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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

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Class 10 Maths Chapter 2 MCQ

Class 10 Maths Chapter 2 MCQ based on Case Study with answers and explanation for the first term exams 2024-25. All the questions including CBSE MCQ set of questions are answered with complete explanation. Class 10 Maths Chapter 2 Case study based MCQ of Polynomials helps the students to understand the pattern of CBSE question papers and way of answering.

During the skipping through skipping rope, its look like the in the form of parabola. It is a natural examples of parabolic shape which is represented by a quadratic polynomial. Similarly, we can observe in many other cases forming a in a variety of forms of different parabolas.

In the standard form of quadratic polynomial, ax² + bx + c, the condition between a, b and c are

Because if a = 0, the equation become linear. Then it is not a quadratic polynomial. Hence, the correct option is (C).

• View Answer

If the roots of the quadratic polynomial are unequal, where the discriminant D = b² – 4ac, then

We know that: If D = b² – 4ac 0, real and unequal roots. Hence, the correct option is (A).

If α and -α are the zeroes of the quadratic polynomial 2x² – 3(k – 4)x – 8, then k is

From the quadratic polynomial 2x² – 3(k – 4)x – 8 Sum of zeros = 3(k – 4)/2 [Because sum of zeros = -b/a] So, α + (- α) = 3(k – 4)/2, therefore, k – 4 = 0 or k = 4 Hence, the correct option is (A).

The graph of x² – 1 = 0

The given equation: x² – 1 = 0 or 1.x² + 0.x – 1 = 0 Here, a = 1, b = 0 and c = – 1 D = b² – 4ac = 0² – 4 х 1 х(- 1) = 4, therefore, there is two real root. So, the graph of the equation intersects x‐axis at two distinct points. Hence, the correct option is (A).

If the sum of the roots is p and product of the roots is -p, then the quadratic polynomial is

We know that the equation of a quadrilateral is given by: k [x² – (sum of roots)x + product of roots)] Therefore, the equation = k(x² – (p)x + (-p)] = k(x² – px – p) Hence, the correct option is (C).

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.

In the standard form of quadratic polynomial, ax² + bx + c, a, b and c are

Because if a = 0, the equation become linear. Then it is not a quadratic equation. Hence, the correct option is (C).

If the roots of the quadratic polynomial are equal, where the discriminant D = b² – 4ac, then

We know that: If D = b² – 4ac 0, real and unequal roots. Hence, the correct option is (D).

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

From the quadratic polynomial 2x² – x + 8k Product of zeros = 8k/4 [Because product of zeros = c/a] So, α x (1/α) = 8k/2 Therefore, 4k = 1 Hence, k = 1/4 Hence, the correct option is (B).

The graph of x² + 1 = 0

The given equation: x² + 1 = 0 or 1.x² + 0.x + 1 = 0 Here, a = 1, b = 0 and c = 1 D = b² – 4ac = 0² – 4 х 1 х 1 = – 4, therefore, there is no real root. So, the graph of the equation neither touches nor intersects x‐axis. Hence, the correct option is (C).

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

We know that the equation of a quadrilateral is given by: k [x² – (sum of roots)x + product of roots)] Therefore, the equation = k(x² – (-p)x + (-1/p)] = k(x² + px – 1/p) Hence, the correct option is (C).

Observe the position of the athlete taking long jump. He use to follow every time a particular shape of path. In the figure, a student can observe that the different positions can be related to representation of quadratic polynomial.

The path of the different positions form a

When we draw a dotted line following the different positions of athlete, it show a parabolic path. So, it is a parabola. Hence, the correct option is (D).

If the above case is represented by quadratic polynomial ax² + bx + c, then

If a > 0, the parabola is upward. If a < 0, the parabola is downward. Hence, the correct option is (C).

If the sum of zeros of quadratic polynomial ax² + bx + c is equal to product of zero, then

Given polynomial: ax² + bx + c Sum of zeros = -b/a, Product of zeros = c/a, According to question, -b/a = c/a Therefore, – b = a or a + b = 0 Hence, the correct option is (C).

