cbse class 10 coordinate geometry case study questions

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CBSE 10th Standard Maths Subject Coordinate Geometry Case Study Questions 2021

By QB365 on 22 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) How far is the library from Shaguns house?

(iii) How far is the library from Alia's house?

(iv) Which of the following is true?

(v) How far is the school from Alia's house than Shaguns house?

(ii) The value of x is equal to

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

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

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

(ii) The distance of the bus stand from the house is

(iii) If the grocery store and electrician's shop lie on a line, the ratio of distance of house from grocery store to that from electrician's shop, is

(iv) The ratio of distances of house from bus stand to food cart is

(v) The coordinates of positions of bus stand, grocery store, food cart and electrician's shop form a

(ii) The centre of circle is the

(iii) The radius of the circle is

(iv) The area of the circle is

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

(ii) If S be the mid-point of line joining P and Q, then coordinates of S are

(iii) If T be the mid-point of line joining Rand Q, then coordinates of T are

(iv) If Ube the mid-point of line joining Rand P, then coordinates of U are

(v) The coordinates of centroid of $\Delta$ STU are

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Cbse 10th standard maths subject coordinate geometry case study questions 2021 answer keys.

(i) (d): Since the coordinates of A and Bare (2, 3) and (2, 1) respectively. $\therefore$ Required distance = AB $=\sqrt{(2-2)^{2}+(1-3)^{2}}=\sqrt{2^{2}}=2 \text { units }$ (ii) (b): Since, library is situated at C(4, 1) $\therefore$ Required distance = BC $=\sqrt{(4-2)^{2}+(1-1)^{2}}=\sqrt{2^{2}+0^{2}}=2 \text { units }$ (iii) (d): Required distance = AC $=\sqrt{(4-2)^{2}+(1-3)^{2}}=\sqrt{2^{2}+2^{2}}=2 \sqrt{2} \text { units }$ (iv) (b): Since AB = BC $\neq$ AC, therefore $\Delta$ ABC is an isosceles triangle. (v) (d): Distance between O and A $=\sqrt{2^{2}+3^{2}}=\sqrt{4+9}=\sqrt{13} \text { units }$ and distance between O and B = $\sqrt{2^{2}+1^{2}}=\sqrt{4+1}=\sqrt{5} \text { units }$ Thus, required distance = $(\sqrt{13}-\sqrt{5}) \text { units }$

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

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

(i) (c): We have, P( -3,4), Q(3, 4) and R( -2, -1). $\therefore$ Coordinates of centroid of $\Delta$ PQR $=\left(\frac{-3+3-2}{3}, \frac{4+4-1}{3}\right)=\left(\frac{-2}{3}, \frac{7}{3}\right)$ (ii) (d): Coordinates of S= $\left(\frac{-3+3}{2}, \frac{4+4}{2}\right)=(0,4)$ (iii) (c): Coordinates of T= $\left(\frac{-2+3}{2}, \frac{-1+4}{2}\right)=\left(\frac{1}{2}, \frac{3}{2}\right)$ (iv) (a): Coordinates of U = $\left(\frac{-2-3}{2}, \frac{-1+4}{2}\right)=\left(\frac{-5}{2}, \frac{3}{2}\right)$ (v) (c): The centroid of triangle formed by joining the mid-points of sides of given triangle is same as that of the given trangle. So, centroid of $\Delta S T U=\left(\frac{-2}{3}, \frac{7}{3}\right)$

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Case Study Questions for Class 10 Maths Chapter 7 Coordinate Geometry

Last modified on: 10 months ago
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Case Study Questions:

Question 1:

The top of a table is shown in the figure given below:

(i) The coordinates of the points H and G are respectively (a) (1, 5), (5, 1) (b) (0, 5), (5, 0) (c) (1, 5), (5, 0) (d) (5, 1), (1, 5)

(ii) The distance between the points A and B is (a) 4 units (b) 4 2 units (c) 16 units (d) 32 units

(iii) The coordinates of the mid point of line segment joining points M and Q are (a) (9, 3) (b) (5, 11) (c) (14, 14) (d) (7, 7)

(iv) Which among the following have same ordinate? (a) H and A (b) T and O (c) R and M (d) N and R

(v) If G is taken as the origin, and x, y axis put along GF and GB, then the point denoted by coordinate (4, 2) is (a) H (b) F (c) Q (d) R

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Class 10 maths case study based questions chapter 7 coordinate geometry cbse board term 1 with answer key.

Class 10 Case Study Based Questions Chapter 7 Coordinate Geometry CBSE Board Term 1 with Answer Key

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Class 10 Maths Case Study Questions Chapter 7 Coordinate Geometry

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Case study Questions in the Class 10 Mathematics Chapter 7 are very important to solve for your exam. Class 10 Maths Chapter 7 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Class 10 Maths Case Study Questions Chapter 7 Coordinate Geometry

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

Coordinate Geometry Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths Chapter 7 Coordinate Geometry

Case Study/Passage-Based Questions

Question 1:

Answer: (d) none of these

(ii) The distance of the bus stand from the house is

Answer: (b) 10 cm

(iii) If the grocery store and electrician’s shop lie on a line, the ratio of the distance of the house from the grocery store to that from the electrician’s shop, is

Answer: (c) 1.2

(iv) The ratio of distances of the house from the bus stand to food cart is

Answer: (c) 1.1

(v) The coordinates of positions of bus stand, grocery store, food cart, and electrician’s shop form a

Question 2:

The class X student’s school in krishnagar has been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

1. Taking A as origin, find the coordinates of P

Answer: a) (4,6)

2. What will be the coordinates of R, if C is the origin?

Answer: c) (10,3)

3. What will be the coordinates of Q, if C is the origin?

b) b) (-6,13)

Answer: d) (13,6)

4. Calculate the area of the triangles if A is the origin

Answer: a) 4.5

5. Calculate the area of the triangles if C is the origin

Answer: d) 4.5

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 7 Coordinate Geometry with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Coordinate Geometry 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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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

$cbse class 10 coordinate geometry case study questions$

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

$cbse class 10 coordinate geometry case study questions$

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

How to Solve Case-Based Questions?

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

What are Class 10 competency-based questions?

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

Case Study Questions in Maths Question Paper

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

Case Studies on CBSE’s Official Website

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

10 Maths Case Studies in myCBSEguide App

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

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CBSE Case Study Questions for Class 10 Maths Coordinate Geometry Free PDF

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

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

CBSE Case Study Questions for Class 10 Maths Coordinate Geometry PDF

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

Chapter 5: Arithmetic Progressions Case Study Questions
Chapter 6: Triangles Case Study Questions
Chapter 8: Introduction to Trigonometry Case Study Questions
Chapter 9: Some Applications of Trigonometry 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 10 Maths Chapter 7 Case Based Questions - Coordinate Geometry

Study case - 1.

The class X students of a school in Rajinder Nagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Mango are planted on the boundary at the distance of 1 m from each other.

Class 10 Maths Chapter 7 Case Based Questions - Coordinate Geometry

Based on the above figure, answer the following questions:

Q4: What will be the coordinates of the vertices of ΔPQR if C is the origin? (a) (14, 3), (11, 2), (8, 6) (b) (15, 4), (12, 3), (9, 7) (c) (14, 2), (11, 1), (8, 5) (d) (15, 3), (12, 2), (9, 6) Ans: (d) Explanation: When C is taken as origin, we will take CB as X-axis and CD as Y-axis. Then, coordinates of points, P, Q and R are (15, 3), (12, 2)and (9, 6) respectively.

Q5: What are the coordinates of P if D is taken as the origin? (a) (−15, 5) (b) (15, 5) (c) (15, 7) (d) (15, 3) Ans: (a) Explanation: When D is taken as origin, we will take DA as negative X-axis and DC as positive Y-axis. Then coordinates of point P is (−15, 5).

Case Study - 2

Based on the above information, give the answer of the following questions:

Study Case - 3

Based on the above information give the answer of the following questions:

Q1: The coordinates of the point A are: (a) (4,9) (b) (5,9) (c) (92,9) (d) (4,8) Ans: (c) Explanation: As the distance of point A is 9/2 units from the Y-axis and 9 units from the X-axis, its coordinates are x = 9/2, y = 9 or (9/2, 9)

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Chapter 7 Class 10 Coordinate Geometry

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Get NCERT Solutions of all Exercise Questions and Examples of Chapter 7 Class 10 Coordinate Geometry. All questions have been solved in an easy to understand way with detailed explanation of each and every step.

Answers to optional exercise is also given

In Coordinate Geometry of Class 9, we learned what is x and y coordinate of a point.

