b), (g, g)}

To find the probability that both children are females, if from that the elder child is a female.

Let E : both children are females F : elder child is a female

E : both children are females

E = {(g, g)}

F : elder child is a female

F = {(g, b), (g, g)}

P(F) = 2/4=1/2

Also, E ∩ F = {(g, g)}

So, P(E ∩ F) = 1/4

= (1/4)/(1/2)

Question 5:

One card is drawn from a well-shuffled pack of 52 cards. What is the probability that a card will be

(i) a diamond

(ii) Not an ace

(iii) a black card

(iv) not a diamond

(i) the probability that a card is a diamond

We know that there are 13 diamond cards in a deck. Therefore, the required probability is:

P( getting a diamond card) = 13/52 = ¼

(ii) the probability that a card is not an ace

We know that there are 4 ace cards in a deck.

Therefore, the required probability is:

P(not getting an ace card) = 1-( 4/52)

= 1- (1/13)

(iii) the probability that a card is a black card

We know that there are26 black cards in a deck.

P(getting a black card) = 26/52 = ½

(iv) the probability that a card is not a diamond

We know that there are 13 diamond cards in a deck.

We know that the probability of getting a diamond card is 1/4

P( not getting a diamond card) = 1- (1/4)

Question 6:

A pack of 50 tickets is numbered from 1 to 50 and is shuffled. Two tickets are drawn at random. Find the probability that (i) both the tickets drawn bear prime numbers (ii) Neither of the tickets drawn bear prime numbers.

The total number of tickets = 50

Prime numbers from 1 to 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.

The total number of prime numbers between 1 and 50 is 15.

(i) Probability that both tickets are drawn bears prime numbers:

P(Both tickets bearing prime numbers ) = 15 C 2 / 50 C 2

Hence, the probability that both tickets are drawn bear prime numbers is 3/35.

(ii) Probability that neither of the tickets drawn bears prime numbers:

P ( Neither of the tickets bearing prime numbers) = 35 C 2 / 50 C 2

Therefore, the probability that neither of the tickets drawn bears a prime number is 17/35.

Question 7:

20 cards are numbered from 1 to 20. If one card is drawn at random, what is the probability that the number on the card is:

  • Prime number
  • A multiple of 5
  • Not divisible by 3

Let S be the sample space.

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

(1) Probability that the card drawn is a prime number:

Let E 1 be the event of getting a prime number.

E 1 = {2, 3, 5, 7, 11, 13, 17, 19}

Hence, P(E 1 ) = 8/20 = 2/5.

(2) Probability that the card drawn is an odd number:

Let E 2 be the event of getting an odd number.

E 2 = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}

Hence, P(E 2 ) = 10/20 = 1/2.

(3) Probability that the card drawn is a multiple of 5

Let E 3 be the event of getting a multiple of 5

E 3 = {5, 10, 15, 20}

Hence, P(E 3 ) = 4/20 = 1/5.

(4) Probability that the card drawn is not divisible by 3:

Let E 4 be the event of getting a number that is not divisible by 3.

E 4 = {1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20}

Hence, P(E 4 ) = 14/20 = 7/10.

Important Questions for Class 11 Maths Chapter 16 Probability – Practice Questions

Practice the problems given below:

  • What is the sample space for throwing a die?
  • What is the sample space for tossing a coin?
  • What is the sample space for the simultaneous toss of a die and a coin?
  • In a single throw of two dice, find the probability of obtaining a total of 8.
  • A bag contains 9 red and 12 white balls. One ball is drawn at random. Find the probability that the ball is drawn is red.
  • What is the probability that the ordinary year has 53 Sundays?
  • A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability of its being a spade or a king.
  • A card is drawn from a deck of 52 cards. Find the probability of getting a king or a heart or a red card?
  • A number is chosen from the number 1 to 100. Find the probability of its being divisible by 4 or 6.
  • Two cards are drawn at random from a pack of 52 cards. What is the probability that both the drawn cards are aces?
  • A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?
  • A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability of being either red or king.

To learn more important questions for class 11 Maths chapters, stay tuned with BYJU’S – The Learning App and download the app to learn all Maths-related concepts quickly by exploring more videos.

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  • Important Questions for CBSE Class 11 Maths Chapter 6 - Linear Inequalities

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CBSE Class 11 Maths Chapter-6 Important Questions - Free PDF Download

Free PDF download of Important Questions with solutions for CBSE Class 11 Maths Chapter 6 - Linear Inequalities prepared by expert Maths teachers from latest edition of CBSE(NCERT) books . Register online for Maths tuition on Vedantu.com to score more marks in your Examination.

