case study questions class 9 maths coordinate geometry pdf

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CBSE Class 9th Maths 2023 : 30 Most Important Case Study Questions with Answers; Download PDF

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CBSE Class 9 Maths exam 2022-23 will have a set of questions based on case studies in the form of MCQs. CBSE Class 9 Maths Question Bank on Case Studies given in this article can be very helpful in understanding the new format of questions.

Each question has five sub-questions, each followed by four options and one correct answer. Students can easily download these questions in PDF format and refer to them for exam preparation.

CBSE Class 9 All Students can also Download here Class 9 Other Study Materials in PDF Format.

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CBSE Class 9th Exam 2024-25 : Skill Subject Sample Papers and Marking Scheme Released; Download PDF

CBSE has released the 2024-25 Class 9th skill subject sample papers and marking schemes. These resources help students understand the exam pattern, improve time management, and boost confidence. Download the PDFs from the CBSE official website to enhance your preparation. Practice consistently with these sample papers to excel in your exams and gain practical knowledge in key skill subjects.

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CBSE Class 9 Mathematics Case Study Questions

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If you’re looking for a comprehensive and reliable study resource and case study questions for class 9 CBSE, myCBSEguide is the perfect door to enter. With over 10,000 study notes, solved sample papers and practice questions, it’s got everything you need to ace your exams. Plus, it’s updated regularly to keep you aligned with the latest CBSE syllabus . So why wait? Start your journey to success with myCBSEguide today!

Significance of Mathematics in Class 9

Mathematics is an important subject for students of all ages. It helps students to develop problem-solving and critical-thinking skills, and to think logically and creatively. In addition, mathematics is essential for understanding and using many other subjects, such as science, engineering, and finance.

CBSE Class 9 is an important year for students, as it is the foundation year for the Class 10 board exams. In Class 9, students learn many important concepts in mathematics that will help them to succeed in their board exams and in their future studies. Therefore, it is essential for students to understand and master the concepts taught in Class 9 Mathematics .

Case studies in Class 9 Mathematics

A case study in mathematics is a detailed analysis of a particular mathematical problem or situation. Case studies are often used to examine the relationship between theory and practice, and to explore the connections between different areas of mathematics. Often, a case study will focus on a single problem or situation and will use a variety of methods to examine it. These methods may include algebraic, geometric, and/or statistical analysis.

Example of Case study questions in Class 9 Mathematics

The Central Board of Secondary Education (CBSE) has included case study questions in the Class 9 Mathematics paper. This means that Class 9 Mathematics students will have to solve questions based on real-life scenarios. This is a departure from the usual theoretical questions that are asked in Class 9 Mathematics exams.

The following are some examples of case study questions from Class 9 Mathematics:

Class 9 Mathematics Case study question 1

There is a square park ABCD in the middle of Saket colony in Delhi. Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak,  Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point O in the direction of   XOY, X’OY, X’OY’ and XOY’ . Their balls stopped as shown in the above image.

Answer the following questions:

Answer Key:

Class 9 Mathematics Case study question 2

• Now he told Raju to draw another line CD as in the figure
• The teacher told Ajay to mark  ∠ AOD  as 2z
• Suraj was told to mark  ∠ AOC as 4y
• Clive Made and angle  ∠ COE = 60°
• Peter marked  ∠ BOE and  ∠ BOD as y and x respectively

Now answer the following questions:

• 2y + z = 90°
• 2y + z = 180°
• 4y + 2z = 120°
• (a) 2y + z = 90°

Class 9 Mathematics Case study question 3

• (a) 31.6 m²
• (c) 513.3 m³
• (b) 422.4 m²

Class 9 Mathematics Case study question 4

How to Answer Class 9 Mathematics Case study questions

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Students need to be careful while solving the Class 9 Mathematics case study questions. They should not make any assumptions and should always check their answers. If they are stuck on a question, they should take a break and come back to it later. With some practice, the Class 9 Mathematics students will be able to crack case study questions with ease.

Class 9 Mathematics Curriculum at Glance

At the secondary level, the curriculum focuses on improving students’ ability to use Mathematics to solve real-world problems and to study the subject as a separate discipline. Students are expected to learn how to solve issues using algebraic approaches and how to apply their understanding of simple trigonometry to height and distance problems. Experimenting with numbers and geometric forms, making hypotheses, and validating them with more observations are all part of Math learning at this level.

The suggested curriculum covers number systems, algebra, geometry, trigonometry, mensuration, statistics, graphing, and coordinate geometry, among other topics. Math should be taught through activities that include the use of concrete materials, models, patterns, charts, photographs, posters, and other visual aids.

CBSE Class 9 Mathematics (Code No. 041)

Class 9 Mathematics question paper design

The CBSE Class 9 mathematics question paper design is intended to measure students’ grasp of the subject’s fundamental ideas. The paper will put their problem-solving and analytical skills to the test. Class 9 mathematics students are advised to go through the question paper pattern thoroughly before they start preparing for their examinations. This will help them understand the paper better and enable them to score maximum marks. Refer to the given Class 9 Mathematics question paper design.

QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)

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Class 9 is an important milestone in a student’s life. It is the last year of high school and the last chance to score well in the CBSE board exams. myCBSEguide is the perfect platform for students to get started on their preparations for Class 9 Mathematics. myCBSEguide provides comprehensive study material for all subjects, including practice questions, sample papers, case study questions and mock tests. It also offers tips and tricks on how to score well in exams. myCBSEguide is the perfect door to enter for class 9 CBSE preparations.

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16 thoughts on “CBSE Class 9 Mathematics Case Study Questions”

This method is not easy for me

aarti and rashika are two classmates. due to exams approaching in some days both decided to study together. during revision hour both find difficulties and they solved each other’s problems. aarti explains simplification of 2+ ?2 by rationalising the denominator and rashika explains 4+ ?2 simplification of (v10-?5)(v10+ ?5) by using the identity (a – b)(a+b). based on above information, answer the following questions: 1) what is the rationalising factor of the denominator of 2+ ?2 a) 2-?2 b) 2?2 c) 2+ ?2 by rationalising the denominator of aarti got the answer d) a) 4+3?2 b) 3+?2 c) 3-?2 4+ ?2 2+ ?2 d) 2-?3 the identity applied to solve (?10-?5) (v10+ ?5) is a) (a+b)(a – b) = (a – b)² c) (a – b)(a+b) = a² – b² d) (a-b)(a+b)=2(a² + b²) ii) b) (a+b)(a – b) = (a + b

MATHS PAAGAL HAI

All questions was easy but search ? hard questions. These questions was not comparable with cbse. It was totally wastage of time.

Where is search ? bar

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Can I have more questions without downloading the app.

I love math

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I am Riddhi Shrivastava… These questions was very good.. That’s it.. ..

For challenging Mathematics Case Study Questions, seeking a writing elite service can significantly aid your research. These services provide expert guidance, ensuring your case study is well-researched, accurately analyzed, and professionally written. With their assistance, you can tackle complex mathematical problems with confidence, leading to high-quality academic work that meets rigorous standards.

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Important Questions for CBSE Class 9 Maths Chapter 3 - Coordinate Geometry

• Class 9 Important Question
• Chapter 3: Coordinate Geometry

Download Important Questions for Class 9 Maths Chapter 3 - Coordinate Geometry - Free PDF

Welcome to our comprehensive collection of Important Questions for CBSE Class 9 Maths Chapter 3 - Coordinate Geometry available in Vedantu. As students progress through their academic journey, mastering the concepts of Coordinate Geometry becomes essential. Our carefully curated list of questions aims to provide students with a thorough understanding of this chapter and boost their problem-solving skills. With a focus on CBSE guidelines and exam patterns, these questions cover various topics such as plotting points, finding distances, and calculating gradients on the coordinate plane. Whether you're looking to strengthen your knowledge or preparing for exams, our curated set of important questions is a valuable resource to excel in Coordinate Geometry. Get ready to explore the fascinating world of coordinates and elevate your mathematical prowess!

Download CBSE Class 9 Maths Important Questions 2024-25 PDF

Also, check CBSE Class 9 Maths Important Questions for other chapters:

Study Important Questions for Class - 9 Mathematics Chapter – 3 Coordinate Geometry

Section - A

1 On which axes do the given points lie?

ii. (0, -3)

iii. (0, 6)

iv. (-5, 0)

i. (7,0) X-axis since the y component is zero

ii. (0, -3) Y-axis since the x component is zero

iii. (0,6) Y-axis since the x component is zero

iv. (-5,0) X-axis since the y component is zero

2 In which quadrants do the given points lie?

ii. (-3, 7)

iii. (-1, -2)

iv. (3, 6) 

i. (4,-2) IV quadrant since the x component is positive and y component is negative

ii. (-3,7) II quadrant since the x component is negative and y component is positive

iii. (-1,-2) III quadrant since the x component is negative and y component is negative

iv. (3,6) I quadrant. since the x component is positive and y component is positive

3. Do P (3, 2) & Q(2, 3) represent the same point? 

Ans: P(3,2) and Q(2,3) do not represent the same point. The first one has the x component is 3 and y is two, while Q has the x component as 2 and y component is 3.

4. In which quadrant points P(3,0), Q(6,0) , R (-7.0), S (0,-6), lie?

Ans: These points do not lie in any quadrant. These points lie on the axes.

5. If a<0 and b<0, then the point P(a,b) lies in

a) quadrant IV

b) quadrant II

c) quadrant III

d) quadrant I

Ans: (c) quadrant III

6. The points (other than the origin) for which the abscissa is equal to the ordinate lie in

a) Quadrant I only

b) Quadrant I and II

c) Quadrant I & III

d) Quadrant II only.

Ans: (c) quadrant I & III. 

In III and I quadrants, the axes have the same sign.

7. The perpendicular distance of the point P(4,3) from the y axis is

c) 7 Units 

Ans: (a) 3 units

Distance from the Y axis is the x coordinate of the point.

8. The area of triangle OAB with 0(0,0), A(4,0) & B(0,6) is

a) 8 sq. unit

b) 12 sq. units

c) 16 sq. units

d) 24 sq. units

Ans: (b) 12 sq. units.

Area is half of the product of base and height of the triangle.

Section - B

9. Write down the coordinates of each of the points P, Q, R, S and T as shown in the following figure?

10. Draw the lines X'OX and YOY as the axes on the plane of a paper and plot the given points.

ii. B (-3, 2)

iii.  C(-5, -4)

iv. D(2,-6) 

Section - C

11. Find the mirror images of the following point using x-axis & y-axis as mirror.

ii.  B(2,-3)

iii. C(-2,3)

iv. D(-2,-3)

Ans:  

i. A’ (2,-3),

ii. B’ (2,3)

iii. C’ (-2,-3), 

iv. D’ (-2,3)

12. Draw the graph of the following equations

i. \[{\bf{y}} = {\bf{3x}} + {\bf{2}}\]

ii. \[{\bf{y}} = {\bf{x}}\]

13. Draw a triangle with vertices 0(0,0) A(3,0) B(3,4). Classify the triangle and also find its area.

Ans:   The points from a right angle triangle

The area of the triangle is half of the product of the base and height i.e. 6 square units.

14. Draw a quadrilateral with vertices A(2,2) B(2,-2) C(-2,-2), D(-2,2). Classify the quadrilateral and also find its area.

This quadrilateral is square of area =16 square units.

15. Find the coordinates of point which are equidistant from these two points P(3,0) and Q(-3,0). How many points are possible satisfying this condition?

Ans: All the point on the Y-axis satisfy this condition.

1 Mark Questions

1. The point of intersection of X and Y axes is called

(a) zero point

(c) null point

(d) none of these 

Ans: (b) origin

2. The distance of the point (-3, -2) from x-axis is

(a) 2 units

(b) 3 units

(c) 5 units

(d) 13 units 

Ans: (a) 2 units

Distance from the x axis is the magnitude/absolute value of the y coordinate of the point.

3. The distance of the point (-6, -2) from y-axis is

(a) 6 units

(b) 10 units

(c) 2 units

(d) 8 units 

Ans : (a) 6 units

Distance from the y axis is the magnitude/absolute value of the x coordinate of the point.

