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Class 8 Mathematics Chapter 13 Introduction To Graphs

Chapter 13 of Class 8 Mathematics, Introduction to Graphs, familiarizes students with the fundamental concepts of graphical data representation. This quiz evaluates students' understanding of various graph types, including bar graphs, pie charts, histograms, and line graphs, each serving a specific purpose in data visualization. Students will learn to plot points on the Cartesian plane, comprehend the significance of coordinates, and interpret data trends effectively. The quiz emphasizes the practical applications of graphs in real-life scenarios, enhancing students' analytical skills and their ability to present data in a clear and concise manner.

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Category: Introduction

1. A line graph shows the temperature of a patient over time. At 6 a.m., the temperature was $37^\circ$C, at 10 a.m., it was $40^\circ$C, and at 2 p.m., it dropped to $38^\circ$C. What is the average temperature during this period?

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Category: Introduction

2. What does the vertical line (y-axis) in a line graph usually represent?

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Category: Purpose of Graphs

3. A line graph displays the temperature of a patient over time. At 6 a.m., the temperature was $37^\circ$C, at 10 a.m., it was $40^\circ$C, at 2 p.m., it was $38^\circ$C, and at 6 p.m., it was $35^\circ$C. What is the difference between the highest and lowest temperatures recorded?

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Category: Purpose of Graphs

4. Why is graphical presentation preferred over tabular presentation of data?

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Category: Graphs provide a visual representation of data.

5. (A) Graphical presentation of data is easier to understand than tabular presentation.
(R) Graphs provide a visual representation of data, making trends and comparisons clearer.

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Category: Graphs provide a visual representation of data.

6. (A) Graphs are visual representations of data.
(R) They make it easier to understand numerical facts quickly and clearly.

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Category: They help in understanding numerical facts quickly and clearly.

7. A table shows the population growth of two cities over 10 years. City A's population increased by 20\% while City B's population increased by 50\%. Which statement is most accurate?

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Category: They help in understanding numerical facts quickly and clearly.

8. (A) Graphs are visual representations of data collected.
(R) Graphs help in understanding numerical facts quickly and clearly.

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Category: Comparison between Tables and Graphs

9. In what scenario is a graphical presentation of data particularly useful?

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Category: Comparison between Tables and Graphs

10. For comparing the quarterly performance of two different companies, which method is more effective and why?

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Category: Graphs make trends and relationships easier to understand.

11. (A) A line graph is always more effective in presenting data trends than a table.
(R) Line graphs provide a visual representation that makes it easier to identify patterns like increases, decreases, or constant trends over time.

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Category: Graphs make trends and relationships easier to understand.

12. A company records its monthly sales data over a year and plots it on a line graph. The graph shows a consistent upward trend from January to June, then a sharp decline in July, followed by a steady increase from August to December. What can be inferred about the company's sales performance?

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Category: Common Types of Graphs

13. (A) A line graph showing the relationship between time and temperature is always a linear graph.
(R) A linear graph is defined as a graph where the relationship between the dependent and independent variables is represented by a straight line.

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Category: Common Types of Graphs

14. Why is graphical presentation of data preferred?

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Category: Line graphs

15. What is the primary purpose of a line graph?

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Category: Line graphs

16. A line graph shows the relationship between time (in hours) and the distance traveled by a car. At 10 a.m., the car has traveled 50 km, and at 12 p.m., it has traveled 150 km. What is the speed of the car in km/h?

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Category: Bar graphs

17. A bar graph displays the rainfall in millimeters for four cities in a week. City X received 40 mm, City Y received 30 mm, City Z received 50 mm, and City W received 20 mm. Which city received the least amount of rainfall?

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Category: Bar graphs

18. (A) Bar graphs are used to represent categorical data.
(R) Bar graphs use vertical or horizontal bars to show the frequency of data in each category.