Download CBSE Class 11 Maths Important Questions 2024-25 PDF

Also, check CBSE Class 11 Maths Important Questions for other chapters:

Study Important Questions for CBSE Class 11 Mathematics Chapter 6 – Linear Inequalities

1 Mark Questions in the PDF

1. Solve  $ \dfrac{3x-4}{2}\ge \dfrac{x+1}{4}-1 $.

Ans: Rewrite the given inequality.

$\dfrac{3x-4}{2}\ge \dfrac{x+1}{4}-\dfrac{1}{1}$ 

$\dfrac{3x-4}{2}\ge \dfrac{x+1-4}{4}$ 

$\dfrac{3x-4}{2}\ge \dfrac{x-3}{4}$ 

Multiply the left-hand side with 2 and the right-hand side by 4.

$2\left( 3x-4 \right)\ge \left( x-3 \right)$ 

$6x-8\ge x-3$ 

Subtract  $ x $  from both sides. Further, add 8 to both sides.

$6x-8-x+8\ge x-3-x+8$ 

$5x\ge 5$ 

Divide both sides by 5.

 $ x\ge 1 $ 

Hence, the solution set is  $ \left[ 1,\infty  \right) $ .

2. Solve  $ 3x+8>2 $  when  $ x $  is a real number.

Ans: Given,  $ 3x+8>2 $ . 

Subtract 2 from both sides.

$3x+8-8>2-8$ 

$3x>-6$  

Divide both parts of the inequality by 3.

$\dfrac{3x}{3}>\dfrac{-6}{3}$ 

$x>-2$  

Hence, the solution set is  $ \left( -2,\infty  \right) $ .

3. Solve the inequality  $ \dfrac{x}{4}<\dfrac{5x-2}{3}-\dfrac{7x-3}{5} $ .

Ans: Given,  $ \dfrac{x}{4}<\dfrac{5x-2}{3}-\dfrac{7x-3}{5} $ . 

Take LCM of the terms at the right-hand side of the inequality.  

$\dfrac{x}{4}<\dfrac{5\left( 5x-2 \right)-3\left( 7x-3 \right)}{15}$ 

$\dfrac{x}{4}<\dfrac{25x-10-21x+9}{15}$ 

$\dfrac{x}{4}<\dfrac{4x-1}{15}$ 

Cross-multiply the terms.

$15x<4\left( 4x-1 \right)$ 

$15x<16x-4$ 

Subtract  $ 16x $ from both sides.

$15x-16x<16x-4-16x$ 

$-x<-4$ 

$x>4$ 

Hence, the solution set is $ \left( 4,\infty  \right) $ .

4. If  $ 4x>-16 $ , then  $ x\,\,\,-4 $ .

Ans: Divide both sides of the inequality,  $ 4x>-16 $ by 4.

$\dfrac{4x}{4}>\dfrac{-16}{4}$ 

$x>-4$ 

Hence,  $ x\,\,-4 $ 

5. Solve the inequality $ \dfrac{1}{2}\left( \dfrac{3x}{5}+4 \right)\ge \dfrac{1}{3}\left( x-6 \right) $ .

Ans: Given,  $ \dfrac{1}{2}\left( \dfrac{3x}{5}+4 \right)\ge \dfrac{1}{3}\left( x-6 \right) $ .

Solve the parenthesis.

$ \dfrac{3x}{10}+2\ge \dfrac{x}{3}-2 $ 

Subtract 2 from both sides and add  $ \dfrac{x}{3} $  to both sides and take LCM. 

$\dfrac{3x}{10}-\dfrac{x}{3}\ge -4$ 

$\dfrac{9x-10x}{30}\ge -4$ 

$\dfrac{-x}{30}\ge -4$  

Multiply both sides by 30. 

$-x\ge -4\left( 30 \right)$ 

$-x\ge -120$ 

Hence, the solution set is $ \left( -\infty ,120 \right]$.

6. Solve the inequalities,   $ 2x-1\le 3 $  and  $ 3x+1\ge -5 $  is.

Ans: Given,  $ 2x-1\le 3 $ and  $ 3x+1\ge -5 $ .

Solve the equation,  $ 2x-1\le 3 $ . 

$2x-1+1\le 3+1$ 

$2x\le 4$ 

$x\le 2$ 

Solve the equation, $ 3x+1\ge -5$ .

$3x+1\ge -5$ 

$3x\ge -6$ 

$x\ge -2$ 

From both the solutions it is concluded that,  $ -2\le x\le 2 $ . Hence, the solution set is          $ \left[ -2,2 \right] $ .

7. Solve  $ 7x+3<5x+9 $. Show the graph of the solution on the number line.

Ans: Given,  $ 7x+3<5x+9 $ .

Subtract  $ 5x $  and 3 from both sides. 