4. The abscissa and ordinate of the point with Co-ordinates (8, 12) is

(a) abscissa 12 and ordinate 8

(b) abscissa 8 and ordinate 12

(c) abscissa 0 and ordinate 20

(d) none of these

Ans: (a) abscissa 12 and ordinate 8

Abscissa is the y coordinate of the point and the ordinate is the x coordinate value.

5. The co-ordinate of origin in

(b) (0, y) 

(d) none of these.

Ans : (c) (0, 0)

For the origin, both abscissa and ordinate are 0.

6. The distance of the point (2,3) from y axis’s

(A) 2 units

(B) 3 units

(C) 5 units

(D) 13 units 

Ans: (A) 2 units

Distance from the x axis is the magnitude/absolute value of the y coordinate of the point. And the distance from the y axis is the magnitude/absolute value of the x coordinate of the point.

7. The point (-2, -1) lies in

(A) 1st quadrant

(B) 2nd quadrant

(C) 3rd quadrant

(D) 4th quadrant

Ans: (C) 3rd quadrant

3 rd quadrant corresponds to both negative x and y values.

8. The point (3,0) lies on

(A) +ve x axis

(B) – ve x axis

(C) + ve y axis

(D) –ve y axis 

Ans: (A) +ve x axis

Since the y coordinate is zero and x-coordinate is positive.

9. The distance of the point (3, 5) from x- axis is

(a) 3 units

(b) 4 units

(d) 6 units  

Ans: (c) 5 units

10. The point (0, -5) lies on

(a) +ve x- axis

(b) +ve y- axis

(c) –ve x- axis

(d) –ve y-axis 

Ans: (d) –ve y-axis

Since the x-coordinate is zero and y is negative.

11. The point (-2, 5) lies in

(a) 1st quadrant

(b) 2nd quadrant

(c) 3rd quadrant

(d) 4th quadrant

Ans: (b) 2nd quadrant.

In the second quadrant, the x-values are negative and y are positive.

12. The distance of the point (3, 0) from x- axis is

(b) 0 units

(c) 9 units

Ans: (a) 3 units.

2 Marks Questions

1. Write the name of each part of the plane formed by Vertical and horizontal lines.

Ans: Vertical line is called y-axis, the horizontal line is called x-axis. And these form four quadrants.

2. Write the Co-ordinates of a point which lies on the x-axis and is at a distance of 4units to the right of origin. Draw its graph.

Ans: (4, 0)

3. Write the mirror image of the point (2, 3) and (-4, -6) with respect to x-axis.

Ans: The mirror image of point (2, 3) is (2, -3) with respect to x-axis.

The mirror image of (-4, -6) is (-4,6) with respect to the x-axis.

4. Write the Coordinates of a point which lies on the y-axis and is at a distance of 3 units above x-axis. Represent on the graph.

Ans: The Coordinates of the point which lies on y-axis and at a distance of 3units above x- axis is (0, 3).

5. Write abscissa and ordinate of point (-3, -4) 

Ans: Abscissa -3 ordinate -4

6. State the quadrant in which each of the following points lie: 

(ii) (-7,11)

(iii) (-6, -4) 

(iv) (-5, -5)

Ans: (2, 1) I Quadrant

(-7, 11) II Quadrant

(-6, -4) III Quadrant

(-5, -5) III Quadrant

7. Which of the following points belongs to 2nd quadrant

(ii) (-3,2)

(iii) (2,0)

(iv)  (-4,2)

Ans: The points (-3, 2), (-4, 2) belong to the 2nd quadrant.

8. What is the name of horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane?

Ans: The horizontal line is called x –axis and the name of vertical line is y – axis

9. Name the points of the plane which do not belong to any of the quadrants.

Ans: The points in a plane which do not belong to any one of the quadrants is origin which is denoted by O (0,0).

10. Which of the following points belong to the x- axis? 

(a) (2, 0) (b) (3, 3) (c) (0, 1) (d) (-2, 0)

Ans: (2, 0) and (-2, 0) belong to the x- axis.

To belong on the y axis the y-component should be zero.

11. Which of the following points belongs to 1st quadrant 

(a) (3, 0) (b) (1, 2) (c) (-3, 4) (d) (3, 4)

Ans: (1, 2) and (3, 4) belong to the 1st quadrant.

12. Which of the following points belongs to 3rd quadrant

(a) (1, 3) (b) (-1, -3) (c) (0, 4) (d) (-4, -2)

Ans: (-1, -3) and (-4, -2) belong to the 3rd quadrant.

3 Marks Questions

1. How will you describe the position of a table lamp on your study table to another person?

Consider the figure of a tabletop, on which a lamp (L)  is placed.

Consider the lamp on the table as a point and the table as a plane. 

Choose one of the corners as the Origin-O (0,0). Measure the distance of the lamp from the shorter edge and the longer edge. Let us assume that the distance of the lamp from the shorter edge is 3m and from the longer edge, its 2m.

Therefore, we can conclude that the position of the lamp on the table can be described in two ways depending on the order of the axes as (3,2).

2. Write the answer of each of the following questions:

(i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

Ans: The horizontal line that is drawn to determine the position of any point in the Cartesian plane is named the x-axis and the vertical line is called the y-axis.

(ii) What is the name of each part of the plane formed by these two lines?

Ans: The name of each part of the plane that is formed by x-axis and y-axis is called a quadrant.

(iii) Write the name of the point where these two lines intersect.

Ans: The point, where the x-axis and the y-axis intersect is called the origin denoted by O(0,0).

3. In which quadrant or on which axis do each of the points (– 2, 4),  (3, – 1),  (-1,0), (1,2) and (–3,–5) lie? Verify your answer by locating them on the Cartesian plane.

Ans: Tpoint (– 2, 4) lies in II quadrant;

the point (3, – 1) lies in IV quadrant;

the point (– 2, 4) lies in II quadrant; 

the point (3, – 1) lies in IV quadrant and  

the point (–1, 0) lies on the x-axis.

These can be verified from the figure below.

4. Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.

5. Locate the points (5, 0), (0, 5), (2, 5), (5, 2), (-3, 5), (-3, -5) and (6, 1) in the Cartesian plane.

6. Take a triangle ABC with A (3, 0), B (-2, 1), C (2, 1). Find its mirror image.

Ans: Mirror images of A (3, 0), B (-2, 1) and C (2, 1) about the x-axis are A’ (3, 0),  B’(-2,-1),  C’(2,-1) respectively. 

7. In fig. write the Co-ordinates of the points and if we join the points write the name of fig. formed. Also write Co-ordinate of intersection point of AC and BD. 

(i) The Co-ordinate of point A is (0, 2), B is (2, 0), C is (0, -2) and D is (-2,0).

(ii) It we joined them we get square.

(iii) Co-ordinate of intersection point of AC and BD is (0, 0).

8. In which quadrant or on which axis do each of the points (-2, 4), (2, -1), (-1, 0), (1, 2) and (-3, -5) lie? Verify your answer by locating them on the Cartesian plane.

(-2, 4) lies in II quadrant;

(2, -1) lies in IV quadrant;

(-1, 0) lies on –ve x-axis;

(1, 2) lies in I quadrant and

(-3, -5) lies in III quadrant.

This can be verified using the following graph: 

9. In fig of vertices find co-ordinates of triangle ABC

Ans: (A) (0, 0) (B) (2, 3) (c) (-2, 3)

10. Take a quadrilateral ABCD

(A) (-5, -4) (B) (-5, 2) (C) (-3, 3) and (D) (-3, 4) find its mirror image with respect to y- axis.

Ans: The mirror image of point.

(A) (-5, 4) (B) (-5, 2) (C) (-3, 3) and (D) (-3, 4) wrt y-axis are.

A’ (5, 4), B’ (5, 2), C’ (3, 3) and D’ (3, 4)

11. Locate the points (A) (-3, 4) (B) (3, 4) and (C) (0, 0) in a Cartesian plane write the name of figure which is formed by joining them.

The figure formed is a triangle.

12. Find Co-ordinates of vertices of rectangle ABCD

Ans: The co- ordinates of vertices of rectangle A (2, 2), B (-2, 2), C (-2, -2) and D (2, -2).

13. Take a rectangle ABCD with A (-6, 4), B (-6, 2), C (-2, 2) and D (-2, 4). Find its mirror image with respect to x- axis.

Ans: The mirror image of A (-6, 4) is A’ (-6, -4) and B (-6, 2) is B’ (-6, -2), C (-2, 2) is C’ (-2, -2) and D (-2, 4) is D’ (-2, -4)

14. The following table gives measures (in degrees) of two acute angles of a right triangle

Plot the point and join them.

15. Plot each of the following points in the Cartesian Plane 

(b) (-3, -4)

(c) (0, -5)

(d) (2, -5)

(e) (2, 0) 

4 Marks Questions

1. (Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.

All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East – West direction. Each cross street is referred to in the following manner: If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:

(i) how many cross - streets can be referred to as (4, 3).

(ii) how many cross - streets can be referred to as (3, 4).

Ans: We need to draw two perpendicular lines as the two main roads of the city that cross each other at the center and let us mark it as N-S and E-W.

Let us take the scale as 1 cm = 200m.

Following figure shows the perpendicular roads .

(i) From the figure it can be inferred that only one point have the coordinates as (4,3). Hence, it can  be concluded that only one cross - street can be referred to as (4, 3).

(ii) Only one point have the coordinates as (3,4). Therefore, it can be concluded that only one cross - street can be referred to as (3, 4).

2. See Fig.3.14, and write the following:  

(i) The coordinates of B. 

Ans: The coordinates of point B in the above figure is the distance of point B from x-axis and y- axis. Therefore, we can conclude that the coordinates of point B are (―5, 2).

(ii) The coordinates of C.

Ans: The coordinates of point C in the above figure is the distance of point C from x-axis and y- axis. Therefore, we can conclude that the coordinates of point C are (5, ―5).

(iii) The point identified by the coordinates (–3, –5).

Ans: The point E represents the coordinates (―3, ―5).

(iv) The point identified by the coordinates (2, – 4). 

Ans: The point G that represents the coordinates (2, ―4).

(v) The abscissa of the point D. 

Ans: The abscissa of point D in the given figure is the distance of point D from the y-axis which is 6.

(vi) The ordinate of the point H. 

Ans: The ordinate of point H in the above figure is the distance of point H from the x-axis which is ―3.

(vii) The coordinates of the point L. 

Ans: The coordinates of point L in the above figure is the distance of point L from x-axis and y-axis. Therefore, we can conclude that the coordinates of point L are (0, 5).

(viii) The coordinates of the point M.

Ans: The coordinates of point M in the above figure is the distance of point M from x-axis and y-axis. Therefore, we can conclude that the coordinates of point M are (―3, 0).

5 Marks Questions

1. See fig. and write the following

(i) The Co-ordinates of B

Ans: (-5,2) 

(ii) The Co-ordinates of C

Ans: (5, -5)

(iii) On which axis point L lies.

Ans: Y-axis

(iv) The abscissa of the point D  

Ans: As shown in the figure the abscissa of point D is 6.

(v) The Co-ordinates of point L

Ans: (0, 5)

(vi) On which axis point M lies. 

Ans: Point M lies on X-axis.

(vii) The ordinate of the point H

Ans: The ordinate of point H is -3

(viii) The Co-ordinates of the point M

Ans: (-3, 0)

(ix) The point identified by the Co-ordinate (2, -4)

Ans: G has the coordinate (2,-4)

(x) The point identified by the Co-ordinates (-3, -5)

Ans: E has the coordinate (-3,-5)

2. Find some ordered pairs of the linear equation \[{\bf{2x}} + {\bf{y}} = {\bf{4}}\] and plot them ‘how many such ordered pairs can be found and plotted?

Ans: The given equation is \[2x + y = 4\] The equation holds if

\[x = 0,\,y = 4\] i.e. (0, 4),

\[x = 1,\,y = 2\] i.e. (1, 2),

\[x = 2,\,y = 0\] i.e. (2, 0) ,

\[x = 3,\,y =  - 2\] i.e. (3, -2)…

Similarly (4,-4), (5,-6), (-1,6), (-2,8) etc. also. These are a few ordered pares which are valid solutions. And there are infinite such ordered pairs

3. The following table given the relation between natural numbers and odd natural numbers

Plot the points and join them. Do you get a straight line by joining these points?