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Category: Pie charts

19. A pie chart represents the distribution of a company's expenses into four categories: \textit{A}, \textit{B}, \textit{C}, and \textit{D}. If the angle corresponding to \textit{A} is $90^\circ$, \textit{B} is $120^\circ$, and \textit{C} is $60^\circ$, what is the percentage of expenses allocated category \textit{D}?

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Category: Pie charts

20. What is the total angle in a pie chart?

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Category: A line graph displays data that changes continuously over time.

21. A line graph shows the temperature (\$^\circ\text{C}\$) recorded at different times of the day as follows: 6 a.m. (37), 10 a.m. (40), 2 p.m. (38), 6 p.m. (35). At which time was the temperature the highest?

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Category: A line graph displays data that changes continuously over time.

22. What does the x-axis represent in a line graph that displays data over time?

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Category: Example: Time-Temperature Graph

23. (A) A time-temperature graph is used to display data that changes continuously over periods of time.
(R) A line graph is a visual representation of data collected, and it is easier to understand trends or comparisons.

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Category: Example: Time-Temperature Graph

24. In a time-temperature graph, the temperature at 6 a.m. is 37°C, and at 2 p.m., it is 38°C. What is the increase in temperature between 6 a.m. and 2 p.m.?

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Category: Understanding a time-temperature graph by plotting temperature readings at different hours.

25. A patient's temperature was recorded every hour. The temperature at 6 a.m. was 37°C, and at 8 a.m., it was 39°C. What was the percentage increase in temperature between 6 a.m. and 8 a.m.?

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Category: Understanding a time-temperature graph by plotting temperature readings at different hours.

26. A patient's temperature was recorded every hour. The temperature at 1 p.m. was 38°C, and at 2 p.m., it was 37.5°C. What was the average rate of change in temperature between 1 p.m. and 2 p.m.?

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Category: Identifying trends in the graph.

27. The following line graph shows the temperature of a patient recorded at different times of the day. What was the increase in temperature from 6 a.m. to 10 a.m.?

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Category: Identifying trends in the graph.

28. What does an upward trend in a graph typically indicate?

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Category: Understanding Line Graphs

29. Using the same line graph of Renu's temperature, if the trend of decreasing temperature continues at the same rate from 2 p.m. to 6 p.m., what would be the expected temperature at 4 p.m.?

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Category: Understanding Line Graphs

30. What does the horizontal line (x-axis) typically represent in a line graph?

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Category: Performance Graph of Two Batsmen

31. In how many matches did Batsman A score less than 40 runs?

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Category: Performance Graph of Two Batsmen

32. (A) The performance graph of Batsman A shows a consistently increasing trend over the matches, indicating a steady improvement in his batting skills.
(R) A consistently increasing trend in a performance graph suggests that the batsman is adapting well to different bowling strategies and improving with each match.

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Category: Analyzing cricket performance using a line graph.

33. (A) Batsman A is more consistent than Batsman B because his highest score is higher.
(R) Consistency in cricket performance is determined by the ability to maintain a steady level of runs across matches.

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Category: Analyzing cricket performance using a line graph.

34. Which line in the graph represents the total runs scored by Batsman A?

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Category: Comparing runs scored in different matches.

35. A player scored 150 runs in Match 1 and 200 runs in Match 2. What is the absolute difference between the runs scored in these two matches?

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Category: Comparing runs scored in different matches.

36. If Team B scored 320 runs in their first innings and 150 runs in their second innings, what is the difference between the runs scored in the first and second innings?

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Category: Identifying trends and consistency in scores.

37. (A) The mean score of a class increases if the highest score in the class increases.
(R) The mean is calculated by dividing the sum of all scores by the number of scores.

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Category: Identifying trends and consistency in scores.

38. (A) The standard deviation of a dataset is zero if all the data points are identical.
(R) Standard deviation measures the variability or dispersion of a dataset.

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Category: Distance-Time Graph

39. What does a horizontal line on a distance-time graph represent?

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Category: Distance-Time Graph

40. (A) The car was moving at a constant speed during the entire journey from City P to City Q.
(R) The distance-time graph for the car's journey is a straight line with a constant slope.