$7x+3-5x-3<5x-5x+9-3$ 

Divide both sides by 2.

$ x<3 $ 

The graph of the solution of the given inequality is represented by the red color in the number line shown below.

Graph of Inequality

8. Solve the inequality, $ \dfrac{2x-1}{3}\ge \dfrac{3x-2}{4}-\dfrac{2-x}{5} $ .     

Ans: Given,  $ \dfrac{2x-1}{3}\ge \dfrac{3x-2}{4}-\dfrac{2-x}{5} $ .

Take the LCM of the terms at the right-hand side.

$\dfrac{2x-1}{3}\ge \dfrac{5\left( 3x-2 \right)-4\left( 2-x \right)}{20}$ 

$\dfrac{2x-1}{3}\ge \dfrac{15x-10-8+4x}{20}$ 

$\dfrac{2x-1}{3}\ge \dfrac{19x-18}{20}$ 

Cross-multiply. 

$20\left( 2x-1 \right)\ge 3\left( 19x-18 \right)$ 

$40x-20\ge 57x-54$ 

$40x-57x\ge -54-20$ 

$-17x\ge -34$

Divide both sides by  $ -17 $ .

$ x\le 2 $ 

Hence, the solution set is  $ \left( -\infty ,2 \right] $ .

9. Solve  $ 5x-3\le 3x+1 $  when  $ x $  is an intege 

Ans: Given,  $ 5x-3\le 3x+1 $ .

Subtract  $ 3x $  from both sides and add  $ 3 $  to both sides.

$5x-3-3x+3\le 3x+1+3-3x$ 

Hence, the solution set is  $ \left\{ \ldots .,-3,-2,-1,0,1,2 \right\} $ .

10. Solve  $ 30x<200 $ when  $ x $  is a natural number

Ans: Given,  $ 30x<200 $ .

Divide both sides by 30.

$x<\dfrac{200}{30}$ 

$x<\dfrac{20}{3}$  

Hence, the solution set that satisfies the given inequality is  $ \left\{ 1,2,3,4,5,6 \right\}$ . 

11.  Solve the inequality  $ \dfrac{x}{2}\ge \dfrac{5x-2}{3}-\dfrac{7x-3}{5} $ .

Ans: Given,  $ \dfrac{x}{2}\ge \dfrac{5x-2}{3}-\dfrac{7x-3}{5} $ .

Take the LCM of the terms at the right-hand side.  

$\dfrac{x}{2}\ge \dfrac{5\left( 5x-2 \right)-3\left( 7x-3 \right)}{15}$ 

$\dfrac{x}{2}\ge \dfrac{25x-10-21x+9}{15}$ 

$\dfrac{x}{2}\ge \dfrac{4x-1}{15}$  

Cross-multiply the terms. 

$15x\ge 2\left( 4x-1 \right)$ 

$15x\ge 8x-2$ 

$15x-8x\ge -2$ 

$7x\ge -2$  

Divide both sides by 7.

$ x\ge \dfrac{-2}{7} $ 

Hence, the solution set that satisfies the given inequality is  $ \left( \dfrac{-2}{7},\infty  \right) $ .

12.  Solve  $ 5x-3<3x+1 $  where  $ x $  is an integer.

Ans: Given,  $ 5x-3<3x+1 $ .

Isolate the like terms to one side of the inequality. 

$5x-3x<1+3$ 

$2x<4$ 

$ x<2 $ 

Hence, when  $ x $  is an integer the solutions of the given inequality are,  $ \left\{ \ldots ,-4,-3,-2,-1,0,1 \right\} $.

4 Mark Questions 

Refer to Page 6-12 for 4 Mark Questions in the PDF

1. Solve  $ 3x-6\ge 0 $  graphically.

Ans: The corresponding equality of the given inequality is  $ 3x-6=0 $ .

Solve the equation,  $ 3x-6=0 $  for  $ x $ .

$3x=6$ 

Now, find the region portioned by the inequality by substituting  $ \left( 0,0 \right) $  in $ 3x-6\ge 0 $.

 $3\left( 0 \right)-6\ge 0$ 

$-6\ge 0$ 

Thus, the inequality is false.

Since the inequality is false then, the solution set will not include the portion of  $ x=2 $ which contains the origin. 

The graph of the inequality  $ 3x-6\ge 0 $  is,

Graph of Inequality

2. Ravi obtained 70 and 75 marks in the first unit test. Find the minimum marks he should get in the third test to have an average of at least 60 marks.

Ans: Let the marks secured by Ravi be  $ x $.

According to the question, 

$\dfrac{70+75+x}{3}\ge 60$ 

$\dfrac{145+x}{3}\ge 60$ 

Multiply the inequality obtained by 3.