Yes a straight line is obtained by joining these points.

Chapter 3 Maths Class 9 Important Questions - Free PDF Download

The Coordinate Geometry Class 9 Important Questions present reliable and accurate learning elements for students to understand the chapter efficiently. The students will receive the necessary understanding of the chapters to clear the difficult problems in class. Expert subject teachers of mathematics prepare these questions. Hence, solving these questions will help students obtain a better understanding of the type of questions asked in the examinations and how to format their answers correctly.

Vedantu presents a free PDF to download for Class 9 Chapter 3 Important Questions so that students can prepare well according to the CBSE syllabus. Students need to understand these guidelines and find solutions with a proper explanation. This free PDF online will surely help students understand their concepts and build a solid base on Coordinate Geometry.

Important Questions for Class 9 Maths Coordinate Geometry

Coordinate geometry is an intriguing subject where students get to learn about the object’s position in a plane, learn about the concepts and coordinates of the cartesian plane and so on. The topics covered in the chapter are : 

Introduction 

Cartesian System 

Plotting a Point 

Coordinate geometry.

Coordinate geometry deals with the locating points on a plane when the aligned numbers, called coordinates for a particular point, are given. It presents geometric aspects in Algebra and allows them to solve geometric problems.

Concepts of Coordinates

The intersection point of the x-axis and the y-axis is identified as the origin. Both x and y are 0 at this point.

The right-hand side of the x-axis values are positive, and the x-axis values on the left-hand side are negative.

Similarly, the values located above the origin on the y-axis, are positive, and the values are negative, which are located below the origin.

It is determined by a collection of two numbers, to locate a point on the plane. 

Cartesian System

A Cartesian coordinate system is a system in two dimensions that can be used to locate a  point with the help of two unique numbers called coordinates. The point along the x-axis is called the x-coordinate and the point along the y-axis is called the y-coordinate.

Two perpendicular directed lines are stipulated to define the coordinates, and the unit length is marked off on the two axes (fig 1). Cartesian coordinate systems are also used in higher space dimensions. 

By using the Cartesian coordinate system, geometric shapes are represented by algebraic equations. For example, radius 2 circle may be defined by the equation x² + y² = 4 (Figure 2).

Distance Between Two Points

Distance between two points of the plane

(x₁, y₁) and (x₂, y₂) is d = [(x₂ – x₁)² + (y₂ – y₁)]¹/²

In case of a three-dimensional system, the formula of the distance between the points 

(x₁, y₁, z₁) and (x₂, y₂, z₂) is d = [(x₂ – x₁)² + (y₂ – y₁)² + (z₂ – z₁)² ] 1/2

Vector Representation

The two-dimensions vector, from the origin to the point with the cartesian coordinates (x, y) can be written as r = xi + yj where i = (1,0) and j = (0,1) are vectors units in the direction of the x-axis and y-axis respectively.

In three-dimensions cases, we will have r = xi + yj + zk, where k = (0,0,1) is the vector unit in the direction of z-axis.

To plot or graph points, we can employ two perpendicular lines called the x-axis and the y-axes. The x-axis is horizontal, and the y axis is the vertical line. The part of the x-axis towards the right of origin is the positive x-axis, and the one towards the left of the origin is the negative x-axis. Similarly, the part of the y-axis above the origin is the positive y-axis, and the part of y-axis below the origin is the negative y-axis. In the coordinate plane, every point is designed by an assigned pair of x and y coordinates.

Let's Consider the Example

Using the Pencil, Plot the Point −4,3

The first coordinates inform about the right or left movement from the origin. The second coordinate tells about the up or down movement from the origin.

Since x coordinate is a −4, there is a movement towards the left 4 units from the origin. The coordinate of y is 3, which means movement two units vertically up to get to the point −4,3. 

List of Important Questions for Class 9 Maths Chapter 3

Chapter 3 Maths Class 9 Important Questions include different types of questions that cover all the sub-topics of the entire chapter. Important questions from each topic are covered in the PDF to provide students with a clear and logical understanding of the chapter. Some of the important questions that are frequently asked in the exam from this chapter are-

In which axis or quadrant do each of the points (–2, 4), (3, –1), (–1, 0),(1, 2) and (–3, –5) lie? Prove your answer by placing them on the Cartesian plane.

Plot the points (y, z) in the following table on the plane, picking proper units of distance on the axes where 

State the name of the point where two lines intersect.

Define the three-dimensional Cartesian coordinate system.

Locate the points in the Cartesian plane (0, 5), (5, 0), (2, 5), (–3, 5), (5, 2),(–3, –5), (5, –3) and (6, 1). 

State the name of vertical lines and the horizontal lines formed to determine the position of any point in the Cartesian plane? 

State the name of every part of the plane developed by two lines?

Describe the Cartesian plane.

Two rolling dice are rolled at the same time. Let the numbers on Dice1 and Dice 2 be denoted by y and z respectively. After each roll, the point S(y, z) is outlined in the plane. Plot all the probable positions of S, and highlight those positions for which the sum of y and z is 8.

In the Cartesian plane plot the five points for which ordinate and the abscissa are equal.

In the Cartesian plane plot the following points - A (1.3, 2.4), B ( - 2.7, 3.2), C ( - 1.1,  - 3.6) and D (4, - 2)

Practice Questions from Class 9 Chapter 3 Maths Coordinate Geometry

1. Find the distance of the point (-3, 4) from the x-axis. 

2. If the points A(x, 2), B(-3, 4) and C(7, -5) are collinear, then find the value of x.

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

4. Find the relation between x and y if the points A(x, y), B(-5, 7) and C(-4, 5) are collinear.

5. Find the ratio in which the y-axis divides the line segment joining the points A(5, -6) and B(-1, -4). Also, find the coordinates of the point of division.

6. Let P and Q be the points of trisection of the line segment joining the points A (2, -2) and B (-7, 4) such that P is nearer to A. Find the coordinates of P.

Benefits of Chapter 3 Maths Class 9 Important Questions

The Basic Concepts of Coordinate Geometry assists students in achieving a high grade by providing a thorough comprehension of the chapter's principles. Pupils that understand the ideas, theories, and calculations can achieve higher percentages on their exams. The following are some of the advantages of significant problems for class 9 mathematics coordinate geometry:

The Coordinate Geometry Class 9 Important Questions PDF is prepared according to the examination guidelines to help students score well in the examinations.

Expert Mathematics subject teachers prepare these questions.

The questions are prepared after a thorough analysis of the previous year's question papers combining the syllabus’s revisions.

The PDF also comprises solutions so that students can refer to them in case of any doubts.

Students can check information about the topics by following the reference books or by searching them on the Vedantu portal.

Practising questions from the PDF will develop the student’s understanding of the concepts and the examination pattern.

Key Features of Important Questions Class 9 Maths Chapter 3 - Coordinate Geometry

All the questions are written from an examination point of view.

Step-by-step solutions for questions with accurate explanations.

The solutions are clear and easy to understand.

Learning is quick as they are clearly written by subject experts to match the curriculum.

These important questions help in developing a good conceptual foundation for students.

These solutions are absolutely free and available in PDF format.

Conclusion 

Crucial Questions for Class 9 Mathematics Coordinate Geometry are essential and reputable sources of study material created for pupils in a well-structured and readily comprehensible style. It will assist pupils in properly comprehending the chapters. The pupils will get the understanding of the chapters required to solve the challenging issues in class. The crucial questions will assist students in covering all of the issues and scoring high marks.

FAQs on Important Questions for CBSE Class 9 Maths Chapter 3 - Coordinate Geometry

1. Which chapter is the most important in Class 9 Maths?

Chapter 3 of Class 9 Maths is about geometry which is the branch of Mathematics concerned with spatial connections among diverse things, individual object forms, and surrounding space characteristics. Class 9 is an important year for high school students since it is during this year that students lay the groundwork for all of the major topics and ideas covered in the Class 10 Board examinations. Students will learn how to identify points in a cartesian system or an XY plane in the chapter Coordinate Geometry. This notion is critical for determining the position of an object in a certain location.

2. How can I practise Chapter 3 of Class 9 Maths?

Geometry is the component of Mathematics that demands a comprehension of the topic as well as certain visualising abilities that students should work on to improve. Vedantu's Crucial Questions for Class 9 Mathematics Coordinate Geometry are valuable and trustworthy sources of study material supplied for students in a well-structured and easily understandable format. These vital questions are available for free on Vedantu (vedantu.com) and its mobile app. It will help pupils understand the chapters thoroughly. Students will get a grasp of the chapters needed to answer the difficult problems in class. The essential questions will help pupils cover all of the issues and achieve good grades.

3. What are case study questions in Class 9 Maths?

Case study questions in Class 9 Maths are the questions that introduce a particular scenario and its mathematical aspect and then proceeds to ask some questions that are relevant to the given chapter i.e. Coordinate Geometry in this case. Case study questions usually involve a real life-based situation where the questions check the students’ analytical ability to follow through and subsequently apply the Maths to it. They are extremely important as they carry a lot of marks and are really simple to get through.

4. How to plot a point?

To plot or graph points, we can use two perpendicular lines known as the x- and y-axes. The horizontal x-axis is parallel to the vertical y-axis. The positive x-axis is located to the right of the origin, while the negative x-axis is located to the left of the origin. Likewise, the positive y-axis is the part of the y-axis above the origin, and the negative y-axis is the part of the y-axis below the origin. Every point in the coordinate plane is defined by a given pair of x and y coordinates.

5. What is coordinate geometry?

Coordinate geometry is concerned with identifying points on a plane when the aligned values, known as coordinates for a certain point, are supplied. It introduces geometric concepts in Algebra and helps students to solve geometric problems. The origin is defined as the point at where the x-axis and y-axis connect. At this moment, both x and y are zero. To identify a point on the plane, a collection of two numbers is used.

CBSE Class 9 Maths Important Questions

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Class 9th Maths - Coordinate Geometry Case Study Questions and Answers 2022 - 2023

Class 9th Maths - Coordinate Geometry Case Study Questions and Answers 2022 - 2023 Study Materials Sep-08 , 2022

QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 9th Maths Subject - Coordinate Geometry, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

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Coordinate geometry case study questions with answer key.

Final Semester - June 2015

(b) What are the coordinates of C and D respectively?

(c) What is the distance between B and D?

(d) What is the distance between A and C?

(e) What are the coordinates of the point of intersection of AC and BD?

(ii) What are the coordinates of Police Station?

(iii) Distance between school and police station:

(iv) What are the coordinates of Library?

(v) In which quadrant the point (-1, 4) lies?  

(b) What are the coordinates of A and B respectively?

(c) The coordinates of point O in the sketch -2 is

(d) The point on the y-axis ( in sketch 2) which is equidistant from the points B and C is 

(e) The point on the x-axis ( in sketch 2) which is equidistant from the points C and D is

(b) What are the coordinates of R, taking A as origin?

(c) Side of lawn is :

(d) Shape of lawn is :

(e) Area of lawn is :

(ii) What are the coordinates of position 'D'?

(iii) What are the coordinates of position 'H'?

(iv) In which quadrant, the point 'C' lie?

(v) Find the perpendicular distance of the point E from the y-axis.

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

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CBSE Case Study Questions for Class 9 Maths - Pdf PDF Download

CBSE Case Study Questions for Class  9 Maths

CBSE Case Study Questions for Class 9 Maths are a type of assessment where students are given a real-world scenario or situation and they need to apply mathematical concepts to solve the problem. These types of questions help students to develop their problem-solving skills and apply their knowledge of mathematics to real-life situations.

Chapter Wise Case Based Questions for Class 9 Maths

The CBSE Class 9 Case Based Questions can be accessed from Chapetrwise Links provided below:

Chapter-wise case-based questions for Class 9 Maths are a set of questions based on specific chapters or topics covered in the maths textbook. These questions are designed to help students apply their understanding of mathematical concepts to real-world situations and events.