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Category: Understanding the motion of a car using a distance-time graph.

41. At what time did the car reach City Q?

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Category: Understanding the motion of a car using a distance-time graph.

42. A car's distance-time graph shows it travels 50 km in the first hour, stops for one hour, then travels 150 km in the next two hours. What is the total time taken for the journey if the car was moving at a constant speed after stopping?

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Category: Identifying changes in speed.

43. An object starts from rest and accelerates uniformly at $3 \text{ m/s}^2$. What is its speed after traveling $54 \text{ m}$?

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Category: Identifying changes in speed.

44. (A) If the speed of an object increases uniformly over time, its acceleration is constant.
(R) Uniform increase in speed implies a constant rate of change in velocity.

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Category: Analyzing stopping points using a horizontal segment in the graph.

45. What does a horizontal segment on a graph of distance vs. time represent?

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Category: Analyzing stopping points using a horizontal segment in the graph.

46. (A) The horizontal segment in the graph between 11 a.m. and 12 noon indicates that the car was stationary during this period.
(R) During the period of 11 a.m. to 12 noon, the distance of the car from City P remained constant at 200 km.

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Category: Some Applications of Graphs

47. A bank offers 10\% simple interest on deposits by senior citizens. If a senior citizen deposits \$500, what will be the total amount after one year?

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Category: Some Applications of Graphs

48. A bank offers 10\% Simple Interest on deposits by senior citizens. If Rs 250 is deposited, what is the annual simple interest earned?

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Category: Concept of Independent and Dependent Variables

49. The cost (\$C\$) of petrol depends on the number of litres (\$L\$) purchased. If the cost increases by \$25 for every 5 litres purchased, and there is no fixed charge, what is the relationship between \$C\$ and \$L\$?

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Category: Concept of Independent and Dependent Variables

50. The amount of water used in a household is directly proportional to the water bill. Which of the following is the independent variable?

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Category: Independent variable: The factor that is controlled (e.g., time, quantity).

51. If the cost of 10 litres of petrol is \$500, what will be the cost of 20 litres of petrol based on the given relationship?

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Category: Independent variable: The factor that is controlled (e.g., time, quantity).

52. A graph represents the relationship between time (independent variable) and the distance traveled by a car. The slope of the graph at a particular point is 60 km/h. What does this slope represent in the context of the graph?

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Category: Dependent variable: The factor that depends on the independent variable (e.g., cost, speed).

53. A company produces a product where the cost (\$C) depends on the number of units produced (\$x). If the cost is given by \$C = 50 + 10x, what is the cost when 20 units are produced?

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Category: Dependent variable: The factor that depends on the independent variable (e.g., cost, speed).

54. If the cost of 10 litres of petrol is \$500, what is the dependent variable in this scenario?

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Category: Quantity and Cost

55. A company produces a product with a fixed cost of \$5000 and a variable cost of \$20 per unit. The selling price per unit is \$50. What is the break-even point in terms of units sold?

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Category: Quantity and Cost

56. A car's petrol tank holds up to 30 litres. If the cost of petrol is \$50 per litre, what is the total cost to fill the tank completely?

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Category: Plotting a graph to show the cost of petrol for different quantities.

57. Using the graph of cost versus quantity of petrol, you estimated that the cost for 12 litres of petrol is \$600. What is the constant of variation?

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Category: Plotting a graph to show the cost of petrol for different quantities.

58. In the context of purchasing petrol for a car, which of the following is the independent variable?

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Category: Using the graph to estimate costs for intermediate values.

59. (A) The graph of a situation where two quantities are in direct variation will always be linear.
(R) In direct variation, the ratio of the two quantities remains constant.

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Category: Using the graph to estimate costs for intermediate values.

60. A graph depicting the relationship between the number of hours worked and the total earnings has a slope of 15. If the base pay is \$50, what would be the total earnings for working 8 hours?

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Category: Principal and Simple Interest

61. If the simple interest on a principal of \$1500 at a rate of 6\% per annum is \$180, how many years has the money been invested?