In this chapter, we will learn

Coordinates of points in x-axis (x, 0) and y-axis (0, y)
How to find distance between two points using Distance Formula
Checking if points form a triangle, or an isoceles triangle, or a square, rectangle. (To do this, we need to learn properties of parallelogram )
Checking if 3 points are collinear using Distance Formula
Finding points equidistant to given points
Then, we will learn about Section Formula - Finding coordinates of a point that divides line joining two points in some ratio
Finding coordinates of mid-point of a line using Section Formula
Finding ratio when coordinates of point of intersection is given
Using properties of parallelogram to do some questions on Section Formula (like finding coordinates of a point, when 4 vertices of parallelogram are given)
Finding Area of triangle when coordinates of all 3 vertices are given
Proving 3 points collinear using Area of Triangle Formula
Finding Area of Quadrialteral using Area of Triangle Formula (dividing Quadrilateral into 2 triangles and finding area)

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CBSE Class 10 Maths Important Questions on Chapter 7 - Coordinate Geometry

Class 10 Important Question
Chapter 7: Coordinate Geometry

CBSE Class 10 Maths Important Questions Chapter 7 - Coordinate Geometry - Free PDF Download

Vedantu has provided the important questions for CBSE Class 10 Maths Chapter 7 - Coordinate Geometry in a manner that students will find easy to understand and study. Our expert teachers have spent dutiful hours in making these questions as close to the ones in the actual paper as possible. Students will most likely find these questions common in their question paper since we follow the CBSE guidelines strictly in this regard. This chapter introduces students to coordinate geometry in mathematics. Mathematics is known to be a tough subject and this article is supposed to help students to figure out how to study the important topics in the chapter by going over the important questions that are provided in Vedantu. This article shows students how to prepare for any upcoming examinations by helping them practise the sums that are relevant and have a higher chance of coming into the exam. Mathematics is a complex subject to study on your own and to help students can use important questions of coordinate geometry class 10 provided to ace their examinations. Class 10 boards are very important for students and to help prepare and do well they can do the questions as a part of their revision.

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Chapter 7 Maths Class 10 Important Questions- Free PDF Download

Students looking to find important questions for coordinate geometry can find it here in this article at the Vedantu website which is free and easily available for the student. The website allows for easy access to its important questions and also it is easily downloadable. Students will find these notes to be helpful during the preparation of their examinations, these important questions are easily downloadable in a pdf format. Students who find it difficult to study on the screen can also print this material so they don't waste too much time on the internet. These questions can come for more marks than what is anticipated and so students need to be thorough with their preparation. Class 10 board examination is an important one for students and students need to know how to prepare well for it so they can do well because the marks they score in 10th will carry on for life long. So students need to prepare early and have continuous revisions and to help them with that they can use this article which will help guide them through this chapter on coordinate geometry.

Important Topics Covered under CBSE Class 10 Maths Chapter 7 - Coordinate Geometry

Coordinate geometry draws the linkage between geometry and algebra using various graphs and lines. Some of the concepts covered in this chapter are as follows

History of Coordinate Geometry

Coordinate geometry was first introduced by a French mathematician known as Rene Descartes; he was the first person to find a method to describe the location of points. Later in his research, he concluded that different curves and lines could be found using equations using coordinate geometry. He was the first person to draw the link between geometry and algebra. His work was considered extremely useful and to honour his work the coordinates of a point are called cartesian coordinates and the coordinate plane is known as the cartesian coordinate plane.

Coordinates

Coordinates are simply the various points on the plane. Using the x-axis and y-axis we can find out the exact location of the point. Because we are using a grid system it is much easier to locate anything because we just need to identify which cell( the intersection of rows and columns) the point falls.

Coordinate Plane

In coordinate geometry, there is a coordinate plane where different points are placed. There are usually two different scales- one with right angles to it is known as the y axis and the one running across from the plane is known as the x-axis. The point of origin is where both the x and y-axis meet and are known as the point of origin, this is usually at point 0.

Co coordinate geometry is quite simple, it uses pairs of numbers to give the location of a point on a plane.

Advantages of Coordinate Geometry

When we know the coordinates of certain points we can do the following- Determine the distance between them

We can find the equation, slope, and midpoint of any line segment.

We can find whether the lines are perpendicular or parallel.

Using the points we can find the perimeter and areas of any polygon.

By Reflecting, moving, and rotating we can transform any shape.

Define various eclipses, curves, and circles.

Find out the distances between different points, lines, and shapes.

Class 10 Maths Chapter 7 Important Questions

This chapter introduces students to coordinate geometry and students can study from this subject the very basics and get to a more intermediate level. The following are the important questions that students must look at when preparing for their examinations-

There are two routes to use to travel from destination A to destination B. First Bus reaches via point C and the second bus reaches from A to B Directly. If Coordinates of A, B, and C are (-2,-3),(2,3), and (3,2) respectively then which bus do you want to travel from A to B? which value is depicted in the question.

On a sports day celebration, Shyam and Ram are standing at positions A and B and their coordinates are (2,-2) and (4,8). The teachers ask Pooja to fix the flag at the midpoint of the line joining points A and B. Find the coordinates of the midpoint? Which type of value would you infer from the question?

To raise awareness of the hazard of smoking and the harm it does to the body, a school decided to start a “ no smoking” campaign. 10 students are asked to prepare campaign flags in the shape of a triangle. If the costs of 1cm2 of each banner are 2 rupees then find the overall cost incurred in the campaign. Which value is depicted in the question?

Find the area of a rhombus if its vertices are (3,0), (4,5),(-1,4) and (-2,-1) taken in the area.

Find the centroid of a triangle whose vertices are(4,-8), (-9,7), and (8, 13).

Prove that in a right-angled triangle the midpoint of the hypotenuse is in equal distance from all its vertices

Prove that the diagonals of a rectangle bisect each other are all equal.

The length of a line segment is 10. If one endpoint (2,-3) and the abscissa of the second endpoint is 10 shows that the ordinate is 3 or -9.

Using section formulas show that points (-1,2),(5,0) and (2,1) are collinear.

Find the relation between x and y such that point (x,y) is equidistant from the points (7,1) and (3,5).

Some Practice Questions on CBSE Class 10 Maths Chapter 7 - Coordinate Geometry

(2a, a – 7) is the centre of a given circle. If the circle is passing through the point (11, –9) and it has a diameter of 10√2 units, then determine the value of a.

Are the points (1, 7), (4, 2), (–1, –1), and (– 4, 4) the vertices of a square? Explain why.

Determine a point on the x-axis that is equidistant from (2, –5) and (–2, 9).

Determine the ratio in which the line segment joining the points (8, –9) and (2, 1) is divided into by the line 2x + 3y – 5 = 0. Also, determine the coordinates of this point of division.

If the vertices of a rhombus are (3, 0), (4, 5), (– 1, 4), and (– 2, – 1), when taken in order, then determine its area. [ Hint : Area of a rhombus = 1/2 (product of its diagonals)]

The distances of P(x, y) from A(5, 1) and B(-1, 5) are equal. Prove that 3x = 2y.

What ratio is the line segment joining the points P(2, -2) and Q(3, 7) divided by the point (24/11, y)? Also, determine the value of y.

The points A (1, –2), B (2, 3) C (a, 2) and D (– 4, –3) form a parallelogram. Determine the value of a and the height of this parallelogram, by considering AB to be the base.

The vertices of a triangle are (1, -1), (-4, 6), and (-3, -5). Determine its area.

The points A(x, y), B(-4, 6), and C(-2, 3) are collinear. Find a relation between x and y.

Benefits of Class 10 Maths Chapter 7 Important Questions

Mathematics can be quite a difficult subject to understand by yourself. So by using the right guide material like the ones found in Vedantu students can utilise it to their maximum and score the best marks possible. A lot of this subject is a theory so students need to just understand the various concepts and don't have to mug up anything like science subjects.

Students can use this text to use their time wisely, it helps boost their confidence after consistent practice and students can plan their preparation accordingly.

Students can utilise and practise the important questions so that they can ace their examinations.

It provides students with a structure with which they will study for his or her upcoming examinations.

This is a fundamental subject for high school kids and plays an important role in higher studies.

Students don’t need to worry about the relevance of these questions as they're all cross-checked and updated consistently with the newest CBSE guidelines and rules. Therefore, the information in Vedantu is genuine and reliable.

Students studying this chapter on coordinate geometry will find that it helps in higher studies and helps them understand the basics in any design engineering field.

Conclusion

Mathematics is known to be a difficult subject. Coordinates are simply the various points on a plane. Using the x-axis and y-axis we can find out the exact location of the point. students will learn how to use various coordinate plans and different ways to locate points, lines, curves, and shapes. Students can use this article to use their time wisely, it helps boost their confidence after consistent practice and students can plan their preparation accordingly. Students can work more diligently towards their goals and strive for higher marks as well. These important questions make sure that students are aware of the various topics in the subject and learn to master all the concepts. This chapter teaches students to coordinate geometry in mathematics the questions provided in this article helps students understand the subject better.

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FAQs on CBSE Class 10 Maths Important Questions on Chapter 7 - Coordinate Geometry

1. What does Class 10 Maths Chapter 7 depict?

Class 10 Maths Chapter 7 depicts Coordinate Geometry which is the branch of Mathematics. It helps us to exactly locate a given point with the help of an ordered pair of numbers.

Coordinate geometry is also well known as Cartesian Geometry. It helps in finding the distance between two points whose coordinates are given. The coordinates of the point can also be found by this theory, which divides the line segment joining two points in the given ratio. Through this, you can also learn how to find the area of a triangle with reference to the coordinate of its vertices.