Chapter 1: Number System

• Case Based Questions: Number System

Chapter 2: Polynomial

• Case Based Questions: Polynomial

Chapter 3: Coordinate Geometry

• Case Based Questions: Coordinate Geometry

Chapter 4: Linear Equations

• Case Based Questions: Linear Equations - 1
• Case Based Questions: Linear Equations -2

Chapter 5: Introduction to Euclid’s Geometry

• Case Based Questions: Lines and Angles

Chapter 7: Triangles

• Case Based Questions: Triangles

Chapter 8: Quadrilaterals

• Case Based Questions: Quadrilaterals - 1
• Case Based Questions: Quadrilaterals - 2

Chapter 9: Areas of Parallelograms

• Case Based Questions: Circles

Chapter 11: Constructions

• Case Based Questions: Constructions

Chapter 12: Heron’s Formula

• Case Based Questions: Heron’s Formula

Chapter 13: Surface Areas and Volumes

• Case Based Questions: Surface Areas and Volumes

Chapter 14: Statistics

• Case Based Questions: Statistics

Chapter 15: Probability

• Case Based Questions: Probability

Weightage of Case Based Questions in Class 9 Maths

Why are Case Study Questions important in Maths Class  9?

• Enhance critical thinking:  Case study questions require students to analyze a real-life scenario and think critically to identify the problem and come up with possible solutions. This enhances their critical thinking and problem-solving skills.
• Apply theoretical concepts:  Case study questions allow students to apply theoretical concepts that they have learned in the classroom to real-life situations. This helps them to understand the practical application of the concepts and reinforces their learning.
• Develop decision-making skills:  Case study questions challenge students to make decisions based on the information provided in the scenario. This helps them to develop their decision-making skills and learn how to make informed decisions.
• Improve communication skills:  Case study questions often require students to present their findings and recommendations in written or oral form. This helps them to improve their communication skills and learn how to present their ideas effectively.
• Enhance teamwork skills:  Case study questions can also be done in groups, which helps students to develop teamwork skills and learn how to work collaboratively to solve problems.

In summary, case study questions are important in Class 9 because they enhance critical thinking, apply theoretical concepts, develop decision-making skills, improve communication skills, and enhance teamwork skills. They provide a practical and engaging way for students to learn and apply their knowledge and skills to real-life situations.

Class 9 Maths Curriculum at Glance

The Class 9 Maths curriculum in India covers a wide range of topics and concepts. Here is a brief overview of the Maths curriculum at a glance:

• Number Systems:  Students learn about the real number system, irrational numbers, rational numbers, decimal representation of rational numbers, and their properties.
• Algebra:  The Algebra section includes topics such as polynomials, linear equations in two variables, quadratic equations, and their solutions.
• Coordinate Geometry:  Students learn about the coordinate plane, distance formula, section formula, and slope of a line.
• Geometry:  This section includes topics such as Euclid’s geometry, lines and angles, triangles, and circles.
• Trigonometry: Students learn about trigonometric ratios, trigonometric identities, and their applications.
• Mensuration: This section includes topics such as area, volume, surface area, and their applications.
• Statistics and Probability:  Students learn about measures of central tendency, graphical representation of data, and probability.

The Class 9 Maths curriculum is designed to provide a strong foundation in mathematics and prepare students for higher education in the field. The curriculum is structured to develop critical thinking, problem-solving, and analytical skills, and to promote the application of mathematical concepts in real-life situations. The curriculum is also designed to help students prepare for competitive exams and develop a strong mathematical base for future academic and professional pursuits.

Students can also access Case Based Questions of all subjects of CBSE Class 9

• Case Based Questions for Class 9 Science
• Case Based Questions for Class 9 Social Science
• Case Based Questions for Class 9 English
• Case Based Questions for Class 9 Hindi
• Case Based Questions for Class 9 Sanskrit

Frequently Asked Questions (FAQs) on Case Based Questions for Class 9 Maths

What is case-based questions.

Case-Based Questions (CBQs) are open-ended problem solving tasks that require students to draw upon their knowledge of Maths concepts and processes to solve a novel problem. CBQs are often used as formative or summative assessments, as they can provide insights into how students reason through and apply mathematical principles in real-world problems.

What are case-based questions in Maths?

Case-based questions in Maths are problem-solving tasks that require students to apply their mathematical knowledge and skills to real-world situations or scenarios.

What are some common types of case-based questions in class 9 Maths?

Common types of case-based questions in class 9 Maths include word problems, real-world scenarios, and mathematical modeling tasks.

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Case Study Questions for Class 9 Maths

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Are you preparing for your Class 9 Maths board exams and looking for an effective study resource? Well, you’re in luck! In this article, we will provide you with a collection of Case Study Questions for Class 9 Maths specifically designed to help you excel in your exams. These questions are carefully curated to cover various mathematical concepts and problem-solving techniques. So, let’s dive in and explore these valuable resources that will enhance your preparation and boost your confidence.

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

CBSE Class 9 Maths Board Exam will have a set of questions based on case studies in the form of MCQs. The CBSE Class 9 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.

If you want to want to prepare all the tough, tricky & difficult questions for your upcoming exams, this is where you should hang out.  CBSE Case Study Questions for Class 9  will provide you with detailed, latest, comprehensive & confidence-inspiring solutions to the maximum number of Case Study Questions covering all the topics from your  NCERT Text Books !

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CBSE Class 9th – MATHS: Chapterwise Case Study Question & Solution

Case study questions are a form of examination where students are presented with real-life scenarios that require the application of mathematical concepts to arrive at a solution. These questions are designed to assess students’ problem-solving abilities, critical thinking skills, and understanding of mathematical concepts in practical contexts.

Chapterwise Case Study Questions for Class 9 Maths

Case study questions play a crucial role in the field of mathematics education. They provide students with an opportunity to apply theoretical knowledge to real-world situations, thereby enhancing their comprehension of mathematical concepts. By engaging with case study questions, students develop the ability to analyze complex problems, make connections between different mathematical concepts, and formulate effective problem-solving strategies.

• Case Study Questions for Chapter 1 Number System
• Case Study Questions for Chapter 2 Polynomials
• Case Study Questions for Chapter 3 Coordinate Geometry
• Case Study Questions for Chapter 4 Linear Equations in Two Variables
• Case Study Questions for Chapter 5 Introduction to Euclid’s Geometry
• Case Study Questions for Chapter 6 Lines and Angles
• Case Study Questions for Chapter 7 Triangles
• Case Study Questions for Chapter 8 Quadilaterals
• Case Study Questions for Chapter 9 Areas of Parallelograms and Triangles
• Case Study Questions for Chapter 10 Circles
• Case Study Questions for Chapter 11 Constructions
• Case Study Questions for Chapter 12 Heron’s Formula
• Case Study Questions for Chapter 13 Surface Area and Volumes
• Case Study Questions for Chapter 14 Statistics
• Case Study Questions for Chapter 15 Probability

The above  Case studies for Class 9 Mathematics will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 9 Maths Case Studies have been developed by experienced teachers of schools.studyrate.in for benefit of Class 10 students.

• Class 9 Science Case Study Questions
• Class 9 Social Science Case Study Questions

How to Approach Case Study Questions

When tackling case study questions, it is essential to adopt a systematic approach. Here are some steps to help you approach and solve these types of questions effectively:

• Read the case study carefully: Understand the given scenario and identify the key information.
• Identify the mathematical concepts involved: Determine the relevant mathematical concepts and formulas applicable to the problem.
• Formulate a plan: Devise a plan or strategy to solve the problem based on the given information and mathematical concepts.
• Solve the problem step by step: Apply the chosen approach and perform calculations or manipulations to arrive at the solution.
• Verify and interpret the results: Ensure the solution aligns with the initial problem and interpret the findings in the context of the case study.

Tips for Solving Case Study Questions

Here are some valuable tips to help you effectively solve case study questions:

• Read the question thoroughly and underline or highlight important information.
• Break down the problem into smaller, manageable parts.
• Visualize the problem using diagrams or charts if applicable.
• Use appropriate mathematical formulas and concepts to solve the problem.
• Show all the steps of your calculations to ensure clarity.
• Check your final answer and review the solution for accuracy and relevance to the case study.

Benefits of Practicing Case Study Questions

Practicing case study questions offers several benefits that can significantly contribute to your mathematical proficiency:

• Enhances critical thinking skills
• Improves problem-solving abilities
• Deepens understanding of mathematical concepts
• Develops analytical reasoning
• Prepares you for real-life applications of mathematics
• Boosts confidence in approaching complex mathematical problems

Case study questions offer a unique opportunity to apply mathematical knowledge in practical scenarios. By practicing these questions, you can enhance your problem-solving abilities, develop a deeper understanding of mathematical concepts, and boost your confidence for the Class 9 Maths board exams. Remember to approach each question systematically, apply the relevant concepts, and review your solutions for accuracy. Access the PDF resource provided to access a wealth of case study questions and further elevate your preparation.

Q1: Can case study questions help me score better in my Class 9 Maths exams?

Yes, practicing case study questions can significantly improve your problem-solving skills and boost your performance in exams. These questions offer a practical approach to understanding mathematical concepts and their real-life applications.

Q2: Are the case study questions in the PDF resource relevant to the Class 9 Maths syllabus?

Absolutely! The PDF resource contains case study questions that align with the Class 9 Maths syllabus. They cover various topics and concepts included in the curriculum, ensuring comprehensive preparation.

Q3: Are the solutions provided for the case study questions in the PDF resource?

Yes, the PDF resource includes solutions for each case study question. You can refer to these solutions to validate your answers and gain a better understanding of the problem-solving process.

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Important Questions Class 9 Maths Chapter 3

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Important Questions Class 9 Mathematics Chapter 3 – Coordinate Geometry

In Class 9 Mathematics, students will learn how to locate the points in a cartesian system or an XY plane throughout the chapter on coordinate geometry. This concept is useful for locating an object in a specific location. Locating points on a map or globe is its main application. In this chapter, you will also learn about terms related to the coordinate plane, as well as terms related to the Cartesian plane.

Extramarks is the preferred online learning destination for lakhs of students. We provide comprehensive NCERT-oriented study solutions, including chapter-wise notes, CBSE revision notes, questions and answers, etc. Students can prepare for all of the concepts included in the CBSE syllabus in a more effective and efficient manner by using our question bank of Important Questions for Class 9 Mathematics Chapter 3.Students are provided with a thorough explanation and key formulas to help them quickly review all topics. By practising questions from our question set of Mathematics Class 9 Chapter 3 Important Questions, students can improve their test preparation.

Our question and answer solution of Important Questions Class 9 Mathematics Chapter 3 will aid in your preparation for the upcoming board exams as well as assist you in getting excellent scores on the exams. We have focused on preparing you for the Class 9 exam using the CBSE curriculum. Your mathematical knowledge will be enhanced by regularly practising questions from our question bank of Important Questions for Class 9 Mathematics Chapter 3, which will also help you grasp the topic better.

In addition to our Class 9 Mathematics Chapter 3 Important Questions, Extramarks has a plethora of other study resources. Students can explore a variety of study materials from Class 1 to Class 12 to expedite their learning process and enhance their academic achievement.

Important Questions Class 9 Mathematics Chapter 3 – With Solutions

We advise students to solve questions from our question bank of Important Questions for Class 9 Mathematics Chapter 3 to gain a deeper understanding of the topics covered in Coordinate Geometry.

Our experienced mathematics faculty members have prepared step-by-step solutions after intensive study. By registering on the Extramarks website, students can access our question bank of Important Questions for Class 9 Mathematics Chapter 3 along with all solutions. The solutions should be practised by students regularly in order to gain maximum benefit from them.

Given below is a list of questionnaires and their answers from our question set of Important Questions for Class 9 Mathematics, Chapter 3.

Question 1: Point (–3, 5) lies in the 

• third quadrant
• second quadrant
• first quadrant
• fourth quadrant

Solution 1: (B) Second Quadrant

Explanation:

(-3,5) is in the form of (-x,y). 

In the given point (-3, 5), the abscissa is negative, and the ordinate is positive. So, it lies in the second quadrant.

Question 2: Signs of abscissa and ordinate of any given point in the second quadrant are respectively

Solution 2: (C) –, +

The signs of the abscissa and ordinate of a given point in the second quadrant are negative and positive respectively.