$145+x\ge 60\left( 3 \right)$ 

$145+x\ge 180$ 

Subtract 145 from both sides. 

$x\ge 180-145$ 

$x\ge 35$  

The minimum mark he should score in the third test is 35.

3. Find all pairs of consecutive odd natural numbers both of which are larger than 10 such that their sum is less than 40.

Ans: Let  $ x $  and  $ x+2 $  be consecutive odd natural number

Since the numbers are larger than 10, then,  $ x>10 $ . Let this equation be  $ \left( 1 \right) $ .

$x+\left( x+2 \right)<40$ 

$2x+2<40$ 

$ 2x<38 $ 

$ x<19 $ 

Let this equation be  $ \left( 2 \right) $ .

From  $ \left( 1 \right) $  and  $ \left( 2 \right) $ . The pairs obtained are,

$ \left( 11,13 \right) $ ,  $ \left( 13,15 \right) $ , $ \left( 15,17 \right) $ , $ \left( 17,19 \right) $ 

Hence, the required pairs are $ \left( 11,13 \right) $ ,  $ \left( 13,15 \right) $ , $ \left( 15,17 \right) $ , and $ \left( 17,19 \right) $ .

4.  A company manufactures cassettes and its cost equation for a week  $ C=300+1.5x $  and its revenue equation is  $ R=2x $, where  $ x $  is the number of cassettes sold in a week. How many cassettes must be sold by the company to get some profit?

Ans: The profit equation is  $ \text{Profit=Revnue}-\text{Cost} $ .

To get the profit, revenue should be more than the cost. Thus,  $ R>C $ .

Substitute  $ R $  as  $ 2x $  and  $ C $  as  $ 300+1.5x $  in the inequality,  $ R>C $

$2x>300+1.5x$ 

$2x-1.5x>300$ 

$0.5x>300  $ 

Divide both sides by  $ 0.5 $.

 $x>\dfrac{300}{0.5}$ 

$x>600$ 

5. The longest side of a  $ \Delta  $  is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the  $ \Delta  $  is at least 61 cm, find the minimum length of the shortest side.

Ans: Let the length of the shortest side be  $ x $  cm, the longest side be  $ 3x $  cm and the third side be  $ \left( 3x-2 \right) $  cm.  

According to the question,

$\left( x \right)+\left( 3x \right)+\left( 3x-2 \right)\ge 61$ 

$7x-2\ge 61$ 

$7x\ge 61+2$ 

$7x\ge 63$ 

$ x\ge 9 $ 

Hence, the shortest side is 9 cm.

6. In drilling the world's deepest hole, it was found that the temperature T in degree Celsius,  $ x $  km below the surface of the earth was given by  $T=30+25\left( x-3 \right) $ ,  $3 < x < 15$ . At what depth will the temperature be between  $ 200{}^\circ  $  C and  $ 300{}^\circ  $  C.

Ans: Let  $ x $  km be the depth where the temperature lies between  $ 200{}^\circ$  C and  $ 300{}^\circ  $ C. Here,  $200^o C<30+25\left( x-3 \right)<300^o C$ .

$200<30+25\left( x-3 \right)<300$ 

$200<30+25x-75<300$ 

$200<25x-45<300$ 

Solve the inequality.

$\dfrac{49}{5} < x < \dfrac{69}{5}$ 

$9.8 < x < 13.8$ 

7. A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second? 

Ans: Let the length of the shortest piece be  $ x $  cm, second piece be  $ \left( x+3 \right) $  cm and the length of the third piece be  $ 2x $  cm.

The total length of the piece is 91 cm. According to the question, 

$x+\left( x+3 \right)+2x\le 91$ 

$4x+3\le 91$ 

$4x\le 91-3$ 

$4x\le 88$ 

Divide both sides by 4.

$x\le \dfrac{88}{4}$ 

$x\le 22$ 

Now, the third piece should be at least 5 cm longer than the second. 

Hence, 

$2x\ge 5+\left( x+3 \right)$ 

$2x-x\ge 5+3$ 

$x\ge 8$  

From  $ x\le 22 $  and  $ x\ge 8 $ ,

$ 8\le x\le 22 $ 

Hence,  $ x\in \left[ 8,22 \right] $ .

8. The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between  $ 7.2 $  and  $ 7.8 $ . If the first pH reading is  $ 7.48 $  and  $ 7.85 $ , find the range of pH value for the third reading that will result in the acidity level is normal.

Ans: Let the third reading of the pH level be  $ x $ . Then, 

$ 7.2<\dfrac{7.48+7.85+x}{3}<7.8 $ 

Multiply all the parts of the inequality by 3.