2. What is Coordinate Geometry?

Coordinate Geometry is considered to be one of the most interesting chapters of Mathematics. Coordinate Geometry (or the analytic geometry) depicts the link between Geometry and Algebra through graphs that involve curves and lines.

Coordinate geometry is named as the study of graphs. Graphs are the visual representations of the data that derives from every aspect of our lives. There are various types of graphs like bar graphs, histograms, line graphs, etc.

3. Why should I opt for Important Questions for Class 10 Maths Chapter 7?

As the name suggests, Important Questions for Class 10 Maths Chapter 7 is the compilation of all the important questions from the specified chapter. These questions are truly important for all the students who are preparing for the board exam and eager to score the best possible marks in the exam. This questionnaire is created on the basis of previous years question papers, textbook exercises, chapter-wise weightage etc.

4. Can I download the solutions of these Important Questions for Class 10 Maths Chapter 7?

Yes, you can download the solutions of these Important Questions for Class 10 Maths Chapter 7 titled Coordinate Geometry from Vedantu website (vedantu.com). These solutions are created by our in-house experts hence you will not have to doubt its accuracy. You can also download the Vedantu app from Google play store to access these important questions along with the readymade so.

5. Is it enough to practice using Vedantu’s important Questions for Chapter 7 of Class 10 Maths?

Chapter 7 of Class 10 Maths requires extensive practice. The most significant course material in this regard is your NCERT textbook and its Solutions. After that, you can practice using Vedantu's Important Question for Chapter 7 of Class 10 Maths. These questions provide you with a ton of practice and are crucial for your board examinations. Another important thing is to practice using sample papers and previous years’ questions. All these together form the most crucial sources of your CBSE exam preparation.

6. Is Class 10 Mathematics Chapter 7 Coordinate Geometry easy?

Coordinate geometry is an important chapter for CBSE board examinations. It is a pretty straightforward chapter in which you can score perfect marks if you understand the concepts well. Questions of a total of 6 marks may be asked from this chapter.

Coordinate Geometry does require lots of practice and Vedantu's Important Questions for Chapter 7 of Class 10 Maths is the ideal place for this. Get tons of practice on a variety of questions thanks to Vedantu .

7. How many questions can I find on Vedantu’s Important Questions for Chapter 7 of Class 10 Maths?

Vedantu's Important Questions for Chapter 7 ‘Coordinate Geometry’ of Class 10 Maths contains 94 questions ranging from 1 to 4 marks along with many value-based questions.

Practising these many questions is bound to perfect your understanding of the chapter and in turn, provide much-needed practise for the CBSE Board examinations. As soon as you finish your NCERT textbook questions you must practice these questions regularly. Frequent practice at regular intervals will help you master all the Class 10 Mathematics chapters.

8. What are some important questions from Coordinate Geometry?

Few Important Questions from Chapter 7 ‘Coordinate Geometry’ of Class 10 Maths are as follows:

If, Q (0,1) is equidistant from P (5, -3) and R (x, 6), find the values of x. also, find the distances QR and PR. (4 Marks)

Find the centre of a circle passing through the points (6, -6), (3, -7), and (3, 3). (3 Marks)

Find the relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5)

9. What are the important topics of Chapter 7 ‘Coordinate Geometry’ of Class 10 Maths ?

Important topics covered in Coordinate Geometry are as follows:

a. Distance Formula

b. Section Formula

c. Special Case of the midpoint of a line segment joining two points

d. Area of a Triangle

To practice important questions from this chapter, visit Vedantu's Important Questions for Chapter 7 ‘Coordinate Geometry’ of Class 10 Maths . These are handpicked from the NCERT textbook, sample papers, and previous years’ question papers. Hence these are the apt test practice tool for Class 10 Mathematics CBSE Board exams. The study material provided by Vedantu is available to download from its website (vedantu.com) absolutely free of cost.

CBSE Class 10 Maths Important Questions

Cbse study materials.

Important Questions for Class 10 Maths Chapter 7 Coordinate Geometry

Chapter 7 coordinate geometry important questions for cbse class 10 maths board exams.

Important Questions for Chapter 7 Coordinate Geometry Class 10 Maths

Coordinate geometry class 10 maths important questions very short answer (1 mark).

Since it is equidistant from the points A(-2, 0) and B(6, 0) then

⇒ AP 2 = BP 2

Using distance formula we have,

[x-(2)] 2 + (0-0) 2 = (x+6) 2 + (0-0) 2

⇒ (x+2) 2 = (x+6) 2

⇒ x 2 + 4x + x = x 2 + 12x + 36

⇒ 8x = -32

⇒ x = -4

Hence, required point P is (-4, 0).

3. Find the distance of a point P(x,y) from the origin.

Distance between origin (0, 0) and point P(x,y) is

When the points are collinear, x 1 (y 2 – y 3 ) + x 2 (y 3 – y 1 ) + x 3 (y 1 – y 2 ) = 0 ⇒ x(-4 – (-5)) + (-3)(-5 – 2) + 7(2 – (-4)) = 0 ⇒ x(1) + 21 + 42 = 0 ⇒ x + 63 = 0 ∴ x = -63

7. For what value of k will k + 9, 2k – 1 and 2k + 7 are the consecutive terms of an A.P.?

As we know, a 2 – a 1 = a 3 – a 2 2k – 1 – (k + 9) = 2k + 7 – (2k – 1) ⇒ 2k – 1 – k – 9 = 2k + 7 – 2k + 1 ⇒ k – 10 = 8 ∴ k = 8 + 10 = 18

8. ABCD is a rectangle whose three vertices are B(4, 0), C(4, 3) and D(0, 3). Calculate the length of one of its diagonals.

AB = 4 units BC = 3 units AC 2 = AB 2 + BC 2 …(Pythagoras’ theorem) = (4) 2 + (3) 2 = 16 + 9 = 25 ∴ AC = 5 cm

Coordinate Geometry Class 10 Maths Important Questions Short Answer-I (2 Marks)

Let the point P be (2y, y). Since PQ = PR, we have

Squaring both sides,

(2y-2) 2 + (y+5) 2 = (2y+3) 2 + (y-6) 2

⇒ -8y + 4 + 10y + 25 = 12y + 9 -12y + 36

⇒ 2y + 29 = 45

⇒ y = 8

Hence, the coordinates of point P are (16,8).

When points are collinear, ∴ Area of ∆ABC = 0 = (x 1 (y 2 – y 3 ) + x 2 (y 3 – y 1 ) + x 3 (y 1 – y 2 )) = 0 = x (7 – 5) – 5 (5 – y) -4 (y – 7) = 0 = 2x – 25 + 5y – 4y + 28 = 0 ∴ 2x + y + 3 = 0 is the required relation.

13. Find a relation between x and y such that the point P(x, y) is equidistant from the points A (2, 5) and B (-3, 7).

Let P (x, y) be equidistant from the points A (2, 5) and B (-3, 7). ∴ AP = BP …(Given) AP 2 = BP 2 …(Squaring both sides) (x – 2) 2 + (y – 5) 2 = (x + 3) 2 + (y – 7) 2 ⇒ x 2 – 4x + 4 + y 2 – 10y + 25 ⇒ x 2 + 6x + 9 + y 2 – 14y + 49 ⇒ -4x – 10y – 6x + 14y = 9 +49 – 4 – 25 ⇒ -10x + 4y = 29 ∴ 10x + 29 = 4y is the required relation.

14. The points A(4,7), B(p,3) and C (7,3) are the vertices of a right triangle, right-angled at B. Find the value of p.

As per question, triangle is shown below. Here ABC is a right angle triangle,

AB 2 + BC 2 = AC 2

(p-4) 2 + (3-7) 2 + (7-p) 2 + (3-3) 2 = (7-4) 2 + (3-4) 2

⇒ (p-4) 2 + (-4) 2 + (7-p) 2 + 0 = 3 2 + (-4) 2

⇒ p 2 - 8p + 16 + 16 + 49 + p 2 - 14p = 9 + 16

⇒ 2p 2 - 22p + 81 = 25

⇒ 2p 2 - 22p + 56 = 0

⇒ p 2 - 11p + 28 = 0

⇒ (p-4) (p-7) = 0

⇒ p = 7 or 4

15. If A(4,3), B(-1,y) and C(3,4) are the vertices of a right triangle , ABC right angled at A, then find the value of y.

As per question, triangle is shown below.

AB 2 + AC 2 = BC 2

(4+1) 2 + (3-y) 2 + (4-3) 2 = (3+1) 2 + (4-y) 2

⇒ 5 2 + (3-y) 2 + (-1) 2 + 1 2 = 4 2 + (4-y) 2

⇒ 25 + 9 - 6y + y 2 + 1 + 1 = 16 + 16 - 8y + y 2

⇒ 36 + 2y - 32 = 0

⇒ 2y + 4 = 0

⇒ y = -2

16. Show that the points (a,a), (-a, -a) and (-√3a, √3a) are the vertices of an equilateral triangle.

Let A(a,a), B(-a, -a) and C(√3a, √3a)

Since AB = BC = AC, therefore ABC is an equilateral triangle.

17. If A(4, 3), B(-1, y) and C(3, 4) are the vertices of a right triangle ABC, right-angled at A, then find the value of y.