Observe the graph given below.

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

The graph of the polynomial cutting the x-axis at four distinct points. So, it has 4 zeros. Hence, the correct option is (D).

The four zeroes in the above shown graph are

The graph of the polynomial cutting x-axis at (-4, 0), (-2, 0), (1, 0) and (3, 0). So, the zeros of polynomial are -4, -2, 1 and 3. Hence, the correct option is (A).

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.

The shape of the poses shown is

The pose shown above are in the format of parabola. Hence, the correct option is (D).

The graph of parabola opens downwards, if

The zeroes of the quadratic polynomial 4√3 x² + 5x – 2√3 are.

Given polynomial: 4√3 x² + 5x – 2√3 = 4√3 x² + 8x – 3x – 2√3 = 4x (√3x + 2) – √3 (√3x + 2) = (√3x + 2) (4x – √3) Putting (√3x + 2) (4x – √3) = 0 x = -2/√3 or x = √3/4 Hence, the correct option is (B).

Observe the following graph:

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

The graph of the polynomial cutting the x-axis at two distinct points. So, it has two zeros. Hence, the correct option is (C).

The two zeroes in the above shown graph are

The graph of the polynomial cutting x-axis at (-2, 0) and (4, 0). So, the zeros of polynomial are -2 and 4. Hence, the correct option is (B).

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.

The shape of the path traced shown is

The graph of parabola opens upwards, if.

Observe the following graph and answer:

The graph of the polynomial cutting the x-axis at three distinct points. So, it has three zeros. Hence, the correct option is (D).

The three zeroes in the above shown graph are

The graph of the polynomial cutting x-axis at (-3, 0), (-1, 0) and (2, 0). So, the zeros of polynomial are -3, -1 and 2. Hence, the correct option is (C).

What will be the expression of the polynomial?

The zeros of polynomial are -3, -1 and 2. Let α = -3, β = -1 and γ = 2 So, α + β + γ = -3 + (-1) + 2 = – 4 + 2 = -2 αβ + βγ + αγ = (-3)(-1) + (-1)(2) + (2)(-3) = 3 – 2 – 6 = – 5 αβγ = (-3)(-1)(2) = 6 Equation of polynomial = x³ – (α + β + γ) x² + (αβ + βγ + αγ) x – αβγ = x³ – (-2)x² + (- 5)x – 6 = x³ + 2x² – 5x – 6

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Case Study Class 10 Maths Questions

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

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

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

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

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

Class 10 Maths has the following chapters.

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

Format of Maths Case-Based Questions

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

Maths Case Study Question Paper 2023

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

Case Study Question in Mathematics

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

Case Study Question – 1

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

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

Case Study Question – 2

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

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

Case Study Question – 3

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

Case Study Question – 4

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

Case Study Question – 5

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

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

Case Study Question – 6

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

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

More Case Study Questions

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

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

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

How to Solve Case-Based Questions?

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

What are Class 10 competency-based questions?

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

Case Study Questions in Maths Question Paper

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

Case Studies on CBSE’s Official Website

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

10 Maths Case Studies in myCBSEguide App

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

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• CBSE Reduced Syllabus Class 10 (2020-21)
• Class 10 Maths Basic Sample Paper 2024
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CBSE 10th Standard Maths Subject Polynomials Case Study Questions With Solution 2021

By QB365 on 21 May, 2021

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

QB365 - Question Bank Software

10th Standard CBSE

Final Semester - June 2015

Case Study Questions

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

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

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

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

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

(iii) The value of p(2) is

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Related 10th Standard CBSE Maths Materials

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Case Study Class 10 Maths Questions and Answers (Download PDF)

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Case Study Class 10 Maths

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CBSE Board will be asking case study questions based on Maths subjects in the upcoming board exams. Thus, it becomes an essential resource to study. 

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Students are advised to access Case Study questions class 10 Maths CBSE chapter wise PDF and learn how to easily solve questions. For gaining the basic knowledge students can refer to the NCERT Class 10th Textbooks. After gaining the basic information students can easily solve the Case Study class 10 Maths questions.