Question 3:  Point (0, –7) lies

• on the x-axis
• in the fourth quadrant
• on the y-axis
• in the second quadrant

Solution 3: (C) on the y-axis

Explanation: Since the abscissa of the Point is 0, Point (0, –7) lies on the y-axis.

Question 4: Point (– 10, 0) will lie

• in the negative direction of the x-axis
• in the negative direction of the y-axis
• in the third quadrant

Solution 4: (A) on the negative direction of the x-axis

Explanation: Point (– 10, 0) predominantly lies in the negative direction of the x-axis.

Question 5:  Abscissa of all the given points on the x-axis is

Solution 5: (D)  any number

Explanation: The abscissa of the points on the x-axis can be any number.

Question 6: Ordinate of all the given points on the x-axis is

Solution 6: (A)  0

Explanation: The ordinate of all the given points on the x-axis is 0.

Question 7: The Point at which the two coordinate axes converge is called the

 Solution 7:

(C)  origin

Explanation: The points where the two coordinate axes exactly meet are called the origin.

Question 8: A point both of whose coordinates are negative will be lying in

• IV quadrant
• III quadrant
• II quadrant

Solution 8: (C)  III quadrant

Explanation: A point whose both coordinates are negative will lie in the III quadrant.

Question 9: Points such as (1, – 1), (2, – 2), (4, – 5), (– 3, – 4)

• will lie in IV quadrant
• wil lie in III quadrant
• will lie in II quadrant
• will not lie in the same quadrant

Solution 9: (D)  will not lie in the same quadrant

Points like (1, – 1), (2, – 2), (4, – 5) lie in the IV quadrant and (– 3, – 4) lie in III quadrants.

Question 10: If the y coordinate of a point taken as zero, then this Point always lies

• in I quadrant
• in II quadrant

Solution 10:

Explanation: We know that if the y-coordinate of a point is zero (ordinate), then this Point always lies on

Question 11:  The given points (–5, 2) and (2, – 5) will lie in the

• same quadrant
• IV and II quadrants, respectively
• II and IV quadrants, respectively
• II and III quadrants, respectively

Solution 11: (C) on x-axis

(-5,2) is in the form (-x,y), so it lies in the II quadrant.

(2,-5) is in the form (x,-y), so it lies in the IV quadrant.

(C) II and IV quadrants, respectively

Question 12: If the perpendicular distance of the given point P from the x-axis is 5 units and the foot of the perpendicular lies in the negative direction of the x-axis, then the point P has

• y – coordinate = – 5 only
• y – coordinate = 5 only
• x – coordinate = – 5
• y – coordinate = 5 or –5

Solution 12: (D) y – coordinate = 5 or –5

Perpendicular distance from the x-axis = 5= Ordinate

The negative direction of the x-axis doesn’t decide the sign of the ordinate.

Question 13: 

The points when the abscissa and ordinate have different signs will lie in

(a) I and II quadrants             (b) I and III quadrants

(c)  II and III quadrants           (d) II and IV quadrants

Solution 13:(d)  

Explanation: The points will be of the form (-x, y) or (x, – y)if the abscissa and ordinate have different signs and these points will lie in II and IV quadrants.

Question 14: 

The Point whose ordinate is 4 and lies on K-axis is

(a)(1,4)         (b) (0,4)            (c)    (4,0)           (d) (4,2)

Solution 14: (b)  

Explanation: Given the ordinate of any point is 4, and the Point lies on Y-axis, thus its abscissa is zero. Hence, the estimated Point is (0, 4).

Question 15: 

Which of the following points P(0, 3), Q(l, 0), R(0, – 1), S(-5, 0) and T(1, 2) does not lie on the X-axis?

(a)    Q, S and T           (b)Q and S only        (c)P, R and T             (d)P and R only

Solution 15: (c)  

Explanation: We are aware that a point will lie on the X-axis if it has the coordinates (x, 0), which means that its y-coordinate is zero. Points P (0, 3), R (0, -1), and T (1, 2) in this case does not lie on the X-axis since their y-coordinates are not zero.

Question 16: 

The Point lying on the Y-axis at a distance of 5 units and in the negative direction of Y-axis is

(a) (0,5)         (b) (-5,0)     (c) (0,-5)            (d) (5,0)  

Solution 16: (C)  

Explanation: The fact that the Point is on the X-axis indicates that its ^-coordinate is zero. Additionally, its y-coordinate is negative because it is 5 units away from the X-axis in the opposite direction.

Thus, the required Point is (0, – 5).

Question 17: 

The perpendicular distance of the point P(3, 4) from the Y-axis is

(a) 3           (b)    5     (c) 4             (d) 7

Solution 17: (a)  

Explanation: We are aware that a point’s abscissa, or x-coordinate, is the angle of that Point with respect to the Y-axis. As a result, point P(3, 4)’s distance from the Y-axis  is equal to 3.

Question 18: The distance of the given Point (-3, -2) from the x-axis is

(a) 2 units

(b) 3 units

(c) 5 units

(d) 13 units 

Solution 18:   (a) 2 units

The magnitude or absolute value of the Point’s y coordinate is its distance from the x-axis.

Question 19: The distance of the given Point (-6, -2) from the y-axis is

(a) 6 units

(b) 8 units

(c) 2 units

(d)  10 units

Solution 19:  (a) 6 units

The magnitude or absolute value of the Point’s x coordinate is its distance from the y axis.

Question 20: The abscissa and ordinate of the given Point with Coordinates (8, 12) is

(a) abscissa 12, ordinate 8

(b) abscissa 8, ordinate 12

(c) abscissa 0 and ordinate 20

(d) none of these

Solution 20:  (a) abscissa 12 and ordinate 8

The abscissa is the y coordinate of the Point and the ordinate is the x coordinate value.

Question 21: The coordinate of origin in

(b) (0, y) 

(d) none of these.

Solution 21: (c) (0, 0)

Explanation: For the origin, both abscissa and ordinate are 0.

Question 22: The distance of the Point (2,3) from y- axis  is 

(A) 2 units

(B) 3 units

(C) 5 units

(D) 13 units 

Solution 22:  (A) 2 units

Explanation: The magnitude or absolute value of the Point’s y coordinate is its distance from the x-axis. The magnitude or absolute value of the Point’s x coordinate is what determines how far the Point is from the y-axis.

Question 23: The point (-2, -1) lies in

(A) 1st quadrant

(B) 2nd quadrant

(C) 3rd quadrant

(D) 4th quadrant

Solution 23:  (C) 3rd quadrant

Explanation: Negative x and y values relate to the third quadrant.

Question 24: The Point (3,0) lies on

(A) +ve x-axis

(B) – ve x-axis

(C) + ve y-axis

(D) –ve y-axis 

Solution 24 : (A) +ve x axis

Explanation: Because the x-coordinate is positive and the y-coordinate is  zero.

Question 25: The distance of the Point (3, 5) from the x-axis is

(a) 3 units

(b) 4 units

(d) 6 units  

Solution 25:   (c) 5 units

Question 26: The Point (0, -5) lies on

(a) +ve x-axis

(b) +ve y-axis

(c) –ve x-axis

(d) –ve y-axis 

Solution 26:  (d) –ve y-axis

Explanation: When the y coordinate is negative and the x coordinate is zero.

Question 27: The point (-2, 5) lies in

(a) 1st quadrant

(b) 2nd quadrant

(c) 3rd quadrant

(d) 4th quadrant

Solution 27:  (b) 2nd quadrant.

Explanation: The x-values are negative and the y-values are positive in the second quadrant.

Question 28: The distance of the Point (3, 0) from the x-axis is

(b) 0 units

(c) 9 units

Solution 28:  (a) 3 units.

Question 29: The points (other than the origin) whose abscissa is equal to the ordinate lie in

• a) Quadrant II only
• b) Quadrant I and II
• c) Quadrant I & III
• d) Quadrant I only

Solution 29: (c) quadrant I & III. 

Explanation: In I and  III quadrants, the axes will have the same sign.

Question 30:The perpendicular distance of the given point P(4,3) from the y axis is

• c) 7 Units 

Solution 30:  (a) 3 units

The Point  x coordinate indicates how far it is from the Y- axis.

Question 31:The area of triangle OAB with points 0(0,0), A(4,0) & B(0,6) is

• a) 24 sq. units
• b) 12 sq. units
• c) 8 sq. unit
• d) 16 sq. units

Solution 31:  (b) 12 sq. units.

Explanation: The triangle’s area is equal to the product of its base and height.

Question 32:  Plot the points A (2, 5), B (–2, 2) and C (4, 2) on graph paper. Join AB, BC and AC . Calculate the area of ∆ ABC .

Solution 32:

Abscissa of D = Abscissa of A = 2

Ordinate of D = Ordinate of B = 2

BC = (2 + 4) units = 6 units

AD = (5 – 2) units = 3 units

Area of ΔABC= 1 2 ×Base×Height

                           = 1 2 ×BC×AD

                           = 1 2 ×6×3

                           =9

Hence, area of ∆ ABC is 9 square units

Question 33: Predict whether the given statements are True / False? Give justification for your answer.

(i) Point (3, 0) lying in the first quadrant.

(ii) Points (1, –1) and (–1, 1) lying in the same quadrant.

(iii) The coordinates of a point whose ordinate is – ½ and abscissa is 1 are – ½ , 1.

(iv) A point lying on the y -axis at  2 units distance from the x -axis. Its coordinates are (2, 0).

(v) (–1, 7) is a point lying in the II quadrant.

Solution 33:

(i) The Point (3, 0) lies in the first quadrant.

The ordinate of the given Point (3, 0) is given zero.

Hence, the Point must lie on the x-axis

(ii) Points (1, –1) and (–1, 1) lie in the same quadrant.

(1, -1) lies in IV quadrant

 while (-1, 1) lies in II quadrant.

(iii) The coordinates of a point for which ordinate is – ½ and abscissa is 1 are – ½ , 1.

The coordinates of a point for which ordinate is – ½ and abscissa is 1 is (1, -1/2).

(iv) A point is lying on the y -axis at a distance of 2 units from the x -axis. Its coordinates are (2, 0).

A point is lying on the y -axis at a distance of 2 units from the x -axis. Thus its coordinates are (0, 2).

(–1, 7) is a point in the II quadrant.

Question 34:

In which quadrant or axis on the following points will lie?

(-3, 5),  (2,0), (2, 2), (-3,-6),(4,-1),

Solution 34:

(i) For point (-3, 5), the x-coordinate is negative while y-coordinate is positive, so it  is lying in II quadrant.

(ii) For point (4,-1), the x-coordinate is positive while the y-coordinate is negative, so it lies in the IV quadrant.

(iii) In Point (2,0), the x-coordinate is positive while the y-coordinate is zero, so it lies on the X-axis.

(iv) In Point (2,2), both x-coordinate and y-coordinate are positive, so it lies in the I quadrant.

(v) In Point (-3, – 6), x-coordinate and y-coordinate both are negative, so it lies in III quadrant.

Question 35: Write the coordinates of the points P, Q, R, S, T and O from the figure given below.

Solution 35:

The coordinates of points P, Q, R, S, T and O are as follows:

Q = (-3, 0)

R = (-2, -3)

T = (4, -2)

Question 36: Without plotting the points find the quadrant in which they will lie, if

(i) ordinate is 5 while abscissa is – 3

(ii) abscissa is – 5 while ordinate is – 3

(iii) abscissa is – 5 while ordinate is 3

(iv) ordinate is 5 while abscissa is 3

Solution 36:

(i) The Point is (-3,5).

Hence, the Point is lying in the II quadrant.

(ii) The Point is (-5,-3).

Hence, the Point is lying in the III quadrant.

(iii) The Point is (-5,3).

(iv) The Point is (3,5).

Hence, the Point is lying in the I quadrant.

Question 37:

Three vertices of any rectangle ABCD are A (3, 1), B (–3, 1) and C (–3, 3). Plot these points on the graph paper and find the coordinates of the fourth vertex D . Also, find the area of rectangle ABCD .

Solution 37: 

Let A (3, 1), B (–3, 1) and C (–3, 3) be three vertices of a rectangle ABCD .

Let the y -axis cut the rectangle ABCD at the points P and Q respectively.

Abscissa of D = Abscissa of A = 3.