We have A(4, 3), B(-1, y) and C(3, 4). In right angled triangle ABC, (BC) 2 = (AB) 2 + (AC) …(Pythagoras theorem) ⇒ (-1 – 3) 2 + (y – 4) 2 = (4 + 1) 2 + (3 – y) 2 + (4 – 3) 2 + (3 – 4) 2 …(using distance formula) ⇒ (-4) 2 + (y 2 – 8y + 16) ⇒ (5) 2 + (9 – 6y + y 2 ) + (1) 2 + (-1) 2 ⇒ y 2 – 8y + 32 = y 2 – 6y + 36 = 0 ⇒ -8y + 6y + 32 – 36 ⇒ -2y – 4 = 0 ⇒ -2y = 4 ∴ y = -2

18. If the mid-point of the line segment joining A(x/2, y+1/2) and B(x+1, y-3) is C(5, -2), find x,y.

If the mid-point of the line segment joining A(x/2, y+1/2) and B(x+1, y-3) is C(5, -2) then at mid point,

⇒ y + 1 + 2y - 6 = -8

⇒ y = -1

19. Show that A(6,4) B(5,-2) and C(7,-2) are the vertices of an isosceles triangle.

We have A(6,4) B(5,-2) and C(7,-2).

Since two sides of a triangle are equal in length, triangle is an isosceles triangle.

20. If the line segment joining the points A(2,1) and B(5,-8) is trisected at the points P and Q, find the coordinates P.

As per question, line diagram is shown below.

Let P(x, y) divides AB in the ratio 1:2.

Using section formula we get,

Hence, coordinates of P are (3,-2).

21. Three vertices of a parallelogram taken in order are (-1, 0), (3, 1) and (2, 2) respectively. Find the coordinates of fourth vertex. (2011D)

Let A(-1, 0), B(3, 1), C(2, 2) and D(x, y) be the vertices of a parallelogram ABCD taken in order. Since, the diagonals of a parallelogram bisect each other. ∴ Coordinates of the mid-point of AC = Coordinates of the mid-point of BD

Hence, coordinates of the fourth vertex, D(-2, 1).

22. If two adjacent vertices of a parallelogram are (3,2) and (-1,0) and the diagonals intersect at (2,-5) then find the co-ordinates of the other two vertices.

Let two other co-ordinates be (x,y) and (x',y') respectively using mid-point formula.

As per question parallelogram is shown below.

Hence, coordinates of C(1,-12) and D(5,-10).

23. If A(5, 2), B(2, -2) and C(-2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t. (2015D)

ABC is a right angled triangle, ∴ AC 2 = BC 2 + AB 2 …(i) …(Pythagoras theorem) Using distance formula, AB 2 = (5 – 2) 2 + (2 + 2) = 25 BC 2 = (2 + 2) 2 + (t + 2) 2 = 16 + (t + 2) 2 AC 2 = (5 + 2) 2 + (2 – t) 2 = 49 + (2 – t) 2 Putting values of AB 2 , AC 2 and BC 2 in equation (i), we get 49 + (2 – t) 2 = 16 + (t + 2) 2 + 25 ∴ 49 + (2 – t) 2 = 41 + (t + 2) 2 ⇒ (t + 2) 2 – (2 – t) 2 = 8 ⇒ (t 2 + 4 + 4t – 4 – t 2 + 4t) = 8 8t = 8 ⇒ t = 1

24. If P(2,-1), Q(3,4), R(-2,3) and S(-3,-2) be four points in a plane, show that PQRS is a rhombus but not a square.

P(2,-1), Q(3,4), R(-2,3) and S(-3,-2)

Since, all the four sides are equal, PQRS is a rhombus.

Since, PQR is not a right triangle, PQRS is a rhombus but not a square.

Coordinate Geometry Class 10 Maths Important Questions Short Answer-II (3 Marks)

25. Find the ratio in which the segment joining the points (1,-3) and (4,5) is divided by x-axis? Also find the coordinates of this point on x-axis.

Let the required ratio be k:1 and the point on x-axis be (x,0).

(x 1 , y 1 ) = (1, -3)

and (x 2 , y 2 ) = (4,5)

Using section formula y coordinate we obtain,

Hence, the required ratio is 3/5 i.e. 3:5.

Now, again using section formula for x, we obtain

Coordinate of P is (117/8, 0).

26. If the point C(-1, 2) divides internally the line segment joining A(2,5) and B(x, y) in the ratio 3 : 4 find the coordinates of B.

From the given information we have drawn the figure as below.

3y + 20 = 14

⇒ 3y = 14 - 20 = -6

Hence, the coordinates of B(x, y) is (-5,-2).

27. If the co-ordinates of points A and B are (-2, -2) and (2, -4) respectively, find the co-ordinates of P such that AP = 3/7 AB, where P lies on the line segment AB.

AP = 3/7 AB

⇒ AP:PB = 3:4

PQ = 10 …(Given) ⇒ PQ 2 = 10 2 = 100 …(Squaring both sides) (9 – x) 2 + (10 – 4) 2 = 100 …(using distance formula) ⇒ (9 – x) 2 + 36 = 100 ⇒ (9 – x) 2 = 100 – 36 = 64 ⇒ (9 – x) = ± 8 …(Taking square-root on both sides) ⇒ 9 – x = 8 or 9 – x = -8 ⇒ 9 – 8 = x or 9+ 8 = x ⇒ x = 1 or x = 17

29. Find the value of y for which the distance between the points A (3,-1) and B (11, y) is 10 units.

AB = 10 units …(Given) ⇒ AB 2 = 10 2 = 100 …(Squaring both sides) (11 – 3) 2 + (y + 1) 2 = 100 ⇒ 8 2 + (y + 1) 2 = 100 ⇒ (y + 1) 2 = 100 – 64 = 36 ⇒ y + 1 = ±6 …(Taking square-root on both sides) ⇒ y = -1 ± 6 ∴ y = -7 or 5

30. The co-ordinates of the vertices of △ABC are A(7, 2), B(9, 10) and C(1, 4). If E and F are the mid-points of AB and AC respectively, prove that EF = 1/2 BC.

Let the mid-points of AB and AC be E(x 1 , y 1 ) and F(x 2 , y 2 ). As per question, triangle is shown below.

32. Find the point on y-axis which is equidistant from the points (5, -2) and (-3, 2).

Let the point be (0,y).

5 2 + (y+2) 2 = 3 2 + (y-2) 2

or, y 2 + 25 + 4y + 4 = 9 - 4y + 4

8y = -16 or, y = -2

or, Point (0, -2)

33. The vertices of △ABC are A(6, -2), B(0, -6) and C(4,8). Find the co-ordinates of mid-points of AB, BC and AC.

Let mid-point of AB, BC and AC be D(x 1 , y 1 ), E(x 2 , y 2 ) and F(x 3 , y 3 ). As per question, triangle is shown below.

Using section formula, the co-ordinates of the points D, E, F are:

The co-ordinates of the mid-points of AB, BC and AC are D(3, -4), E(2,1) and F(5,3) respectively.

PA = QA …(Given) ⇒ PA 2 = QA 2 …(Squaring both sides) (3 – 6) 2 + (y – 5) 2 = (3 – 0) 2 + (y + 3) 2 ⇒ 9 + (y – 5) 2 = 9 + (y + 3) 2 ⇒ (y – 5) 2 = (y + 3) 2 ⇒ y – 5 = ±(y + 3) …(Taking square root of both sides) ⇒ y – 5 = y + 3 y – 5 = -y – 3 0 = 8 …(not possible) ∴ y = 1

35. If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b), prove that bx = ay.

PA = PB …(Given) PA 2 = PB 2 …(Squaring both sides) ⇒ [(a+b) – x] 2 + [(b-a) – y) 2 = [(a–b) – x] 2 + [(a+b) – y] 2 ⇒ (a+b) 2 + x 2 – 2(a+b)x + (b–a) 2 + y 2 – 2(b–a)y = (a–b) 2 + x 2 – 2(a–b)x + (a+b) 2 + y 2 – 2(a+b)y …[∵ (a–b) 2 = (b–a) 2 ] ⇒ -2(a + b)x + 2(a – b)x = -2(a + b)y + 2(b – a)y ⇒ 2x(-a – b + a – b) = 2y(-a – b + b – a) ⇒ -2bx = –2ay ⇒ bx = ay

36. If the point P(k – 1, 2) is equidistant from the points A(3, k) and B(k, 5), find the values of k.

PA = PB …(Given) PA 2 = PB 2 …(Squaring both sides) ⇒ (k – 1 – 3) 2 + (2 – k) 2 = (k – 1 – k) 2 + (2 – 5) 2 ⇒ (k – 4) 2 + (2 – k) 2 = (-1) 2 + (-3) 2 ⇒ k 2 – 8k + 16 + 4 + k 2 – 4k = 1 + 9 ⇒ 2k 2 – 12k + 20 – 10 = 0 ⇒ 2k 2 – 12k + 10 = 0 …(Dividing by 2) ⇒ k 2 – 6k + 5 = 0 ⇒ k 2 – 5k – k + 5 = 0 ⇒ k(k – 5) – 1(k – 5) = 0 ⇒ (k – 5) (k – 1) = 0 ⇒ k – 5 = 0 or k – 1 = 0 ∴ k = 5 or k = 1

37. Find the area of the rhombus of vertices (3,0), (4,5), (-1,4) and (-2,-1) taken in order.

A(3,0), B(4,5), C(-1,4) and D(-2,-1)

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Chapter 7: Coordinate Geometry

Important Questions Class 10 Maths Chapter 7 Coordinate Geometry

Important Questions Class 10 Maths Chapter 7 Coordinate Geometry are given at BYJU’S with stepwise solutions. Students who are preparing for the board exams of 2022-23 are advised to practice these important questions of Coordinate Geometry to score high marks in the Maths exam. These questions will provide good practice to students to solve any problem asked in the exam from this chapter. Solving these questions will also help in revision, and it will boost the confidence level of students.