$21.6 < 15.33+ x < 23.4$ 

$6.27 < x < 7.07$ 

9. A plumber can be paid under two schemes as given below.

 $ \text{I}\text{.} $ Rs 600 and Rs 50 per hr.

 $ \text{II}\text{.} $ Rs 170 per hr.

If the job takes  $ n $  hour for what values of  $ n $  does the scheme  $ \text{I} $  gives the plumber the better wages.

Ans: The total wage of the labor in scheme  $ \text{I} $ is  $ 600+50n $  and the total wage in scheme  $ \text{II} $  is  $ 170n $ . According to the question,

$600+50n>170n$ 

$50n-170n>-600$ 

$-120n>-600$ 

Thus, for better wages, the working hours should be less than 5 hours.

10.  Solve the inequality $ 3x+4y\le 12 $  graphically.

Ans: Given,  $ 3x+4y\le 12 $ .

The corresponding equality is  $ 3x+4y=12 $ .

The two coordinates through which the line passes are,

Put  $ \left( 0,0 \right) $  in the equation,  $ 3x+4y\le 12$ . 

$3\left( 0 \right)+4\left( 0 \right)\le 12$ 

$0\le 12$ 

The inequality is true. Thus, the solution region of the given inequality will be that portion of the graph of  $ 3x+4y=12 $ that contains the origin.

Graph of Inequality

11. Solve graphically  $ x-y\le 0 $ .

 Ans: Given,  $ x-y\le 0 $ .

The corresponding equality is  $ x-y=0 $ . Thus,  $ x=y $ . It will be the straight line passing through the origin.

Put  $ \left( 1,0 \right) $  in inequality,  $ x-y\le 0 $ . 

$1-0\le 0$ 

$1\le 0$ 

The inequality is false. Thus, the solution region of the given inequality will be that portion of the graph of  $ x=y $  that is away from the point  $ \left( 1,0 \right) $ .

Graph of Inequality

12. Solve the inequality  $ 3x+2y>6 $  graphically.

Ans: Given,  $ 3x+2y>6 $ .

The corresponding equality is  $ 3x+2y=6 $ .

Put  $ \left( 0,0 \right) $  in the equation,  $ 3x+2y>6 $ .

$3\left( 0 \right)+2\left( 0 \right)>6$ 

$0>6$ 

The inequality is false. Thus, the solution region of the given inequality will be that portion of the graph of  $ 3x+2y=6 $  that does not contain the point  $ \left( 0,0 \right) $ . 

Graph of Inequality

6 Mark Questions

Refer to Page 13-18 for 6 Mark Questions in the PDF

1. The IQ of a person is given by the formula  $ \text{IQ=}\dfrac{\text{MA}}{\text{CA}}\times 100 $  where MA is mental age and CA is chronological age. If  $ 80\le \text{IQ}\le 140 $  for a group of 12 yr old children, find the range of their mental age.

Ans: Given,  $ 80\le \text{IQ}\le 140 $ .

Substitute  $ \text{IQ} $ as  $ \dfrac{\text{MA}}{\text{CA}}\times 100 $ .

$ 80\le \dfrac{\text{MA}}{\text{CA}}\times 100\le 140 $ 

The chronological age,  $ \text{CA} $ is 12 yr. Thus, substitute  $ \text{CA} $ as 12.

$ 80\le \dfrac{\text{MA}}{\text{12}}\times 100\le 140 $ 

Multiply the inequality obtained by  $ \dfrac{12}{100} $ .

$80\times \dfrac{12}{100}\le \dfrac{\text{MA}}{{12}}\times {100}\times \dfrac{{12}}{{100}}\le 140\times \dfrac{12}{100}$ 

$80\times \dfrac{12}{100}\le \text{MA}\le 140\times \dfrac{12}{100}$ 

$\dfrac{96}{100}\le \text{MA}\le \dfrac{168}{10}$ 

$9.6\le \text{MA}\le 16.8$  

Hence, the required range is  $ 9.6\le \text{MA}\le 16.8 $ .

2. Solve graphically  $ 4x+3y\le 60 $ ,  $ y\ge 2x $ ,  $ x\ge 3 $ ,  $ x,y\ge 0 $ .

Ans: The corresponding equality of  $ 4x+3y\le 60 $ is $ 4x+3y=60 $ .

Put  $ \left( 0,0 \right) $  in the equation,  $ 4x+3y\le 60 $ . 

$4\left( 0 \right)+3\left( 0 \right)\le 60$ 

The inequality is true. Thus, the solution region of the given inequality will be that portion of the graph of  $ 3x+2y=6 $  that contains the point  $ \left( 0,0 \right) $ . 

The corresponding equality of  $ y\ge 2x $ is $ y-2x=0 $ .