Ordinate of D = Ordinate of C = 3.

∴ coordinates of D are (3, 3).

AB = ( BP + PA ) = (3 + 3) units = 6 units.

BC = ( OQ – OP ) = (3 – 1) units = 2 units.

Ar(rectangle ABCD ) = ( AB × BC )

                               = (6 × 2) sq. units

                               = 12 sq. units

Hence, the area of rectangle ABCD is 12 square units.

Question 38:

Which of the following points is lying on the Y-axis?

A(l, 1), B(1, 0), C(0, 1), D(0, 0), E(0, -1), F(-1, 0), G(0, 5), H(-7, 0) and I(3 ,3).

Thinking Process

The Point lying on the Y-axis means the x-coordinate of the Point will be zero. Check this condition for each and every given Point and find out the correct Point.

Solution 38:

We know that a point will be lying on the Y-axis, if its x-coordinate is zero. Given, x-coordinate of the points C(0, 1), D(0, 0), E(0,-1) and G(0, 5) are zero. So, these points tend to lie on the Y-axis. Also, D(0, 0) is the Point of intersection for both the axes, so we can consider that it lies on the Y-axis as well as on the X-axis.

Question 39: In the figure given below, LM is a parallel line to the y-axis at 3 units distance.

(i) What will be the coordinates of points P, R and Q?

(ii) What is the difference between the abscissas of points L and M?

Solution 39:

(i) The given coordinates are:

(ii) Since, all the points lying on the line have the same abscissa = 3.

The difference in abscissas of L and M is 0.

Question 40:

Find the possible coordinates of the Point

(i) which lies both on X and Y-axes .

(ii) whose ordinate is – 4 and lies on the Y-axis.

(iii) whose abscissa is 5 and lies on the X-axis.

Solution 40:

(i) The Point which lies both on the X and Y-axes  is the origin and the coordinates are (0, 0).

(ii) The Point having ordinate – 4 and lies on Y-axis, i.e., the x-coordinate is zero, is (0,-4).

(iii) The Point whose abscissa is 5 and lies on X-axis, and the y-coordinate is zero, is (5, 0).

Question 41: See the figure given below and complete the following statements:

(i) The abscissa and the ordinate of any point B are _ _ _ and _ _ _, respectively.

Hence, the coordinates of B are (_ _, _ _).

(ii) The x-coordinate and the y-coordinate of any point M are _ _ _ and _ _ _,

respectively. Hence, the coordinates of M are (_ _, _ _).

(iii) The x-coordinate and the y-coordinate of any point L are _ _ _ and _ _ _,

respectively. Hence, the coordinates of L are (_ _, _ _).

(iv) The x-coordinate and the y-coordinate of any point S are _ _ _ and _ _ _,

respectively. Hence, the coordinates of S are (_ _, _ _).

Solution 41: (i) Since the distance of point B from the y – axis is 4 units, the x – coordinate or abscissa of point B is 4. The distance of point B from the x-axis is 3 units; therefore, the y – coordinate, i.e., the ordinate of point B is 3.

Thus, the coordinates of point B are (4, 3).

As in (i) above :

(ii) The x – coordinate and the y – coordinate of Point M are –3 and 4, respectively.

Hence, the coordinates of point M are (–3, 4).

(iii) The x – coordinate and the y – coordinate of point L are –5 and – 4, respectively.

Thus, the coordinates of any point L are (–5, – 4).

(iv) The x – coordinate and the y- coordinate of point S are 3 and – 4, respectively.

Thus, the coordinates of point S are (3, – 4).

Question 42:  How will you describe the table lamp position on your study table to another person?

Solution 42:

We use two lines, a perpendicular and a horizontal line, to describe the location of the table lamp on the study table. Using the horizontal and perpendicular lines as the X and Y axes of the table, respectively, and the perpendicular line as the Y axis. Consider the intersection of the X and Y axes in one of the table’s corners as the origin. The table’s length is now its Y axis, and its width is its X axis. Create a point by connecting the line from the origin to the table light. It is necessary to compute the Point’s separation from the X and Y axes before expressing the results in terms of coordinates.

The table lamp will be in the coordinates (x, y) because the Point is separated from the X- and Y-axis by x and y, respectively.

Here, (x, y) = (15, 25)

Question 43: Write the answer for the following questions:

(i) What is the name of the lines that are drawn horizontally and vertically to represent the positions of all points in the Cartesian plane?

(ii) What are the names of the various components of the plane that these two lines form?

(iii) Indicate the name of the intersection location of these two lines.

Solution 43:

(i) The x-axis and y-axis are the names of the horizontal and vertical lines drawn to calculate the position of any point in the Cartesian plane.

(ii) The quadrants are the names of each section of the plane created by the x-axis and y-axis.

(iii)The origin is the location where these two lines intersect.

Question 44: Without plotting any of the points, indicate the quadrant in which they will lie, if

(i) the ordinate is 5 while abscissa is – 3

(ii) the abscissa is – 5 while the ordinate is – 3

(iii) the abscissa is – 5 while ordinate is 3

(iv) the ordinate is 5 while abscissa is 3

Solution 44:

Therefore, the Point lies in the II quadrant.

Therefore, the Point lies in the III quadrant.

Therefore, the Point lies in the I quadrant.  

Question 45: Write the coordinates of any points marked on the axes in the figure given below.

Solution 45: Part 1

You can see that :

(i) The Point A is at + 4 units distance from the y – axis and at zero distance from the x-axis. Thus, the x – coordinate of A is 4, and the y – coordinate will be 0. Hence, the coordinates of Point A are (4, 0).

(ii) The coordinates of point B are (0, 3). 

(iii) The coordinates of point C are (– 5, 0).

(iv) The coordinates of point D are (0, – 4). 

(v) The coordinates of E are ( 2 3 ,0).

The y coordinate of any point situated on the x-axis is always zero because every Point on the x-axis is at zero distance from the x-axis. Any point on the x-axis, therefore, has coordinates of the form (x, 0), where x represents the distance of the Point from the y-axis. Similar to the x-axis, any point’s coordinates on the y-axis are of the form (0, y), where y is the Point’s distance from the x-axis.

Part 2: What are the coordinates of the origin O?

Its abscissa and ordinate are both zero since it is at zero distance from both axes. Consequently, the origin’s coordinates are (0, 0).

It is possible that you have noticed the correlation between a point’s coordinate sign and the quadrant in which it  is located.

(i) Since the first quadrant is bounded by the positive x-axis and the positive y-axis, a point in the first quadrant will have the form ( +, +).

(ii) Because the second quadrant is bounded by the negative x-axis and the positive y-axis, a point in the second quadrant will have the form (-, +).

(iii)Because the third quadrant is bounded by the negative x-axis and the negative y-axis, a point in the third quadrant will have the form (-, -).

(iv) Given that the fourth quadrant is bounded by the positive x-axis and the negative y-axis, a point in the fourth quadrant will have the form (+, -).

Question 45: Write the answer to the following questions:

(i) What are the names of the lines that are drawn horizontally and vertically to represent the positions of every Point in the Cartesian plane?

Solution 45:

(i)  The x-axis and y-axis are the names of the horizontal and vertical lines drawn to calculate the position of any point in the Cartesian plane.

(ii)  Each section of the plane created by the x- axis and y-axis is referred to as a quadrant.

(iii) The Point where these two lines converge is called the origin.

Question 46: On which axis will the given points lie?

iii. (0, 6)

Solution 46:

• (7,0) lies on X-axis since the y component is zero
• (0, -3) lies on Y-axis since the x component is zero

iii. (0,6) lies on Y-axis since the x component is zero

• (-5,0) lies on X-axis since the y component is zero

Question 47: In which quadrants will the given points lie?

iii. (-1, -2)

Solution 47: 

• The x component is positive, and the y component is negative. Hence the IV quadrant is (4,-2)
• Due to the negative x component and the positive y component, the second quadrant is (-3,7).

iii. Due to the negative x and y components, the third quadrant is located at (-1,-2).

• Since both the x and y components are positive, the Point (3, 6) lies in quadrant I.

Question 48: Does P (3, 2) represent the same Point as Q(2, 3), or not?

Solution 48:  The points P(3,2) and Q(2,3) are not the same, hence the answer is no. Unlike Q, which has an x component of 2 and a y component of 3, the first one has an x component of 3 and a y component of 2.

Question 49: Locate the given points (5, 0), (0, 5), (2, 5), (5, 2), (–3, 5), (–3, –5), (5, –3) and

 (6, 1) in the Cartesian plane.

Solution 49 : We take 1cm = 1 unit; we now draw the x-axis and the y – axis. The positions of

the given points are shown by dots in figure below

You can see that the positions of (0, 5) and (5, 0) are not identical. The placements of (2, 5) and (5, 2) are also different. Additionally, the positions of (-3, 5) and (-5, -3) are different. You can demonstrate this by using multiple instances to show that if x y, then the positions of (x, y) in the Cartesian plane are not the same (y, x). The position of (y, x) will be different from the position of (y, x) if the coordinates x and y are switched (x, y). This implies that it’s crucial to consider x and y’s order when (x, y).

Therefore, (x, y) is called an ordered pair. The ordered pair (x, y) ≠ ordered pair (y, x) if x ≠ y. Also (x, y) = (y, x), if x = y.

Question 52: Find the coordinates of Point equidistant from the given two points P(3,0) and Q(-3,0). How many points possibly satisfy this condition?

Solution 52:  All the points on the Y-axis satisfy this condition.

Question 53: Plot the following given ordered pairs (x, y) of numbers as points in the Cartesian plane. Using the scale 1cm = 1 unit on the axes.

Solution 53 : The pairs of numbers represented in the table can be indicated by the points

(– 3, 7), (0, –3.5), (– 1, – 3), (4, 4) and (2, – 3). The locations of the given points are shown

by dots in the figure given below.

Question 54: Name each part of the given plane formed by the Vertical and horizontal lines.

Solution 54:  The vertical line is called the y-axis and the horizontal line is called the x-axis. And these form four quadrants.

Question 55: Write the mirror image of the given Point (2, 3) and (-4, -6) with respect to the x-axis.

Solution 55:  The mirror image of the given Point (2, 3) is (2, -3) with respect to the x-axis.

The mirror image of the Point (-4, -6) is (-4,6) with respect to the x-axis.

Question 56: Write the abscissa and ordinate of a point (-3, -4) 

Solution 56:  The Abscissa will be -3 and ordinate will be -4

Question 57: State the quadrant in which each of the following points will lie: 

(ii) (-7,11)

(iii) (-6, -4) 

(iv) (-5, -5)

Solution 57:   (2, 1) lie in the I quadrant

(-7, 11) lie in the II Quadrant

(-6, -4) lie in the III Quadrant

(-5, -5) lie in the III Quadrant

Question 58: What is the name of the horizontal and vertical lines which are  drawn to determine the position of any given point in the Cartesian plane?

Solution 58:  The horizontal line is called the x-axis while the vertical line is called the y – axis

Question 59: List the points on the plane that do not fall into any of the four quadrants.

Solution 59: The points in a plane that do not belong to any one of the quadrants is origin and are denoted by point O (0,0).

Question 60: Which of the given points belong to the x-axis? 

(a) (2, 0) (b) (3, 3) (c) (0, 1) (d) (-2, 0)

Solution 60: (2, 0) and (-2, 0) belong to the x- axis.

For the Point to belong to the y-axis, the y-component must be zero.

Question 61: Which of the given points belongs to the 1st quadrant 

(a) (3, 0) (b) (1, 2) (c) (-3, 4) (d) (3, 4)

Solution 61: (1, 2) and (3, 4) belong to the 1st quadrant.

Question 62: Which of the given points belongs to 3rd quadrant

(a) (1, 3) (b) (-1, -3) (c) (0, 4) (d) (-4, -2)

Solution 62: (-1, -3) and (-4, -2) belong to the 3rd quadrant.

Question 63: Answer each of the following questions:

(i) In order to locate any point in the Cartesian plane, what is the name of the horizontal and vertical lines that are drawn?

Solution (i) :  The x-axis and the y-axis are the lines that are drawn to determine the positions of any points in the Cartesian plane, respectively.