This chapter has some important formulas to help students with their board exam preparation and competitive exams. Some of the important questions from the distance formula, section formula, and the triangle area are provided here. Students can also get the solutions for all the questions of the Class 10 NCERT textbook for Maths.

Coordinate Geometry Formulas
Coordinate Geometry For Class 10
Coordinate System

Important Questions & Answers For Class 10 Maths Chapter 7 Coordinate Geometry

Q. 1: Find the distance of the point P (2, 3) from the x-axis.

We know that,

(x, y) = (2, 3) is a point on the Cartesian plane in the first quadrant.

x = Perpendicular distance from y-axis

y = Perpendicular distance from x-axis

Therefore, the perpendicular distance from x-axis = y coordinate = 3

Q. 2: Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).

Let P(x, y) be equidistant from the points A(7, 1) and B(3, 5).

Then, AP = BP

AP 2 = BP 2

Using distance formula,

(x – 7) 2 + (y – 1) 2 = (x – 3) 2 + (y – 5) 2

x 2 – 14x + 49 + y 2 – 2y + 1 = x 2 – 6x + 9 + y 2 – 10y + 25

Hence, the relation between x and y is x – y = 2.

Q. 3: Find the coordinates of the points of trisection (i.e., points dividing into three equal parts) of the line segment joining the points A(2, – 2) and B(– 7, 4).

Let P and Q be the points of trisection of AB, i.e., AP = PQ = QB.

Therefore, P divides AB internally in the ratio 1: 2.

Let (x 1 , y 1 ) = (2, -2)

(x 2 , y 2 ) = (-7, 4)

m 1 : m 2 = 1 : 2

Therefore, the coordinates of P, by applying the section formula,

= (-3/3, 0/3)

Similarly, Q also divides AB internally in the ratio 2 : 1. and the coordinates of Q by applying the section formula,

= (-12/3, 6/3)

Hence, the coordinates of the points of trisection of the line segment joining A and B are (–1, 0) and (– 4, 2).

Q. 4: Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).

Let the ratio in which the line segment joining ( -3, 10) and (6, -8) is divided by point ( -1, 6) be k:1.

Therefore by section formula,

-1 = ( 6k-3)/(k+1)

–k – 1 = 6k -3

Hence, the required ratio is 2 : 7.

Q. 5: Find the value of k if the points A(2, 3), B(4, k) and C(6, –3) are collinear.

A(2, 3)= (x 1 , y 1 )

B(4, k) = (x 2 , y 2 )

C(6, -3) = (x 3 , y 3 )

If the given points are collinear, the area of the triangle formed by them will be 0.

½ [x 1 (y 2 – y 3 ) + x 2 (y 3 – y 1 ) + x 3 (y 1 – y 2 )] = 0

½ [2(k + 3) + 4(-3 -3) + 6(3 – k)] = 0

½ [2k + 6 – 24 + 18 – 6k] = 0

½ (-4k) = 0

Q. 6: Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

Let the vertices of the triangle be A(0, -1), B(2, 1) and C(0, 3).

Let D, E, F be the mid-points of the sides of this triangle.

Using the mid-point formula, coordinates of D, E, and F are:

D = [(0+2)/2, (-1+1)/2] = (1, 0)

E = [(0+0)/2, (-1+3)/2] = (0, 1)

F = [(0+2)/2, (3+1)/2] = (1, 2)

class 10 maths chapter 7 important questions

Area of triangle DEF = ½ {(1(2 – 1) + 1(1 – 0) + 0(0 – 2)}

= ½ (1 + 1)

Area of triangle DEF = 1 sq.unit

Area of triangle ABC = ½ {0(1 – 3) + 2(3 – (-1)) + 0(-1 – 1)}

Area of triangle ABC = 4 sq.units

Hence, the ratio of the area of triangle DEF and ABC = 1 : 4.

Q. 7: Name the type of triangle formed by the points A (–5, 6), B (–4, –2) and C (7, 5).

The points are A (–5, 6), B (–4, –2) and C (7, 5).

d = √ ((x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 )

AB = √((-4+5)² + (-2-6)²)

BC=√((7+4)² + (5+2)²)

=√(121 + 49)

AC=√((7+5)² + (5-6)²)

Since all sides are of different lengths, ABC is a scalene triangle.

Q.8: Find the area of triangle PQR formed by the points P(-5, 7), Q(-4, -5) and R(4, 5).

P(-5, 7), Q(-4, -5) and R(4, 5)

Let P(-5, 7) = (x 1 , y 1 )

Q(-4, -5) = (x 2 , y 2 )

R(4, 5) = (x 3 , y 3 )

Area of the triangle PQR = (½)|x 1 (y 2 – y 3 ) + x 2 (y 3 – y 1 ) + x 3 (y 1 – y 2 )|

= (½) |-5(-5 – 5) + (-4)(5 – 7) + 4(7 + 5)|

= (½) |-5(-10) -4(-2) + 4(12)|

= (½) |50 + 8 + 48|

= (½) × 106

Therefore, the area of triangle PQR is 53 sq. units.

Q.9: If the point C(-1, 2) divides internally the line segment joining A(2, 5) and B(x, y) in the ratio 3 : 4, find the coordinates of B.

C(-1, 2) divides internally the line segment joining A(2, 5) and B(x, y) in the ratio 3 : 4.

A(2, 5) = (x 1 , y 1 )

B(x, y) = (x 2 , y 2 )

m : n = 3 : 4

Using section formula,

C(-1, 2) = [(mx 2 + nx 1 )/(m + n), (my 2 + ny 1 )/(m + n)]

= [(3x + 8)/(3 + 4), (3y + 20)/(3 + 7)]

By equating the corresponding coordinates,

(3x + 8)/7 = -1

3x + 8 = -7

3x = -7 – 8

(3y + 20)/7 = 2

3y + 20 = 14

3y = 14 – 20

Therefore, the coordinates of B(x, y) = (-5, -2).

Q.10: Find the ratio in which the line x – 3y = 0 divides the line segment joining the points (-2, -5) and (6, 3). Find the coordinates of the point of intersection.

Let the given points be:

A(-2, -5) = (x 1 , y 1 )

B(6, 3) = (x 2 , y 2 )

The line x – 3y = 0 divides the line segment joining the points A and B in the ratio k : 1.

Point of division P(x, y) = [(kx 2 + x 1 )/(k + 1), (ky 2 + y 1 )/(k + 1)]

x = (6k – 2)/(k + 1) and y = (3k – 5)/(k + 1)

Here, the point of division lies on the line x – 3y = 0.

[(6k – 2)/(k + 1)] – 3[(3k – 5)/(k + 1)] = 0

6k – 2 – 3(3k – 5) = 0

6k – 2 – 9k + 15 = 0

-3k + 13 = 0

Thus, the ratio in which the line x – 3y = 0 divides the line segment AB is 13 : 3.

Therefore, x = [6(13/3) – 2]/ [(13/3) + 1]

= (78 – 6)/(13 + 3)

y = [3(13/3) – 5]/ [(13/3) + 1]

= (39 – 15)/(13 + 3)

Therefore, the coordinates of the point of intersection = (9/2, 3/2).

Q.11: Write the coordinates of a point on the x-axis which is equidistant from points A(-2, 0) and B(6, 0).

Let P(x, 0) be a point on the x-axis.

Given that point, P is equidistant from points A(-2, 0) and B(6, 0).

Squaring on both sides,

(AP)² = (BP)²

(x + 2)² + (0 – 0)² = (x – 6)² + (0 – 0)²

x² + 4x + 4 = x² – 12x + 36

4x + 12x = 36 – 4

Therefore, the coordinates of a point on the x-axis = (2, 0).

Q.12: If A(-2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence, find the lengths of its sides.

Given vertices of a parallelogram ABCD are:

A(-2, 1), B(a, 0), C(4, b) and D(1, 2)

We know that the diagonals of a parallelogram bisect each other.

So, midpoint of AC = midpoint of BD

[(-2 + 4)/2, (1 + b)/2] = [(a + 1)/2, (0 + 2)/2]

2/2 = (a + 1)/2 and (1 + b)/2 = 2/2

a + 1 = 2 and b + 1 = 2

a = 1 and b = 1

Therefore, a = 1 and b = 1.