Case Study Questions Class 10 Maths Chapter 1 Real Numbers

Case Study Questions Class 10 Maths Chapter 2 Polynomials

Case Study Questions Class 10 Maths Chapter 3 Pair of Equations in Two Variables

Case Study Questions Class 10 Maths Chapter 4 Quadratic Equations

Case Study Questions Class 10 Maths Chapter 5 Arithmetic Progressions

Case Study Questions Class 10 Maths Chapter 6 Triangles

Case Study Questions Class 10 Maths Chapter 7 Coordinate Geometry

Case Study Questions Class 10 Maths Chapter 8. Introduction to Trigonometry

Case Study Questions Class 10 Maths Chapter 9 Some Applications of Trigonometry

Case Study Questions Class 10 Maths Chapter 10 Circles

Case Study Questions Class 10 Maths Chapter 12 Areas Related to Circles

Case Study Questions Class 10 Maths Chapter 13 Surface Areas & Volumes

Case Study Questions Class 10 Maths Chapter 14 Statistics

Case Study Questions Class 10 Maths Chapter 15 Probability

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Case Study Questions Class 10 History -Nationalism In India

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Case study Questions in Class 10 Social Science History Chapter 2  are very important to solve for your exam. Class 10 Social Science Chapter 2 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Case Study Questions Class 10 History Chapter 2 Nationalism in India

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In CBSE Class 10 Social Science 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.

Nationalism in India Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Social Science  Chapter 2 Nationalism in India

Case Study/Passage-Based Questions

Case Study 1: To the altar of this revolution, we have brought our youth as incense’. Many nationalists thought that the struggle against the British could not be won through non-violence. In 1928, the Hindustan Socialist Republican Army (HSRA) was founded at a meeting in Feroz Shah Kotla ground in Delhi. Amongst its leaders were Bhagat Singh, Jatin Das, and Ajoy Ghosh. In a series of dramatic actions in different parts of India, the HSRA targeted some of the symbols of British power. In April 1929, Bhagat Singh and Batukeshwar Du3 threw a bomb in the Legislative Assembly. In the same year, there was an a3empt to blow up the train that cord Irwin was traveling in. Bhagat Singh was 2: when he was tried and executed by the colonial government. During his trial, Bhagat Singh stated that he did not wish to glorify ‘the cult of the bomb and pistol’ but wanted a revolution in society ‘Revolution is the inalienable right of mankind. Freedom is the imprescriptible birthright of all. The laborer is the real sustainer of society Z To the altar of this revolution we have brought our youth as incense, for no sacrifice is too great for so magnificent a cause. We are content. We await the advent of the revolution. Inquilab Zindabad

Why Hindustan Socialist Republican Army was formed? With reference to the above context, infer the appropriate option. (a) To fight against the British colonial rule with the principle of non-violence (b) To fight against British colonial rule in India (c) To achieve independence for the country through an armed rebellion

(d) Both (b) and (c)

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

(ii) Consider the following statements and find the incorrect from the given options. I. Bhagat Singh and Batukeshwar Dutta threw a bomb in the Central Legislative Assembly. II. Hindustan Socialist Republican Army was based on the principles given by Mahatma Gandhi. III. Bhagat Singh wanted a revolution in the society.

Codes (a) Only I (b) Only II (c) Only III (d) Both II and III

Answer: (b) Only II

What lessons does Bhagat Singh’s life have for modern-day India? Identify the correct option. (a) He emphasised on socio-economic changes rather than changing political leaders. (b) He inspired the masses to break social barriers of casteism. (c) He taught people to shed away the fear of British rulers. (d) All of the above

Answer: (d) All of the above

The HSRA and Bhagat Singh focussed on which section of the society to bring a revolution? Identify the correct option. (a) Labourers (b) Leaders (c) Youth (d) Merchants

Answer: (c) Youth

During whose tenure as the Viceroy of India were the great martyrs Bhagat Singh, Sukhdev and Rajguru hanged? Choose the best suitable option. (a) Lord Canning (b) Lord Irwin (c) Lord Minto (d) Lord Curzon