(ii)  What are the names of the various components of the plane that these two lines form?

Solution (ii) :  The term “quadrant” refers to each section of the plane that is created by the x- and y-axes.

(iii)  Indicate the name of the intersection location of these two lines.

Solution (iii): The origin, symbolised by O, is the location where the x- and y-axes connect (0,0).

Question 64: Find the ordered pairs of the linear equation

and plot them as ‘how many such ordered pairs can be present and plotted?

Solution 64: The given equation is

The equation will hold if

thus, (0, 4),

thus, (1, 2),

thus,(2, 0) ,

i.e. (3, -2)…

Likewise, (4,-4), (5,-6), (-1,6), (-2,8) etc. also. These are a few ordered pairs which are 

valid solutions. And  such ordered pairs are infinite.

Question 65: What is coordinate geometry?

Solution 65: In order to present geometric forms in a two-dimensional plane and learn about their properties, coordinate geometry is a crucial area of mathematics. In order to get a basic concept of coordinate geometry, we’ll try to learn about the coordinate plane and a point’s coordinates here.

Question 66: What is a Coordinate plane?

Solution 66: In order to make it simple to locate the points, a cartesian plane divides the plane space into two dimensions. The coordinate plane is another name for it. The horizontal x-axis and the vertical y-axis are the two axis of the coordinate plane. The origin is the place where these coordinate axis connect, and they divide the plane into four quadrants (0, 0). Additionally, any point in the coordinate plane is denoted by the coordinates (x, y), where x represents the Point’s position in relation to the x-axis and y represents its position in relation to the y-axis.

Question 67: What are the properties of a point?

Solution 67: The properties of the Point in the coordinate plane’s four quadrants are as follows:

• The origin O is the location where the x- and y-axes intersect, and its coordinates are (0, 0).
• The positive x-axis is to the right of the origin O, while the negative x-axis is to the left of the origin O. Additionally, the positive and negative y-axis are located above and below the origin O, respectively.
• The first quadrant’s Point (x, y) is plotted with reference to the positive x-axis and the positive y-axis because it has both positive values.
• With reference to the negative x-axis and positive y-axis, the point (-x, y) in the second quadrant is drawn.
• Plotting is done with reference to the negative x-axis and negative y-axis for the Point depicted in the third quadrant (-x, -y).
• The positive x-axis and the negative y-axis are used to plot the Point (x, -y) that is located in the fourth quadrant.

Question 68: Explain the coordinates of a point.

Solution 68: 

Image source: Internet

An address that aids in locating a spot in space is a coordinate. The coordinates of a point in a two-dimensional space are (x, y). Let’s note these two crucial terms right now.

• Abscissa:  The distance from the origin along the x-axis is represented by the x value at the Point (x, y).
• Ordinate:  It is the y value at the coordinates (x, y) and the angle at which the Point lies in relation to the x-axis, which runs parallel to the y-axis.

A point’s coordinates can be used for a variety of tasks, including calculating distance, midpoint, a line’s slope, and its equation.

Question 69: Write the distance formula in coordinate geometry.

Solution 69: The square root of the sum of squares of the difference between the x coordinate and the y coordinate of the two supplied points is equal to the distance between two points (x1, y1) and (x2, y2) in this example. The following is a formula for calculating the separation between two points.

D = (x 2 – x 1 ) 2 + (y 2 – y 1 ) 2

Benefits of Solving Important Questions Class 9 Mathematics Chapter 3

The benefits of answering questions from our Chapter 3 Class 9 Mathematics important questions are listed below.

• Our Important Questions Class 9 Mathematics Chapter 3 question bank follows the NCERT exam style and is based on the  recent CBSE syllabus. It thus includes questions with a variety of formats, such as multiple-choice questions (MCQs), fill-in-the-blank questions, and long and short responses  in order to expose students to actual board exam paper patterns. This encourages pupils to perform better on exam day and earn higher grades.
• Mathematics subject experts  with years of experience have prepared the answers. Additionally, experts   work continuously to review and improve the responses. As a result, students may confidently rely on our solutions as they adhere to  recent CBSE syllabus and exam guidelines.
• Students can completely review the ideas presented in the chapter by practising the various high-level questions included in the Important Questions Class 9 Mathematics Chapter 3. This will enable them to review the material once more and provide an opportunity for them to identify and correct any weaknesses before their final exams. Maintain a strict study routine as well if you want to pass with flying colours.
• While practising these questions students will get used to the questions with varying levels of difficulty and some of them are tweaked to test the understanding level of the students, questions are also repeated to strengthen their understanding and even provide enough practice to improve their speed along with analytical skills.
• Scoring a high percentage is not difficult. You just require the right strategies and correct understanding of the concepts to ensure 100% result in Mathematics.

The answers given to all questions in our Class 9 Mathematics Chapter 3 Important Questions adequately cover all of the key points with explanations. 

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Q.1 Plot the following points in a Cartesian plane:

(-2,4), (3,-1), (-1, 0), (1, 2) & (-3, -5)

Marks :4 Ans

Q.2 Which of the following points:

B(1, 0), C(0,1 ), E (-1, 0),  F ( 0, -1),  G (4, 0),  H (0, -7)

(i) lie on x ?axis?

(ii) lie on y ? axis?

Marks :3 Ans

(i)The point whose ordinate is 0 lies on x axis.

Therefore, the point B (1,0), E (-1,0), G(4,0) lie on x axis.

(ii) The point whose abscissa is 0 lies on y  axis.

Therefore, the points C (0,1), F (0,-1) , H (0,-7) lie on y-axis.

 Q.3 See the figure, and write the following:

1)  The coordinates of B.

2)  The point identified by the point (-3, -5).

3) The abscissa of point D.

4) The ordinate of the point E.

5)  The point identified by the coordinates (2, -4).

1) Coordinate of B(2, 2).

2) A(-3, -5)

3) Abscissa of point D is 5.

4) Ordinate of point E is -4.

5) E(2, -4)

 Q.4 The coordinates of the vertices of the triangle ABC, as shown in the figure, are __________________.

• (2, 2), (1,3) and (1, 0) / (2, 2), (1, 3) and (1, 0)
• (2, 2), (1, 3) and (0, 1) / (2, 2), (1, 3) and (0, 1)
• (2, 2), (1, 3) and (1, 0) / (2, 2), (1, 3) and (1, 0)
• (2, 2), (?1, 3) and (0, 1) / (2, 2), (1, 3) and (0, 1)

Marks :1 Ans

(2, 2), (1, 3) and (1, 0)

 Q.5 After walking 6 units in the direction parallel to the x-axis to the left of the origin, Jacob reaches point P. If he started from the point (1, 2), then the coordinates of point P are _____________.

• ( 5, 2) (5, 0)
• (4, 2) (4, 2)

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Faqs (frequently asked questions), 1. which is the best mathematics guide for class 9 mathematics.

Students are advised to first study the syllabus from NCERT textbooks and then practise questions from NCERT exemplar books. Along with that students should register with Extramarks to get access to a comprehensive set of study materials including NCERT chapter-wise solutions, CBSE revision notes, questions and answers solutions, CBSE solved sample papers, etc. One of the most important study materials is our question bank of Important Questions Class 9 Chapter 3 Mathematics and other chapters that will give a consolidated set of questions from different sources. It’s a crucial study aid as it will help students to practise a lot of exam oriented questions and significantly  improve their scores  in final exams.

2. How much time should a Class 9 student spend practising Mathematics?

The time limit  is not important for any of the  subjects, especially  Mathematics and Science. Mathematics is a core subject  of many career streams and its application will be required in daily life. So it’s important for students to have a good hold on the subject. 

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NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry

NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry Ex 3.1 are part of NCERT Solutions for Class 9 Maths . Here we have given NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry Ex 3.1.

NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry Ex 3.1

NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry (निर्देशांक ज्यामिति) (Hindi Medium) Ex 3.1

NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry Ex 3.2

Ex 3.2 Class 9 Maths   Question 1 Write the answer of each of the following questions: (i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane? (ii) What is the name of each part of the plane formed by these two lines? (iii) Write the name of the point where these two lines intersect. Solution: (i) The horizontal line: x – axis and the vertical line: y – axis. (ii) Each part is called “Quadrant”. (iii) Origin

NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry Ex 3.3

NCERT Solutions for Class 9 Maths

• Chapter 1 Number systems
• Chapter 2 Polynomials
• Chapter 3 Coordinate Geometry
• Chapter 4 Linear Equations in Two Variables
• Chapter 5 Introduction to Euclid Geometry
• Chapter 6 Lines and Angles
• Chapter 7 Triangles
• Chapter 8 Quadrilaterals
• Chapter 9 Areas of Parallelograms and Triangles
• Chapter 10 Circles
• Chapter 11 Constructions
• Chapter 12 Heron’s Formula
• Chapter 13 Surface Areas and Volumes
• Chapter 14 Statistics
• Chapter 15 Probability
• Class 9 Maths (Download PDF)

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Coordinate Geometry Class 9 Notes - Chapter 3

Cbse class 9 maths coordinate geometry notes:- download pdf here.

Coordinate geometry is significant because it provides a link between geometry and algebra through line graphs and curves. Coordinate geometry is useful in mathematics because it allows us to locate points on any plane. It also has applications in trigonometry, calculus, and other disciplines. Get the complete concept of coordinate geometry, such as the Cartesian system, coordinate points, how to plot the points in the coordinate axes, quadrants with signs, and so on. Go through the below article to learn coordinate geometry for Class 9.

To know more about coordinate geometry, click here .

Cartesian System

The Cartesian system is a system for describing the position of a point in a plane. A point is located by referring to two perpendicular lines in a Cartesian system. The X-axis is the horizontal line XX’, and the Y-axis is the vertical line YY’.

To know more about the coordinate system, click here .

The origin, indicated by the letter ‘O,’ is the place where the horizontal and vertical lines intersect. Here, positive directions are OX and OY, while negative directions are OX’ and OY’.

Coordinate Axes and Quadrants

The plane is divided into four sections by the X and Y axes. The quadrants (one-fourth section) are numbered I, II, III, and IV in anti-clockwise order from OX. The Cartesian plane, also known as the coordinate plane or the XY plane, comprises these axes and quadrants. These axes are also known as coordinate axes.

Points in Different Quadrants

Signs of coordinates of points in different quadrants:

I Quadrant: ‘+’ x – coordinate and ‘+’ y – coordinate. Eg. (2, 3)

II Quadrant: ‘-’ x – coordinate and ‘+’ y – coordinate. Eg. (-1, 4)

III Quadrant: ‘-’ x – coordinate and ‘-’ y – coordinate. Eg. (-3, -5)

IV Quadrant: ‘+’ x – coordinate and ‘-’ y – coordinate. Eg. (6, -1)

To know more about Quadrants, visit here .

Plotting on a Graph

Using the coordinate axes, we can describe any point in the plane using an ordered pair of numbers. Point A is represented by an ordered pair ( x ,  y ) where  x is the abscissa and y is the ordinate of the point.

Position of a point in a plane

To know more about the Cartesian plane, visit here .

Plotting a Point in the Plane if Its Coordinates Are Given

The coordinate points will define the location in the Cartesian plane. The distance of a point from the y-axis is known as the x-coordinate or abscissa, and the distance of the point from the x-axis is known as the y-coordinate, or ordinate. For example, Point (3, 2) is 3 units away from the positive y-axis and 2 units away from the positive x-axis. Therefore, a point (3, 2) can be plotted below. Similarly, (-2, 3), (-1, -2) and (2, -3) are plotted.

Plotting a point in the plane

Solved Example on Class 9 Maths Chapter 3 Coordinate Geometry

Each of the coordinates (-2, 4),(3, -1), (-1, 0),(1, 2), and (-3, -5) lies in which quadrant or on which axis? Locate them on the Cartesian plane to verify your solution.

Negative abscissa and positive ordinate characterize the point (-2, 4).

(-2,4) is located in the second quadrant.

Positive abscissa and negative ordinate characterize the position (3, -1).

(3, -1) is located in the fourth quadrant.

Negative abscissa and zero ordinate characterize the point (-1, 0).

∴ On the negative x-axis is the point (-1, 0).