Let us find the lengths of sides of a parallelogram, i.e. AB, BC, CD and DA

Using the distance formula,

AB = √[(1 + 2)² + (0 – 1)²] = √(9 + 1) = √10 units

BC = √[(4 – 1)² + (1 – 0)²] = √(9 + 1) = √10 units

And CD = √10 and DA = √10 {the opposite sides of a parallelogram are parallel and equal}

Hence, the length of each side of the parallelogram ABCD = √10 units.

Q.13: If A(-5, 7), B(-4, -5), C(-1, -6) and D(4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

Given vertices of a quadrilateral are:

A(-5, 7), B(-4, -5), C(-1, -6) and D(4, 5)

The quadrilateral ABCD can be divided into two triangles ABD and BCD.

Area of the triangle with vertices (x 1 , y 1 ), (x 2 , y 2 ), and (x 3 , y 3 ) = (½) |x 1 (y 2 – y 3 ) + x 2 (y 3 – y 1 ) + x 3 (y 1 – y 2 )|

Area of triangle ABD = (½) |-5(-5 – 5) + (-4)(5 – 7) + 4(7 + 5)|

Area of triangle BCD = (½) |-4(-6 – 5) + (-1)(5 + 5) + 4(-5 + 6)|

= (½) |-4(-11) -1(10) + 4(1)|

= (½) |44 – 10 + 4|

Therefore, the area of quadrilateral ABCD = Area of triangle ABD + Area of triangle BCD

= 72 sq.units

Q.14: Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3). Hence, find m.

Let P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3) in the ratio k : 1.

P(4, m) = (x, y)

A(2, 3) = (x 1 , y 1 )

B(6, -3) = (x 2 , y 2 )

p(x, y) = [(kx 2 + x 1 )/(k + 1), (ky 2 + y 1 )/(k + 1)]

(4, m) = [(6k + 2)/(k + 1), (-3k + 3)/(k + 1)]

By equating the x-coodinate,

(6k + 2)/(k + 1) = 4

6k + 2 = 4k + 4

6k – 4k = 4 – 2

Thus, the point P divides the line segment joining A and B in the ratio 1 : 1.

Now by equating the y-coodinate,

(-3k + 3)/(k + 1) = m

Substituting k = 1,

[-3(1) + 3]/(1 + 1) = m

m = (3 – 3)/2

Q.15: Find the distance of a point P(x, y) from the origin.

Coordinates of origin = O(0, 0)

Let P(x, y) = (x 1 , y 1 )

O(0, 0) = (x 2 , y 2 )

OP = √[(x 2 – x 1 )² + (y 2 – y 1 )²]

= √[(x – 0)² + (y – 0)²]

= √(x² + y²)

Hence, the distance of the point P(x, y) from the origin is √(x² + y²) units.

Practice Questions For Class 10 Maths Chapter 7 Coordinate Geometry

The centre of a circle is (2a, a – 7). Find the values of a, if the circle passes through the point (11, –9) and has a diameter 10√ 2 units.
Find the ratio in which the line 2x + 3y – 5 = 0 divides the line segment joining the points (8, –9) and (2, 1). Also, find the coordinates of the point of division.
Show that the points (1, 7), (4, 2), (–1, –1) and (– 4, 4) are the vertices of a square.
Find the point on the x-axis, which is equidistant from (2, –5) and (–2, 9).
Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken in order. [ Hint : Area of a rhombus = 1/2 (product of its diagonals)]
If the points A (1, –2), B (2, 3) C (a, 2) and D (– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as the base.
Find a relation between x and y if the points A(x, y), B(-4, 6) and C(-2, 3) are collinear.
Find the area of a triangle whose vertices are given as (1, -1), (-4, 6) and (-3, -5).
If the distances of P(x, y) from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y.
In what ratio does the point (24/11, y) divide the line segment joining the points P(2, -2) and Q(3, 7)? Also, find the value of y.

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CBSE Class 10 Maths Case Study Questions PDF

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

CBSE Class 10 Mathematics Exam 2024 will have a set of questions based on case studies in the form of MCQs. The CBSE Class 10 Mathematics Question Bank on Case Studies, provided in this article, can be very helpful to understand the new format of questions. Share this link with your friends.

Table of Contents

Chapterwise Case Study Questions for Class 10 Mathematics

Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

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

Class 10th Science Case Study Questions
Assertion and Reason Questions of Class 10th Science
Assertion and Reason Questions of Class 10th Social Science

Class 10 Maths Syllabus 2024

Chapter-1 real numbers.

Starting with an introduction to real numbers, properties of real numbers, Euclid’s division lemma, fundamentals of arithmetic, Euclid’s division algorithm, revisiting irrational numbers, revisiting rational numbers and their decimal expansions followed by a bunch of problems for a thorough and better understanding.

Chapter-2 Polynomials

This chapter is quite important and marks securing topics in the syllabus. As this chapter is repeated almost every year, students find this a very easy and simple subject to understand. Topics like the geometrical meaning of the zeroes of a polynomial, the relationship between zeroes and coefficients of a polynomial, division algorithm for polynomials followed with exercises and solved examples for thorough understanding.

Chapter-3 Pair of Linear Equations in Two Variables

This chapter is very intriguing and the topics covered here are explained very clearly and perfectly using examples and exercises for each topic. Starting with the introduction, pair of linear equations in two variables, graphical method of solution of a pair of linear equations, algebraic methods of solving a pair of linear equations, substitution method, elimination method, cross-multiplication method, equations reducible to a pair of linear equations in two variables, etc are a few topics that are discussed in this chapter.

Chapter-4 Quadratic Equations

The Quadratic Equations chapter is a very important and high priority subject in terms of examination, and securing as well as the problems are very simple and easy. Problems like finding the value of X from a given equation, comparing and solving two equations to find X, Y values, proving the given equation is quadratic or not by knowing the highest power, from the given statement deriving the required quadratic equation, etc are few topics covered in this chapter and also an ample set of problems are provided for better practice purposes.

Chapter-5 Arithmetic Progressions

This chapter is another interesting and simpler topic where the problems here are mostly based on a single formula and the rest are derivations of the original one. Beginning with a basic brief introduction, definitions of arithmetic progressions, nth term of an AP, the sum of first n terms of an AP are a few important and priority topics covered under this chapter. Apart from that, there are many problems and exercises followed with each topic for good understanding.

Chapter-6 Triangles

This chapter Triangle is an interesting and easy chapter and students often like this very much and a securing unit as well. Here beginning with the introduction to triangles followed by other topics like similar figures, the similarity of triangles, criteria for similarity of triangles, areas of similar triangles, Pythagoras theorem, along with a page summary for revision purposes are discussed in this chapter with examples and exercises for practice purposes.

Chapter-7 Coordinate Geometry

Here starting with a general introduction, distance formula, section formula, area of the triangle are a few topics covered in this chapter followed with examples and exercises for better and thorough practice purposes.

Chapter-8 Introduction to Trigonometry

As trigonometry is a very important and vast subject, this topic is divided into two parts where one chapter is Introduction to Trigonometry and another part is Applications of Trigonometry. This Introduction to Trigonometry chapter is started with a general introduction, trigonometric ratios, trigonometric ratios of some specific angles, trigonometric ratios of complementary angles, trigonometric identities, etc are a few important topics covered in this chapter.

Chapter-9 Applications of Trigonometry

This chapter is the continuation of the previous chapter, where the various modeled applications are discussed here with examples and exercises for better understanding. Topics like heights and distances are covered here and at the end, a summary is provided with all the important and frequently used formulas used in this chapter for solving the problems.

Chapter-10 Circle

Beginning with the introduction to circles, tangent to a circle, several tangents from a point on a circle are some of the important topics covered in this chapter. This chapter being practical, there are an ample number of problems and solved examples for better understanding and practice purposes.

Chapter-11 Constructions

This chapter has more practical problems than theory-based definitions. Beginning with a general introduction to constructions, tools used, etc, the topics like division of a line segment, construction of tangents to a circle, and followed with few solved examples that help in solving the exercises provided after each topic.

Chapter-12 Areas related to Circles

This chapter problem is exclusively formula based wherein topics like perimeter and area of a circle- A Review, areas of sector and segment of a circle, areas of combinations of plane figures, and a page summary is provided just as a revision of the topics and formulas covered in the entire chapter and also there are many exercises and solved examples for practice purposes.

Chapter-13 Surface Areas and Volumes

Starting with the introduction, the surface area of a combination of solids, the volume of a combination of solids, conversion of solid from one shape to another, frustum of a cone, etc are to name a few topics explained in detail provided with a set of examples for a better comprehension of the concepts.

Chapter-14 Statistics

In this chapter starting with an introduction, topics like mean of grouped data, mode of grouped data, a median of grouped, graphical representation of cumulative frequency distribution are explained in detail with exercises for practice purposes. This chapter being a simple and easy subject, securing the marks is not difficult for students.