Put  $ \left( 0,0 \right) $  in the equation,  $ y\ge 2x $ .

$y-2x\ge 0$ 

$0\ge 0$ 

The inequality is true. Thus, the solution region of the given inequality will be that portion of the graph of  $ y-2x=0 $  that contains the point  $ \left( 0,0 \right) $ . 

The corresponding equality of  $ x\ge 3 $ is $ x=3 $ .

Put  $ \left( 0,0 \right) $  in the equation,  $ x\ge 3 $ .

 $ 0\ge 3 $ 

The inequality is false. Thus, the solution region of the given inequality will be that portion of the graph of  $ x\ge 3 $  that does not contain the point  $ \left( 0,0 \right) $ . 

The graph of the inequalities is given below. The solution region is labelled as a feasible region.

Graph of Inequality

3. A manufacturer has 600 litre of a  $ 12% $  sol. of acid. How many litres of a $ 30% $  acid sol. must be added to it so that the acid content in the resulting mixture will be more than  $ 15% $  but less than  $ 18% $ .

Ans: Let  $ x $ litres of  $ 30% $  acid sol. is required to be added in the mixture. The inequality that shows that the acid content will be more than  $ 15% $  is,

$ 30%\text{ of }x+12%\text{ of 60015 }\!\!%\!\!\text{  of }\left( x+600 \right) $ Solve the inequality.

$\dfrac{30x}{100}+\dfrac{12}{100}\times \text{600}\,>\,\dfrac{15}{100}\times \left( x+600 \right)$ 

$0.30x+12\times \text{6}>\,\text{0}\text{.15}\times \left( x+600 \right)$ 

$0.30x+12\times \text{6}>\text{0}\text{.15}x+0.15\times 600$ 

$0.30x+72>\text{0}\text{.15}x+90$ 

$0.15x>18$

Divide both sides by  $ 0.15 $ .

$ x>120 $ 

The other inequality that shows the acid content will be less than  $ 18% $  is, \[30%\text{ of }x+12%\text{ of 600}<18%\text{ of }\left( x+600 \right)\]. Solve the inequality.

$\dfrac{30x}{100}+\dfrac{12}{100}\times \text{600}<\dfrac{18}{100}\times \left( x+600 \right)$ 

$0.30x+12\times \text{6}<\text{0}\text{.18}\times \left( x+600 \right)$ 

$0.30x+12\times \text{6}<\text{0}\text{.18}x+0.18\times 600$ 

$0.30x+72<\text{0}\text{.18}x+108$ 

$0.12x<36$

Divide both sides by  $ 0.12 $ .

 $ x<300 $ 

Hence,  $120 < x < 300$. 

4. Solve graphically  $ x-2y\le 3 $ ,  $ 3x+4y\ge 12 $ ,  $ x\ge 0 $ ,  $ y\ge 1 $ .

Ans: The corresponding equality of  $ x-2y\le 3 $ is $ x-2y=3 $ .

Substitute $ \left( 0,0 \right) $  in the equation,  $ x-2y\le 3 $ .

$0-2\left( 0 \right)\le 3$ 

$0\le 3$ 

The inequality is true. Thus, the solution region of the given inequality will be that portion of the graph of  $ x-2y\le 3 $  that contains the point  $ \left( 0,0 \right) $ . 

The corresponding equality of  $ 3x+4y\ge 12 $ is $ 3x+4y=12 $ .

Put  $ \left( 0,0 \right) $  in the equation,  $ 3x+4y\ge 12 $ . 

$3\left( 0 \right)+4\left( 0 \right)\ge 12$ 

$0\ge 12$ 

The inequality is false. Thus, the solution region of the given inequality will be that portion of the graph of  $ 3x+4y=12 $  that does not contain the point  $ \left( 0,0 \right) $ . 

The corresponding equality of  $ y\ge 1 $ is $ y=1 $ .

Put  $ \left( 0,0 \right) $  in the equation,  $ y\ge 1 $ .

$ 0\ge 1 $ 

The inequality is false. Thus, the solution region of the given inequality will be that portion of the graph of  $ y=1 $  that does not contain the point  $ \left( 0,0 \right) $ . 

The graph of the inequalities is given below. The solution region is labelled as feasible region.

Graph of Inequality

5. A solution of  $ 8% $   boric acid is to be diluted by adding a  $ 2% $  boric acid sol. to it. The resulting mixture is to be more than  $ 4% $  but less than  $ 6% $  boric acid. If we have 640 litres of the  $ 8% $ solution how many litres of the  $ 2% $  sol. will be added.

Ans: Let  $ x $ litres of the  $ 2% $  solution be added. 