Answer: (b) Lord Irwin

Which of the following were the Revolutionary activities of HSRA? Choose the correct option. (a) Central Assembly Bombing Case. (b) An attempt to blow up the train that Lord Irwin was travelling in. (c) Both (a) and (b) (d) Involved in Lahore Conspiracy Case

Answer: (c) Both (a) and (b)

Case Study 2: The chapter “Nationalism in India” in Class 10 History explores the growth of nationalism in India during the colonial period and the various movements and leaders that shaped the Indian independence struggle. It delves into the impact of British colonial rule, the emergence of the Indian National Congress (INC), the role of Mahatma Gandhi, and the significance of the non-cooperation and civil disobedience movements. Additionally, it examines the role of various social and religious movements, such as the Rowlatt Satyagraha and the Khilafat Movement, in mobilizing the masses and fostering a sense of unity among Indians.

MCQ Questions:

Which chapter in Class 10 History focuses on the growth of nationalism in India?

a) Chapter 1: The Rise of Nationalism in Europe

b) Chapter 3: Nationalism in India

c) Chapter 5: The Age of Industrialization

d) Chapter 7: Print Culture and The Modern World

Answer: b) Chapter 3: Nationalism in India

What is the significance of the Indian National Congress (INC) in the nationalist movement?

a) It promoted violent resistance against British rule.

b) It advocated for the continuation of British colonial rule.

c) It provided a platform for nationalist leaders to voice their demands.

d) It focused solely on religious reforms in India.

Answer: c) It provided a platform for nationalist leaders to voice their demands.

Who is considered as the leader of the non-cooperation and civil disobedience movements in India?

a) Jawaharlal Nehru

b) Bhagat Singh

c) Subhash Chandra Bose

d) Mahatma Gandhi

Answer: d) Mahatma Gandhi

Which movements played a significant role in mobilizing the masses and fostering unity during the Indian independence struggle?

a) The Rowlatt Satyagraha and the Khilafat Movement

b) The Swadeshi Movement and the Quit India Movement

c) The Non-Aligned Movement and the Dandi March

d) The Green Revolution and the White Revolution

Answer: a) The Rowlatt Satyagraha and the Khilafat Movement

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Social Science History Chapter 2 Nationalism in India with Answers Pdf free download has been useful to an extent. If you have any other queries about the CBSE Class 10 Social Science Nationalism in India Case Study and Passage-Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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Class 10 Science: Case Study Chapter 2 Acids, Bases, and Salts PDF Download

In CBSE Class 10 Science 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.

Here we are providing you with Class 10 Science Chapter 2 Acids, Bases, and Salts Case Study Questions, by practicing this Case Study and Passage Based Questions will help you in your Class 10th Board Exam.

Case Study Chapter 2 Acids, Bases, and Salts

Here, we have provided case-based/passage-based questions for Class 10 Science  Chapter 2 Acids, Bases, and Salts

Case Study/Passage-Based Questions

Question 1:

A compound, X of sodium forms a white powder. It is a constituent of baking powder and is used in some antacids. When heated it gives a compound, Y which is anhydrous and absorbs water to become a hydrated salt. When this salt is kept in the open air, it loses water molecules in a process called efflorescence. When dissolved in water it forms a strong base and a weak acid, Z.

(i) What is the compound, X?

Answer: (c) NaOH.

(ii) The compound, Y is

Answer: (c) Na2CO3.10H2O

(iii) What is the nature of the solution formed by dissolving Y in water?

Answer: (a) Alkaline

(iv) Identify the compound, Z.

Answer: (b) H2CO3

(v) Sodium carbonate is a basic compound because it is a salt of a

Answer: (c) strong acid and weak base

Question 2:

pH is quite useful to us in a number of ways in daily life. Some of its applications are:

Control of pH of the soil : Plants need a specific pH range for proper growth. The soil may be acidic, basic, or neutral depending upon the relative concentration of H* and OH-. The pH of any soil can be determined by using pH paper. If the soil is too acidic, it can be corrected by adding lime to it. If the soil is too basic, it can be corrected by adding organic manure which contains acidic materials.