Chapter-15 Probability

Probability is another simple and important chapter in examination point of view and as seeking knowledge purposes as well. Beginning with an introduction to probability, an important topic called A theoretical approach is explained here. Since this chapter is one of the smallest in the syllabus and problems are also quite easy, students often like this chapter

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CBSE Class 10 Maths Case Study

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

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

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

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

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

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

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

CBSE Class 10th Case study Questions

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

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

CBSE Class 10th Assertion Reasoning Questions

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

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

CBSE Class 10 Maths Case Based MCQ

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

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

Class 10th Mathematics Multiple Choice Questions

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

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

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

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

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

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CBSE Class 11 Syllabus

CBSE Class 11th Maths Syllabus 2024-25: Download PDF for Board Exam

Cbse class 11 maths syllabus 2024-25: download the cbse class 11 maths syllabus for the 2024-25 academic session here. check out the recent syllabus to know the course structure and question paper design along with practical details prescribed by cbse for class 11 maths..

CBSE Class 11 Maths Syllabus 2024-25: The Central Board of Secondary Education (CBSE) has released the class 11 Maths syllabus on its official website. The article provides an overview of Class 11 Maths syllabus. The syllabus is designed in such a way that it can help students.The CBSE Class 11 Maths syllabus and complete curriculum can be checked and downloaded here.

In addition to outlining the course structure and project requirements, the article also covers the question paper pattern and additional details. Furthermore, a link to download the complete syllabus is provided at the conclusion of the article. For more details about class 11 Maths syllabus read the full article till end.

CBSE Class 11 Maths Syllabus 2024-25: Objectives

To acquire knowledge and critical understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles, symbols and mastery of underlying processes and skills.
To feel the flow of reasons while proving a result or solving a problem.
To apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method.
To develop a positive attitude to think, analyze and articulate logically.
To develop interest in the subject by participating in related competitions.
To acquaint students with different aspects of Mathematics used in daily life.
To develop an interest in students to study Mathematics as a discipline.
To develop awareness of the need for national integration, protection of the environment, observance of small family norms, removal of social barriers, elimination of gender biases.
To develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics.

Chapter wise-weightage:

Cbse class 11 maths 2024-25 course structure , unit-i: sets and functions, 1. sets , 2. relations & functions ordered pairs. , 3. trigonometric functions , unit-ii: algebra, 1. complex numbers and quadratic equations, 2. linear inequalities, 3. permutations and combinations, 4. binomial theorem, 5. sequence and series, unit-iii: coordinate geometry, 1. straight lines, 2. conic sections, 3. introduction to three-dimensional geometry, unit-iv: calculus, 1. limits and derivatives, unit-v statistics and probability, 1. statistics, 2. probability, cbse class 11 maths 2024-25 question paper design .

No chapter wise weightage. Care to be taken to cover all the chapters
Suitable internal variations may be made for generating various templates keeping the overall weightage to different form of questions and typology of questions same.

There will be no overall choice in the question paper.

Prescribed Books:

Mathematics Textbook for Class XI, NCERT Publications
Mathematics Exemplar Problem for Class XI, Published by NCERT
Mathematics Lab Manual class XI, published by NCERT

CBSE Class 11 Maths Syllabus 2024-25

Get a PDF download of the latest CBSE Class 11 Maths curriculum here. The key pointers of this article is syllabus weightage, course overview and practical evaluation scheme . Students can access the direct link to the PDF to download and check the latest update regarding the CBSE Class 11 Maths syllabus.

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School Guide
Class 12 Syllabus
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Maths Notes Class 12
Physics Notes Class 12
Chemistry Notes Class 12
Biology Notes Class 12
NCERT Solutions Class 12 Maths
RD Sharma Solutions Class 12
NCERT Solutions Class 8 Geography Chapter 5 Human Resources
NCERT Solutions for Class 10 Geography Social Science Chapter 1 : Resource and Development
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry
NCERT Solutions for Class 10 Science Chapter-13 Our Environment
NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry
NCERT Solutions for Class 12 Biology Chapter 7 Human Health and Disease
NCERT Solutions For Class 10 Geography Chapter 4 Agriculture
NCERT Solutions for Class 10 Geography Chapter 6 : Manufacturing Industries
NCERT Solutions For Class 10 Geography Chapter 3 : Water Resources
NCERT Solutions For Class 9 Geography Social Science Chapter 4: Climate
NCERT Solutions For Class 10 Geography Chapter 5 : Minerals and Energy Resources
NCERT Geography Class-9 Chapter-Wise Solutions
NCERT Solutions Class 8 Geography Chapter 1 Resources
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula
NCERT Solutions For Class 10 Economics Social Science Chapter 1 : Development
NCERT Solutions for Class 9 Geography Social Science Chapter 3: Drainage
CBSE Notes Class 10 Geography Chapter 1- Resources and Development
NCERT Solutions for Class 12 Chapter 2 Human Reproduction
Class 12 Geography Notes Chapter 6 Hill Area Development Programme

NCERT Solutions For Class-12 Geography Chapter-3 Human Development

NCERT Solutions For Class Class 12 Geography Chapter 3 Human Development- This article includes free NCERT Solutions For Class Class 12 Geography Chapter 3 Human Development to help students of Class 12 learn the solutions and ace their exams.

It has been developed by the subject matter experts at GFG, according to the latest CBSE Syllabus 2023-24 , and guidelines to help the students of Class 12 create a solid conceptual base for Class 12 Geography Chapter 3 Human Development.

NCERT Solutions for Class 12 Geography Chapter-3 Human Development

The solutions for Chapter 3, Human Development, are provided below, and students can refer to NCERT Solutions for Class 12 for other subjects as well.

Exercise Pages No. 20

1. choose the right answer from the four alternatives given below., (i) which one of the following best describes development.

(a) an increase in size (c) a positive change in quality

(b) a constant in size (d) a simple change in the quality

(c) a positive change in quality

(ii) Which one of the following scholars introduced the concept of Human Development?

(a) Prof. Amartya Sen (c) Dr Mahabub-ul-Haq

(b) Ellen C. Semple (d) Ratzel

(c) Dr Mahabub-ul-Haq

2. Answer the following questions in about 30 words.

(i) what are the three basic areas of human development.

The three basic areas of human development are education, health, and income, collectively referred to as the Human Development Index (HDI), which measures overall well-being and standard of living. Education: Access to quality education and literacy rates are essential for personal development, social mobility, and economic prosperity. Health: Access to healthcare services, sanitation, nutrition, and disease prevention measures are vital for ensuring physical well-being and longevity. Income: Economic opportunities, employment prospects, and income levels are crucial factors influencing living standards and overall quality of life.

(ii) Name the four main components of human development?

The four main components of human development are education, health, income, and gender equality, collectively shaping individuals’ capabilities, opportunities, and overall well-being in society. Education: Access to quality education and lifelong learning opportunities. Health: Availability of healthcare services, disease prevention, and well-being. Income: Economic opportunities, employment, and income levels. Gender Equality: Equal rights, opportunities, and empowerment for all genders.

(iii) How are countries classified on the basis of human development index?

Countries are classified into four categories based on their Human Development Index (HDI) scores: very high, high, medium, and low human development, providing a comparative measure of overall well-being and living standards . Very High Human Development: Countries with HDI scores in the top percentile, indicating high levels of education, health, and income. High Human Development: Countries with HDI scores above the global average, reflecting significant progress in human development indicators. Medium Human Development: Countries with HDI scores below those of high human development but above the global average, indicating moderate levels of development. Low Human Development: Countries with HDI scores significantly below the global average, reflecting limited progress in education, health, and income indicators.

3. Answer the following questions in not more than 150 words.

(i) what do you understand by the term human development.

Human development refers to the process of expanding individuals’ capabilities and opportunities to lead lives they value, including various dimensions such as education, health, income, and social well-being. It goes beyond economic growth to focus on improving people’s quality of life, ensuring they have the means to reach their full potential and participate actively in society. Human development considers factors like access to education, healthcare, employment, and social services, as well as promoting gender equality, human rights, and environmental sustainability. Human development measures include indices like the Human Development Index (HDI), which provide comparative assessments of countries’ progress in enhancing human well-being. It emphasizes holistic approaches to development that prioritize the well-being and dignity of individuals, aiming to create inclusive, equitable, and sustainable societies where all people can thrive and contribute to collective progress. Some challenges to human development include: Poor medical conditions, Poverty, Population growth, Malnutrition, Contagious diseases, Pollution, and Epidemics.

(ii) What do equity and sustainability refer to within the concept of human development?

Equity within the concept of human development refers to ensuring fairness and justice in the distribution of opportunities, resources, and outcomes among all individuals. It involves addressing inequalities based on factors such as gender, ethnicity, socio-economic status, and geographical location to ensure that everyone has equal access to education, healthcare, employment, and social services. Equity aims to create inclusive societies where everyone has the chance to reach their full potential and participate in decision-making processes. Sustainability, on the other hand, means meeting the needs of the present generation without compromising the ability of future generations to meet their own needs. It involves responsible stewardship of natural resources, environmental conservation, and minimizing negative impacts on ecosystems and biodiversity. Sustainable development seeks to balance economic, social, and environmental considerations to promote long-term well-being and ensure that development efforts are viable and beneficial in the long run.