$2%\text{ of }x+8%\text{ of 640}>\text{4 }\!\!%\!\!\text{  of }\left( 640+x \right)$ 

$\dfrac{2x}{100}+\dfrac{8}{100}\times \text{640}>\dfrac{4}{100}\times \left( 640+x \right)$ 

$2x+8\times 640 > 4\left( 640+x \right)$ 

$2x+5120 > 2560+4x$ 

Subtract  $ 4x $  from both sides and then subtract 5120 from both sides. 

$2x-4x>2560-5120$ 

$-2x>-2560 $ 

Divide both sides by  $ -2 $ .

$ x>1280 $ 

Let this equation be  $ \left( 1 \right) $ .

Now, the second inequality is \[12%\text{ of }x+8%\text{ of }640<6%\text{ of }\left( 640+x \right)\].

$\dfrac{2x}{100}+\dfrac{8}{100}\times \text{640}>\dfrac{6}{100}\times \left( 640+x \right)$ 

$2x+8\times 640>6\left( 640+x \right)$ 

$2x+5120>3840+6x$ 

Subtract  $ 6x $  from both sides and then subtract 5120 from both sides.

\[-4x>-1280\]

Divide both sides by  $ -4 $ .

$ x<320 $ 

Let this be inequality  $ \left( 2 \right) $ .

From  $ \left( 1 \right) $  and  $ \left( 2 \right) $ .

 $ 320 < x < 1280 $ 

Hence,  $ 320 < x < 1280 $ .

6. Solve graphically  $ x+2y\le 10 $ ,  $ x+y\ge 1 $ ,  $ x-y\le 0 $ ,  $ x\ge 0 $ ,  $ y\ge 0 $ .

Ans: The corresponding equality of  $ x+2y\le 10 $ is $ x+2y=10 $ .

Substitute  $ \left( 0,0 \right) $  in the equation,  $ x+2y\le 10 $ .

$0+2\left( 0 \right)\le 10$ 

$0\le 10 $ 

The inequality is true. Thus, the solution region of the given inequality will be that portion of the graph of  $ x+2y\le 10 $  that contains the point  $ \left( 0,0 \right) $ . 

The corresponding equality of  $ x+y\ge 1 $ is $ x+y=1 $ .

Put  $ \left( 0,0 \right) $  in the equation,  $ x+y\ge 1 $ . 

$\left( 0 \right)+\left( 0 \right)\ge 1$ 

$0\ge 1$ 

The inequality is false. Thus, the solution region of the given inequality will be that portion of the graph of  $ x+y\ge 1 $  that does not contain the point  $ \left( 0,0 \right) $ . 

The corresponding equality of  $ x-y\le 0 $ is $ x-y=0 $ . Thus,  $ x=y $ . From the equation, it can be seen that it is a straight line passing through the origin.

Put  $ \left( 1,0 \right) $  in inequality,  $ x-y\le 0 $ .

Graph of Inequality

7. How many litres of water will have to be added to 1125 litres of the  $ 45% $  sol. of acid so that the resulting mixture will contain more than  $ 25% $  but less than  $ 30% $  acid content.

Ans: Let  $ x $ litres of water be added to 1125 litres of 45 acid sol. in the resulting mixture.

According to the question,  $ 45%\text{ of }1125>25%\text{ of }\left( x+1125 \right) $  and  $ 45%\text{ of }1125<30%\text{ of }\left( x+1125 \right) $ .

Solve the inequality,  $ 45%\text{ of }1125>25%\text{ of }\left( x+1125 \right) $.

$\dfrac{45}{100}\times 1125>\dfrac{25}{100}\times \left( x+1125 \right)$ 

$0.45\times 1125>0.25\times \left( x+1125 \right)$ 

$506.25>0.25x+281.25$

Subtract \[281.25\] from both sides.

$506.25-281.25>0.25x$ 

$225>0.25x$

Divide both sides by  $ 0.25 $.

$\dfrac{225}{0.25}>x$ 

$900>x$ 

Solve the inequality,  $ 45%\text{ of }1125<30%\text{ of }\left( x+1125 \right) $.

$\dfrac{45}{100}\times 1125<\dfrac{30}{100}\times \left( x+1125 \right)$ 

$0.45\times 1125<0.3\left( x+1125 \right)$ 

$506.25<0.3x+337.5$ 

Subtract  $ 337.5 $  from both sides.

 $506.25-337.5<0.3x$ 

$168.75<0.3x$

$\dfrac{168.75}{0.3}>x$ 

$562.3>x$ 

From both the inequalities  $ 900>x>562.5 $ .

Hence, the required amount of water to be added is  $ 900>x>562.5 $ .