Regaining shine of a tarnished copper vessel by use of acids :  A copper vessel gets tarnished due to formation of an oxide layer on its surface. On rubbing lenion on the vessel, the surface is cleaned and the vessel begins to shine again. This is due to the fact that copper oxide is basic in nature, which reacts with the acid (citric acid) present in lemon to form a salt (copper citrate) which is washed away with water. As a result, the layer of copper oxide is removed from the surface of the vessel and the shining surface is exposed.

Self-defence by animals through chemical warfare :  Stings of bees and ants contain methanoic acid. When stung, it causes lot of pain and irritation. This can be cured by rubbing the affected area with mild base like baking soda.

(i) When black copper oxide placed in a beaker is treated with dilute HCl, its color changes to ( a) white (b) dark red (c) bluish-green (d) no change.

Answer: (c) bluish green

(ii) P is an aqueous solution of acid and Q is an aqueous solution of base. When these two are diluted separately, then (a) pH of P increases while that of Q decreases till neutralization.

(b) pH of P decreases while that of Q increases till neutralization. (C) pH of both P and Q decrease. (d) pH of both P and Q increase.

Answer: (a) pH of P increases while that of Q decreases till neutralisation.

(iii) Which of the following acids is present in bee sting? (a) Formic acid (b) Acetic acid (c) Citric acid (d) Hydrochloric acid

Answer: (c) Citric acid

(iv) Sting of ant can be cured by rubbing the affected area with soap because (a) it contains oxalic acid which neutralises the effect of formic acid (b) it contains aluminium hydroxide which neutralises the effect of formic acid (c) it contains sodium hydroxide which neutralises the effect of formic acid (d) none of these

Answer: (c) it contains sodium hydroxide which neutralises the effect of formic acid

(v) The pH of soil X is 7.5 while that of soil Y is 4.5. Which of the two soils, should be treated with powdered chalk to adjust its pH? (a) X only (b) Y only (c) Both X and Y (d) none of these

Answer: (b) Y only

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Case Study Questions Class 10 Science Life Processes

Case study questions class 10 science chapter 6 life processes.

At Case Study Questions there will given a Paragraph. In where some Important Questions will made on that respective Case Based Study. There will various types of marks will given 1 marks, 2 marks, 3 marks, 4 marks.

CBSE Case Based Questions Class 10 Science Chemistry Chapter 6

CASE STUDY : 1

Carbon and energy requirements of the autotrophic organism are fulfilled by photosynthesis. It is the process by which autotrophs take in substances from the outside and convert them into stored forms of energy. This material is taken in the form of carbon dioxide and water which is converted into carbohydrates in the presence of sunlight and chlorophyll. Carbohydrates are utilised for providing energy to the plant.

i) Write a chemical reaction which occur during photosynthesis?

Ans: 6CO2 +12H2O + Chlorophyll & sunlight👉 C6H12O6 + 6O2 + 6H2O

ii) In which form of carbohydrates does the plant stored in them?

Ans: The carbohydrates are stored in the form of starch as the internal energy.

iii) What is stomata?

Ans: The process present in the surface of a leaf or the stem of a plant to allow the exchange of gases.

iv) What are the functions of stomata?

Ans: i) Exchange of gases i.e oxygen and CO2

ii) Transpiration

v) What is Chloroplast?

Ans: Chloroplast is a cell organelles which contains photosynthetic pigment called as chlorophyll which help in the absorption of sunlight.

CASE STUDY : 2

The alimentary canal is basically a long tube extending from the mouth to the anus. In Fig. 6.6, we can see that the tube has different parts. Various regions are specialised to perform different functions.

We eat various types of food which has to pass through the same digestive tract. Naturally the food has to be processed to generate particles which are small and of the same texture. This is achieved by crushing the food with our teeth

i) Which enzyme is present in our mouth to digest starch?

Ans: Salivary amylase from salivary glands.

ii) What are the types of enzymes released by our stomach?

Ans: Hydrochloric acid, pepsin and a mucus.

iii) Which is the longest part of our alimentary canal in our body?