Chapter-3 Human Development Summary

Chapter 3 of NCERT Class 12 Geography focuses on human development, emphasizing its multidimensional nature and the factors influencing it. It explores various aspects such as education, health, income, gender equality, and social inclusion, highlighting their interconnectedness and importance in fostering well-being and prosperity. The chapter discusses indices like the Human Development Index (HDI) as tools for measuring human development progress globally, providing insights into countries’ achievements and areas for improvement. It also addresses issues of equity and sustainability within the context of human development.

Important Topics Discussed in the Chapter Measuring Human Development What is the basic goal of Human Development? Who introduced the concept of Human Development? Human Development Index (HDI) Approaches to Human Development

FAQs on NCERT Solutions For Class-12 Geography Chapter-3 Human Development

What are the 4 pillars of human development.

The four pillars of human development are education, health, income, and gender equality, collectively shaping individuals’ capabilities and opportunities for well-being and prosperity.

What is the main idea of human development?

The main idea of human development is to ensure that all individuals have the opportunity to lead fulfilling lives and reach their full potential, fostering well-being and prosperity for everyone.

What is an example of a human development?

An example of human development is increasing access to quality education for marginalized communities, empowering individuals and enhancing their opportunities for socio-economic advancement.

What are the four types of human development?

The four types of human development include physical, cognitive, social, and emotional development, encompassing various aspects of individual growth and well-being.

What are the features of human development?

The features of human development include multidimensionality, interdependence, sustainability, equity, and participation, emphasizing holistic approaches to fostering well-being and prosperity for all individuals.

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JEE Advanced 2024: Boost your scores with these last-minute revision tips for high weightage chapters

High weightage chapters to revise in Physics

Mechanics: 31 marks (25%)
Electrodynamics: 28 marks (22.58%)
Modern Physics: 23 marks (18.55%)
Optics: 18 marks (14.52%)
Heat and Thermodynamics: 16 marks (12.9%)
Electromagnetic Induction: 21-22%
Thermodynamics: 14-15%
Optics and Fluid Mechanics :11-12% (each)

High weightage chapters to revise in Chemistry

P-Block- 11 marks
Amines- 11 marks
Mole Concept- 9 marks
Chemical Bonding, General Organic Chemistry and Chemical Kinetics - 8 marks (each)
Aldehydes, Ketones and Carboxylic Acids: 14-15%
Atomic Structure: 14-15%
Hydrocarbons: 13-14%
P-Block Elements: 13-14%
Organic Chemistry: 11-12%

High weightage chapters to revise in Maths

Differential & Integral Calculus- 38 marks
Coordinate Geometry- 18 marks
Matrices- 14 marks
Vector & 3D- 11marks
Application of Derivatives: 14-15%
Circles: 9-10%
Definite Integral, Matrices and Parabola: 11-12% (each)

JEE Main 2024: Generic tips to ace it

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Ye Zhang 1 ,
Yanni Chen 1 &
Don Hadwin 2

In this paper, we consider a class of generalized closed linear manifolds in a nonseparable Hilbert space H , which is closely related to the generalized Fredholm theory. We first investigate properties of the set ${\mathcal {B}}_{\vartriangleleft }=\{T\in {\mathcal {M}}:\overline{T(H)}\subset A(H)$ for some $A\in {\mathcal {B}}\},$ where ${\mathcal {B}}$ is a $C^*$ -subalgebra of a von Neumann algebra ${\mathcal {M}}$ . It is proved that a selfadjoint ${\mathcal {B}}_{\vartriangleleft }$ is always an ideal in ${\mathcal {M}}$ . In a type $\textrm{II}_\infty $ factor, we show that there exists a tracial weight (whose range containing infinite cardinals) such that two projections are equivalent if and only if they have the same tracial weight, which leads to a complete characterization of such selfadjoint ${\mathcal {B}}_{\vartriangleleft }$ when ${\mathcal {M}}$ is a factor. Then we introduce the concept of closed manifolds with respect to a pair of C *-algebras and study some properties. Finally, when m is an infinite cardinal, as a special important case we focus on m -closed subspaces and operators which preserve m -closed subspaces. It is proved that these operators are either of rank less than m , or the generalized left semi-Fredholm operators.

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Breuer, M.: Fredholm theories in von Neumann algebras I. J. Math. Anna. 4 , 243–254 (1968)

Article MathSciNet Google Scholar

Breuer, M.: Fredholm theories in von Neumann algebras II. J. Math. Anna. 4 , 313–325 (1969)

Campbell, S., Meyer, D.: Generalized Inverses of Linear Transformations. Pitman, London (1979)

Google Scholar

Christensen, O.: An Introduction to Frames and Riesz Bases. Springer, Birkhäuser (2016)

Conway, J.: A Course in Functional Analysis. Springer, New York (1996)

Conway, J.: A Course in Operator Theory. American Mathematical Society, Providence (2000)

Du, H.: On the operators with closed range. J. Shaanxi Normal Univ. 2 , 18–25 (1983)

Edgar, G., Ernest, J., Lee, G.: Weighing operator spectra. Indiana Univ. Math. J. 21 , 61–80 (1971)

Ernest, J.: Left invertiblility of closed operators modulo an $\alpha $ -compact operators. Tohoku Math. J. 30 , 529–537 (1972)

Hou, J., Cui, J.: Linear maps preserving essential spectral functions and closeness of operator ranges. Bull. Lond. Math. Soc. 4 , 575–582 (2007)

Hadwin, D.: Nonseparable approximate equivalence. Trans. Am. Math. Soc. 266 , 203–231 (1981)

Ivković, S.: On operators with closed range and semi-Fredholm operators over W*-algebras. Russ. J. Math. Phys. 27 , 48–60 (2020)

Ivković, S.: On Drazin invertible C*-operators and generalized C*-Weyl operators. Ann. Funct. Anal. 36 , 1–22 (2023)

MathSciNet Google Scholar

Ivković, S.: Semi-Fredholm theory in C*-algebras. Banach J. Math. Anal. 51 , 1–19 (2023)

Kadison, R., Ringrose, J.: Fundamentals of the theory of operator algebras, Vol. II (Advanced theory). Amer. Math. Soc. Providence (1997)

Olsen, C.: Index theory in von Neumann algebras. Mem. Am. Math. Soc. 47 , 1–71 (1984)

Taylor, A., Lay, D.: Introduction to Functional Analysis. Wiley, New York (1980)

Zhang, Y., Hadwin, D., Chen, Y.: The distance of operators of infinite multiplicity to the normals and nonseparable BDF theory (in Chinese). Sci. Sin. Math. 46 , 123–128 (2016)

Zhang, Y., Chen, Y., Hadwin, D.: Some topologies related to nonseparable Hilbert spaces and their applications. J. Math. Anal. Appl. 514 , 1–14 (2022)

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Acknowledgements

The authors would like to thank the referee for carefully reading the paper, and many valuable comments and suggestions.

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School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, 710119, Shaanxi, China

Ye Zhang & Yanni Chen

Department of Mathematics, University of New Hampshire, Durham, NH, 03824, USA

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Correspondence to Yanni Chen .

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Communicated by Woo-Young Lee.

This research was supported by the National Natural Science Foundation of China (Nos. 11601298 and 11971283), the Fundamental Research Funds for the Central Universities (No. GK201903008).

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Zhang, Y., Chen, Y. & Hadwin, D. A class of closed manifolds in nonseparable Hilbert spaces. Banach J. Math. Anal. 18 , 45 (2024). https://doi.org/10.1007/s43037-024-00352-y

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Published : 27 May 2024

DOI : https://doi.org/10.1007/s43037-024-00352-y

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CBSE Board has introduced the case study questions for the ongoing academic session 2021-22. The board will ask the paper on the basis of a different exam pattern which has been introduced this year where 50% syllabus is occupied for MCQ for Term 1 exam. Selfstudys has provided below the chapter-wise questions for CBSE Class 10 Maths.
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Class 10 Coordinate Geometry Important questions
Application of mid point formula
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a ...
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Chapter 3 of NCERT Class 12 Geography focuses on human development, emphasizing its multidimensional nature and the factors influencing it. It explores various aspects such as education, health, income, gender equality, and social inclusion, highlighting their interconnectedness and importance in fostering well-being and prosperity.
Root2x+Root3y=0 Root3x-Root8y=0
Root2x+Root3y=0 Root3x-Root8y=0 | Solve √2x +√3y = 0 √3x-√8y = 0 Solve using Substitution Method Question 1. Solve the following pair of linear equations by the substitution method. (v) √2 x + √3 y= 0; √3 x - √8 y= 0 About This Video: Here you learn NCERT solutions for Ch 3 Class 10 Maths from Linear Equations in Two Variables Class 10. To solve this problem we will use ...
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A class of closed manifolds in nonseparable Hilbert spaces
The notion of an operator having closed range plays an important role in operator theory, particularly, in the theory of Fredholm operators and generalized inverses, for example, see [3,4,5, 7, 10, 12, 13] and [].Moreover, in [], Ivkovi $\acute{c}$ gives examples of C*-Fredholm operators with non-closed range.Recall that in the classical case, a Hilbert space operator T is Fredholm if and ...

CBSE 10th Standard Maths Subject Coordinate Geometry Case Study Questions 2021

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