The abscissa and ordinate are both positive at points (1, 2).

∴ The first quadrant contains points (1,2).

Both the abscissa and ordinate are negative at the location (-3, -5).

∴ The 3rd quadrant contains the point (-3, -5).

These points are represented in the Cartesian plane as A(-2, 4), B(3, -1), C(-l, 0), D(l, 2), and E (-3, -5), as shown in the diagram.

Video lesson on Coordinate Geometry toughest problems

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Case Study Questions for Class 9 Maths Chapter 12 Herons Formula

Case study questions for class 9 maths chapter 9 areas of parallelograms and triangles, case study questions for class 9 maths chapter 6 lines and angles, case study questions for class 9 maths chapter 7 triangles, case study questions for class 9 maths chapter 5 introduction to euclid’s geometry, case study and passage based questions for class 9 maths chapter 14 statistics, case study questions for class 9 maths chapter 1 real numbers, case study questions for class 9 maths chapter 4 linear equations in two variables, case study questions for class 9 maths chapter 3 coordinate geometry, case study questions for class 9 maths chapter 15 probability, case study questions for class 9 maths chapter 13 surface area and volume, case study questions for class 9 maths chapter 10 circles, case study questions for class 9 maths chapter 9 quadrilaterals, case study questions for class 9 maths chapter 2 polynomials.

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CBSE Case Study Questions Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry PDF Download

Case Study Questions Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry  is very important to solve for your exam. Class 9 Maths Chapter 5 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  case study-based   questions for Class 9 Maths Chapter 5  Introduction to Euclid’s Geometry

CBSE Case Study Questions for Class 9 Maths Euclids Geometry PDF

Case study questions class 9 maths chapter 5.

Case Study 1: In a mathematics class, students were learning about Euclid’s Geometry and the properties of lines and angles. The teacher drew the following figure on the board:

Using this figure, the teacher presented some statements and asked the students to determine whether they were true or false. Let’s see how well you can answer these questions:

Q1. In triangle ABC, if AB = AC, then the triangle is: (a) Equilateral (b) Isosceles (c) Scalene (d) Right-angled

Answer: (b) Isosceles

Q2. If lines AB and AC are perpendicular to each other, then the measure of angle BAC is: (a) 45 degrees (b) 90 degrees (c) 180 degrees (d) It cannot be determined

Answer: (b) 90 degrees

Q3. In triangle ABC, if angle B = angle C, then the triangle is: (a) Equilateral (b) Isosceles (c) Scalene (d) Right-angled

Q4. In triangle ABC, if angle B = angle C = 60 degrees, then the triangle is: (a) Equilateral (b) Isosceles (c) Scalene (d) Right-angled

Answer: (a) Equilateral

Q5. In triangle ABC, if AB = BC, then the triangle is: (a) Equilateral (b) Isosceles (c) Scalene (d) Right-angled

Case Study 2. A group of students is studying geometrical shapes and their properties. They came across the following figure:

The students were given statements related to this figure and were asked to determine whether they were true or false. Let’s see if you can answer these questions:

Q1. In the given figure, line segment AB is perpendicular to line segment CD. True or False?

Answer: (b) False

Q2. In the given figure, angle CAB is supplementary to angle BCD. True or False?

Q3. In the given figure, angle CAD is complementary to angle BCD. True or False?

Q4. In the given figure, line segments AC and BD are parallel. True or False?

Answer: (a) True

Q5. In the given figure, angle CAD is equal to angle CDB. True or False?

Case Study 3. A group of students was learning about the properties of quadrilaterals. The teacher presented them with the following figure:

The teacher then asked the students to identify the type of quadrilateral based on its properties. Let’s see if you can answer the questions correctly:

Q1. In the given figure, if all four sides of the quadrilateral ABCD are equal, then it is a: (a) Rectangle (b) Rhombus (c) Square (d) Parallelogram

Answer: (b) Rhombus

Q2. In the given figure, if opposite sides of the quadrilateral ABCD are parallel, then it is a: (a) Rectangle (b) Rhombus (c) Square (d) Parallelogram

Answer: (d) Parallelogram

Q3. In the given figure, if opposite angles of the quadrilateral ABCD are equal, then it is a: (a) Rectangle (b) Rhombus (c) Square (d) Parallelogram

Q4. In the given figure, if all four angles of the quadrilateral ABCD are right angles, then it is a: (a) Rectangle (b) Rhombus (c) Square (d) Parallelogram

Answer: (a) Rectangle

Q5. In the given figure, if all four sides of the quadrilateral ABCD are equal and all four angles are right angles, then it is a: (a) Rectangle (b) Rhombus (c) Square (d) Parallelogram

Answer: (c) Square

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• Circles Class 9 Case Study Questions Maths Chapter 9

Last Updated on September 8, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 9 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 9 maths. In this article, you will find case study questions for CBSE Class 9 Maths Chapter 9 Circles. It is a part of Case Study Questions for CBSE Class 9 Maths Series.

Table of Contents

Case Study Questions on Circles

Government of India is working regularly for the growth of handicapped persons. For these three STD booths situated at point P, Q and R are as shown in the figure, which are operated by handicapped persons. These three booths are equidistant from each other as shown in the figure.

On the basis of the above information, solve the following questions:

Q. 1. Which type of ΔPQR in the given figure?

Q. 2. Measure angle ∠QOR.

Q. 3. Find the value of ∠OQR.

Q. 4. Is it true that points P, Q and R lie on the circle?

1. Given $P, Q$ and $R$ are equidistant. It means their distances are equal.

Note: In an equilateral triangle, length of all three sides are equal. So, $\triangle P Q R$ is an equilateral triangle.

2. Since, $\triangle P Q R$ is an equilateral triangle.

$$ \therefore \angle \mathrm{PQR}=\angle \mathrm{PRQ}=\angle \mathrm{QPR}=60^{\circ} $$

The angle subtended by an arc at the centre is double the angle subtended by it any point on the remaining part of the circle.

$$ \therefore \angle Q O R=2 \angle Q P R=2 \times 60^{\circ}=120^{\circ} $$

3. In $\triangle O Q R$,

$$ O Q=O R[\text { Radii of a circle }) $$

$\Rightarrow \angle \mathrm{ORQ}=\angle \mathrm{OQR}$ [Angles opposite to equal sides of a triangle are equal] Using angle sum property of a triangle,

$$ \begin{aligned} & \angle \mathrm{OQR}+\angle \mathrm{ORQ}+\angle \mathrm{QOR}=180^{\circ} \\ & \Rightarrow \angle \mathrm{OQR}+\angle \mathrm{OQR}+120^{\circ}=180^{\circ} \end{aligned} $$

$$ \begin{gathered} \Rightarrow 2 \angle O Q R=60^{\circ} \\ \therefore \angle O Q R=30^{\circ} \end{gathered} $$

4. Yes, it is true that points $P, Q$ and $R$ lie on the circle.

Understanding Circles

Circle: A collection of all points in a plane which are at a constant distance from a fixed point. The fixed point is called the centre of the circle and the constant distance is called the radius.

In figure, O is the centre, OA is the radius and AB is the diameter of the circle.

Chord: A line segment joining any two points on the circle. In figure, AC is the chord.

Diameter: Longest chord of the circle that passes through the centre of the circle.

Circumference: Length of the boundary of a circle.

Arc: Any part of the circumference of a circle.

In figure, PRQ is minor arc represented as PRQ and PSQ is major arc represented as PSQ.

Semi-circle: Parts of a circle that are divided by its diameter.

Segment: The region between a chord and either of its arcs (major or minor). The segment formed with a minor arc is called minor segment and that formed with a major arc is called major segment.

Sector: The region enclosed by an arc and the two radii joining the centre to the end points of the arc.

The sector corresponding to minor arc is called minor sector i.e., AOB and that corresponding to major arc is called major sector. i.e., AOBCA

• Heron’s Formula Class 9 Case Study Questions Maths Chapter 10
• Quadrilaterals Class 9 Case Study Questions Maths Chapter 8
• Triangles Class 9 Case Study Questions Maths Chapter 7
• Lines and Angles Class 9 Case Study Questions Maths Chapter 6
• Introduction to Euclid’s Geometry Class 9 Case Study Questions Maths Chapter 5
• Linear Equations in Two Variables Class 9 Case Study Questions Maths Chapter 4
• Coordinate Geometry Class 9 Case Study Questions Maths Chapter 3

Polynomials Class 9 Case Study Questions Maths Chapter 2

Number systems class 9 case study questions maths chapter 1, topics from which case study questions may be asked.

• Equal chords of a circle subtend equal angles at the center and (motivate) its converse.
• The perpendicular from the center of a circle to a chord bisects the chord and onversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.
• Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.
• The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
• Angles in the same segment of a circle are equal.
• If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.
• The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

Circles having same centre are called concentric circles.

Case study questions from the above given topic may be asked.

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Frequently Asked Questions (FAQs) on Circles Case Study

Q1: what is the definition of a circle in class 9 maths.

A1: A circle is defined as the collection of all points in a plane that are at a fixed distance (radius) from a fixed point called the center. In Class 9, the concept of a circle is used to study properties related to chords, tangents, arcs, and sectors.

Q2: What is the difference between a chord and a diameter?

A2: A chord is a line segment joining two points on the circumference of a circle, whereas the diameter is a special chord that passes through the center of the circle. The diameter is the longest chord of the circle and is equal to twice the radius.

Q3: What are tangents and how are they important in this chapter?

A3: A tangent to a circle is a line that touches the circle at exactly one point. Tangents are important in this chapter as you learn properties like “a tangent to a circle is perpendicular to the radius at the point of contact.” You also explore problems involving two tangents drawn from an external point.

Q4: What are the main properties of circles discussed in Class 9 Maths?

A4: The main properties include: (i) The radius is perpendicular to the tangent at the point of contact. (ii) Equal chords are equidistant from the center. (iii) The angle subtended by a chord at the center of the circle is twice the angle subtended by the same chord at any other point on the circumference.

Q5: What are cyclic quadrilaterals, and how are they related to circles?

A5: A cyclic quadrilateral is a four-sided figure where all its vertices lie on the circumference of a circle. The sum of the opposite angles in a cyclic quadrilateral is always 180°. This property is crucial in solving various geometric problems involving circles.

Q6: How can we prove that the angle subtended by a diameter on the circumference is 90 degrees?

A6: This is a key result derived from the properties of circles. Using the theorem “the angle subtended by a chord at the center is twice the angle subtended at any other point on the circumference,” and since a diameter subtends a straight angle (180°) at the center, it subtends a right angle (90°) on the circumference.

Q7: How many tangents can be drawn from a point outside a circle?

A7: From any point outside a circle, exactly two tangents can be drawn. These tangents have equal lengths from the external point to their points of contact on the circle.

Q8: What are the most important theorems in Chapter 9 of Class 9 Maths?

A8: The two key theorems in this chapter are: (i) The perpendicular from the center of a circle to a chord bisects the chord. (ii) The length of tangents drawn from an external point to a circle are equal.

Q9: Are there any online resources or tools available for practicing Circles case study questions?

A9: We provide case study questions for CBSE Class 9 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.

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CBSE MCQ for Class 9 Maths Chapter 3 Coordinate Geometry Free PDF

Guys, we are working very hard to provide you with TOPIC-WISE MCQs (as listed below). Till then, attached below is the Master PDF having all the topics. Hope you understand. Enjoy your preparation! All the Best!

CBSE MCQ for Class 9 Maths Chapter 3 Coordinate Geometry PDF

The CBSE MCQ for Class 9 Maths Chapter 3 Coordinate Geometry  are provided above, in detailed and free to download PDF format. The solutions are latest , comprehensive , confidence inspiring , with easy to understand explanation . To download NCERT Class 9 Solutions PDF for Free, just click ‘ Download pdf ’.

Other MCQ Questions for Maths Class 9th CBSE

• CBSE MCQ for Class 9 Maths Chapter 1 Number System
• CBSE MCQ for Class 9 Maths Chapter 2 Polynomials
• CBSE MCQ for Class 9 Maths Chapter 4 Linear Equations in Two Variables
• CBSE MCQ for Class 9 Maths Chapter 5 Euclid’s Geometry

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

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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

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