Ans: Small intestine

iv) What are villi?

Ans: Villi are finger like projection present inside the inner lining of the small intestine which increases the surface area for absorption.

v) What are the enzymes that are released by pancreas?

Ans: Enzyme released by pancreas – • trypsin- Digestion of protein

lipase – breakdown of emulsified fats

CASE  STUDY : 3

The food material taken in during the process of nutrition is used in cells to provide energy for various life processes. Diverse organisms do this in different ways – some use oxygen to break-down glucose completely into carbon dioxide and water, some use other pathways that do not involve oxygen (Fig. 6.8). In all cases, the first step is the break-down of glucose, a six-carbon molecule, into a three-carbon molecule called pyruvate. This process takes place in the cytoplasm.

i) What is anaerobic respiration?

Ans: The conversion of pyruvate into ethanol, CO2 & energy take place in the absence of air(oxygen),  it is called anaerobic respiration.

ii) Explain the process which happen in our muscle cells?

Ans- The conversion of pyruvate to lactic acid( 3 carbon molecule)  and energy due to the lack of oxygen.

iii) In which form our body used the energy?

Ans: It is in the form of ATP molecule i.e Adenosine Triphosphate.

iv) Why there is a faster breathing rate of aquatic animals then the terrestrial animals?

Ans- The amount of O2 dissolved in water is low as compared to amount of O2 present in air. Therefore, aquatic animals have faster breathing rate.

v) Write the name of organ used for respiration by different organism- fish, frog?

Ans- i) fish- gills

ii) frog- skin, lungs

CASE STUDY : 4

The excretory system of human beings includes a pair of kidneys, a pair of ureters, a urinary bladder and a urethra. Kidneys are located in the abdomen, one on either side of the backbone. Urine produced in the kidneys passes through the ureters into the urinary bladder where it is stored until it is released through the urethra.

i) What is the purpose of making urine?

Ans: Urine is to filter out the blood i e to remove waste product from the blood such as urea.

ii) What is Bowman’s capsule?

Ans: A cup shaped end of a coiled tube which is associated with capillaries to collect filterate.

iii) What is dialysis?

Ans: To remove nitrogenous waste from your blood by using machine when kidney does not its function i.e in case of kidney failure.

iv) What is the function of urinary bladder?

Ans: It is used to stored urine until the pressure comes from the brain to pass it out.

v) What are the different parts of nephrons?

Ans: Renal artery, Bowman’s capsule, glomerulus, tubular part of nephron and a collecting duct.

CASE STUDY : 5

The heart is a muscular organ which is as big as our fist. Because both oxygen and carbon dioxide have to be transported by the blood, the heart has different chambers to prevent the oxygen-rich blood from mixing with the blood containing carbon dioxide. The carbon dioxide-rich blood has to reach the lungs for the carbon dioxide to be removed, and the oxygenated blood from the lungs has to be brought back to the heart. This oxygen-rich blood is then pumped to the rest of the body.

i) How many chambers are present in the heart of mammals and reptiles?

Ans: Mammals- 4 chamber heart and reptiles- 3 chambered heart

ii) Who carry deoxygenated blood from body to heart?

Ans: Vena cava carries deoxygenated blood from body to heart.

iii) What do you meant by the term double circulation?

Ans: The blood goes through the heart twice during each cycle known as double circulation.

iv) What is hypertension?

Ans: The force that blood experts against the wall of a vessels is called hypertension or high blood pressure.

V) Which device measured blood pressure?

Ans: Sphygmomanometer

CASE STUDY : 6

Plant transport systems will move energy stores from leaves and raw materials from roots. These two pathways are constructed as independently organised conducting tubes. One, the xylem moves water and minerals obtained from the soil. The other, phloem transports products of photosynthesis from the leaves where they are synthesised to other parts of the plant

i) What are the different parts of xylem?

Ans: vessels, tracheids, xylem parenchyma and fibres.

ii) What do you meant by the term transpiration?

Ans: The loss of water in the form of vapour from the aerial parts of the plant.

iii) What are the advantages of transpiration?