8. Solve graphically  $ 3x+2y\le 150 $ ,  $ x+4y\le 80 $ ,  $ x\le 15 $ ,  $ y\ge 0 $ ,  $ x\ge 0 $ .

Ans: The corresponding equality of  $ 3x+2y\le 150 $ is $ 3x+2y=150 $ .

Substitute  $ \left( 0,0 \right) $  in the equation,  $ 3x+2y\le 150 $ .

$3\left( 0 \right)+2\left( 0 \right)\le 150$ 

$0\le 150$ 

The inequality is true. Thus, the solution region of the given inequality will be that portion of the graph of  $ 3x+2y\le 150 $  that contains the point  $ \left( 0,0 \right) $ . 

The corresponding equality of  $ x+4y\le 80 $ is $ x+4y=80 $ .

Put  $ \left( 0,0 \right) $  in the equation,  $ x+4y\le 80 $ .

$0+4\left( 0 \right)\le 80$ 

$0\le 80$ 

The inequality is true. Thus, the solution region of the given inequality will be that portion of the graph of  $ x+4y\le 80 $  that contains the point  $ \left( 0,0 \right) $ . 

The corresponding equality of  $ x\le 15 $ is $ x=15 $ .

Put  $ \left( 0,0 \right) $  in the equation,  $ x\le 15 $ .

 $ 0\le 15 $ 

The inequality is true. Thus, the solution region of the given inequality will be that portion of the graph of  $ x\le 15 $  that contains the point  $ \left( 0,0 \right) $ . 

The graph of the inequalities is given below. The solution region is labeled as a feasible region.

Graph of Inequality

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Case Study Questions for Class 11 Maths Chapter 8 Binomial Theorem

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Case Study Questions for Class 11 Maths Chapter 8 Binomial Theorem

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[PDF] Download Case Study Questions for Class 11 Maths Chapter 8 Binomial Theorem

Here we are providing case study questions for class 11 maths. In this article, we are sharing Class 11 Maths Chapter 8 Binomial Theorem . All case study questions of class 11 maths are solved so that students can check their solutions after attempting questions.

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What is meant by case study question.

In the context of CBSE (Central Board of Secondary Education), a case study question is a type of question that requires students to analyze a given scenario or situation and apply their knowledge and skills to solve a problem or answer a question related to the case study.

Case study questions typically involve a real-world situation that requires students to identify the problem or issue, analyze the relevant information, and apply their understanding of the relevant concepts to propose a solution or answer a question. These questions may involve multiple steps and require students to think critically, apply their problem-solving skills, and communicate their reasoning effectively.

Importance of Solving Case Study Questions for Class 11 Maths

Case study questions are an important aspect of mathematics education at the Class 11 level. These questions require students to apply their knowledge and skills to real-world scenarios, helping them develop critical thinking, problem-solving, and analytical skills. Here are some reasons why case study questions are important in Class 11 maths education:

  • Real-world application: Case study questions allow students to see how the concepts they are learning in mathematics can be applied in real-life situations. This helps students understand the relevance and importance of mathematics in their daily lives.
  • Higher-order thinking: Case study questions require students to think critically, analyze data, and make connections between different concepts. This helps develop higher-order thinking skills, which are essential for success in both academics and real-life situations.
  • Collaborative learning: Case study questions often require students to work in groups, which promotes collaborative learning and helps students develop communication and teamwork skills.
  • Problem-solving skills: Case study questions require students to apply their knowledge and skills to solve complex problems. This helps develop problem-solving skills, which are essential in many careers and in everyday life.
  • Exam preparation: Case study questions are included in exams and tests, so practicing them can help students prepare for these assessments.

Overall, case study questions are an important component of Class 11 mathematics education, as they help students develop critical thinking, problem-solving, and analytical skills, which are essential for success in both academics and real-life situations.

Feature of Case Study Questions on This Website

Here are some features of a Class 11 Maths Case Study Questions Booklet:

Many Case Study Questions: This website contains many case study questions, each with a unique scenario and problem statement.

Different types of problems: The booklet includes different types of problems, such as optimization problems, application problems, and interpretation problems, to test students’ understanding of various mathematical concepts and their ability to apply them to real-world situations.

Multiple-choice questions: Questions contains multiple-choice questions to assess students’ knowledge, understanding, and critical thinking skills.

Focus on problem-solving skills: The questions are designed to test students’ problem-solving skills, requiring them to identify the problem, select appropriate mathematical tools, and analyze and interpret the results.

Emphasis on practical applications: The case studies in the booklet focus on practical applications of mathematical concepts, allowing students to develop an understanding of how mathematics is used in real-life situations.

Comprehensive answer key: The booklet includes a comprehensive answer key that provides detailed explanations and step-by-step solutions for all the questions, helping students to understand the concepts and methods used to solve each problem.

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