Ans: i) help in the absorption and the upward movement of water

ii) temperature regulation

iv) What is translocation?

Ans: The transport of soluble products of photosynthesis is called translocation.

v) How does plant remove their waste product?

Ans: They remove their waste product in the form of fallen leaves, resins and gums.

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Case Study Questions for Class 10 Social Science Geography Chapter 2 Forest and Wildlife Resources

• Last modified on: 7 months ago
• Reading Time: 10 Minutes

Table of Contents

Here we are providing case study questions for Class 10 Social Science Geography Chapter 2 Forest and Wildlife Resources

Case Study Question 1:

Read the source given below and answer the questions that follow by choosing the most appropriate option:

Nature worship is an age-old tribal belief based on the premise that all creations of nature have to be protected. Such beliefs have preserved several virgin forests in pristine form called Sacred Groves (the forests of God and Goddesses). These patches of forest or parts of large forests have been left untouched by the local people and any interference with them is banned.

Certain societies revere a particular tree which they have preserved from time immemorial. The Mundas and the Santhal of Chota Nagpur region worship mahua (Bassia latifolia) and kadamba (Anthocaphalus cadamba) trees, and the tribals of Odisha and Bihar worship the tamarind (Tamarindus indica) and mango (Mangifera indica) trees during weddings. To many of us, peepal and banyan trees are considered sacred.

Indian society comprises several cultures, each with its own set of traditional methods of conserving nature and its creations. Sacred qualities are often ascribed to springs, mountain peaks, plants and animals which are closely protected. You will find troops of macaques and langurs around many

temples. They are fed daily and treated as a part of temple devotees. In and around Bishnoi villages in Rajasthan, herds of blackbuck, (chinkara), nilgai and peacocks can be seen as an integral part of the community and nobody harms them.

Q 1. How is nature worship an age old tribal belief ? Ans. Nature worship is an age old tribal belief as it is based on the promise that all creations of nature have to be protected. Such beliefs have preserved several virgin forests in pristine form called Sacred groves. These patches of forests, have been left untouched by the local people and any interference with them is banned.

Q 2. Which tribal societies used to worship tress during weddings? Ans. The Mundas and the Santhal of Chota Nagpur region worship mahua (Bassia latifolia) and Kadamba trees. The tribes of Odisha and Bihar worship the tamarind and mango trees during weddings.

Q 3. Name the animals that are treated as a part of temple devotees and the community. Ans. The animals that are treated as a part of temple devotees and the community are macaques and langurs while the herds of blackbuck, nilgai and peacocks can be seen as an integral part of community in and around Rajasthan.

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Tips to prepare for case study questions for class 10 social science.

Preparing for case study and passage-based questions in class 10 social science can be challenging, but it is important to remember that with the right approach, you can effectively tackle these types of questions. Here are some steps you can take to prepare for case study questions for class 10 social science:

• Understand the format of case study questions: Case study questions for class 10 social science usually require you to read a scenario or a passage and answer a set of questions based on it. These questions can be based on various topics like history, geography, economics, or civics.
• Read and analyze the case study or passage carefully: The first step in answering case study questions is to read the scenario or passage carefully. Try to identify the main idea or theme of the passage and note down any important details that you think are relevant. Pay attention to any maps, graphs, or charts that are included as they can be helpful in answering the questions.
• Identify the type of questions being asked: After reading the case study or passage, you should analyze the questions being asked. Try to identify the type of question, whether it is a factual question or an analytical question. Factual questions require you to provide specific details from the passage, while analytical questions require you to use your critical thinking skills to analyze the information presented in the passage.
• Use your textbook and notes: To prepare for case study questions for class 10 social science, it is important to have a thorough understanding of the topics covered in your textbook. Go through your notes and textbook to revise the relevant topics and concepts. This will help you to answer the questions more accurately.
• Practice sample questions: One of the best ways to prepare for case study questions is to practice answering sample questions. Try to find sample questions online or in your textbook and practice answering them. This will help you to get comfortable with the format of the questions and improve your speed and accuracy.

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