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Category: Principal and Simple Interest

62. (A) For a deposit of 400, the annual simple interest at 10\% is 40.
(R) The formula for calculating simple interest is $I = P \times R \times T$, where $P$ is the principal amount, $R$ is the rate of interest, and $T$ is the time period in years.

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Category: Plotting the relationship between money deposited and the simple interest earned.

63. (A) The graph of the relationship between the sum deposited and the simple interest earned is a straight line passing through the origin.
(R) Simple interest is directly proportional to the principal amount deposited.

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Category: Plotting the relationship between money deposited and the simple interest earned.

64. A person deposits \$5000 in a bank that offers a simple interest rate of 5\% per annum. What will be the total amount after 3 years?

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Category: Using the graph to determine missing values.

65. A graph shows the distance covered by a car over time. The car covers 30 km in the first hour, 60 km in the second hour, and 90 km in the third hour. What is the distance covered in the fourth hour?

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Category: Using the graph to determine missing values.

66. A patient's temperature is recorded at different times of the day. The temperature at 10 a.m. was $38^\circ C$ and at 2 p.m. it was $39^\circ C$. If the temperature increased linearly between these two times, what would be the expected temperature at 12 p.m.?

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Category: Time and Distance

67. A car travels at a speed of 80 km/h for the first half of its journey and then increases its speed to 120 km/h for the second half. If the total distance of the journey is 480 km, what is the average speed of the car for the entire journey?

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Category: Time and Distance

68. A car travels from City P to City Q at a speed of 60 km/h. It stops at a rest area for 30 minutes and then continues at the same speed. If the total distance between the cities is 180 km, what is the total time taken for the journey?

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Category: Representing the journey of a vehicle using a distance-time graph.

69. A car starts from City P at 8 a.m. and reaches City Q at 2 p.m. If the distance between the cities is 350 km, what is the total time taken for the journey?

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Category: Representing the journey of a vehicle using a distance-time graph.

70. In a distance-time graph, if the line is horizontal, what can be inferred about the vehicle?

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Category: Identifying periods of rest and calculating speed.

71. (A) The courier-person cycled fastest between 10 a.m. and 11 a.m.
(R) The slope of the distance-time graph is steepest between 10 a.m. and 11 a.m.

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Category: Identifying periods of rest and calculating speed.

72. A cyclist travels from Town A to Town B with a distance-time graph showing that he traveled 10 km in the first 30 minutes, rested for 15 minutes, and then traveled another 20 km in the next 45 minutes. What is the average speed of the cyclist during his journey?

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Category: Drawing Graphs

73. (A) The slope of a straight-line graph represents the rate of change between two variables.
(R) The slope is calculated as the ratio of the vertical change to the horizontal change between two points on the graph.

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Category: Drawing Graphs

74. Using the graph plotting cost (\$) against liters of petrol, if 12 litres of petrol costs \$600, what would be the cost for 18 litres?

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Category: Steps to Plot a Graph

75. What is the first step in plotting a graph?

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Category: Steps to Plot a Graph

76. The cost of petrol is \$50 per litre. If the number of litres is plotted on the horizontal axis and the total cost on the vertical axis, which of the following points will lie on the graph?

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Category: Choosing an appropriate scale.

77. If the horizontal axis represents time with a scale of 1 unit = 5 minutes and the vertical axis represents distance with a scale of 1 unit = 15 meters, how many units on the graph represent 20 minutes and 75 meters?

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Category: Choosing an appropriate scale.

78. A cyclist covers 20 km every hour. If the horizontal axis represents time in hours and the vertical axis represents distance in km, which scale would be most appropriate to plot this data?

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Category: Labeling the axes.

79. What is the correct label for the vertical axis in a graph showing temperature over time?

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Category: Labeling the axes.

80. A graph is plotted showing the velocity of a car over time. The velocity increases at a constant rate. What is the most appropriate label for the x-axis?

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Category: Plotting given data points.

81. (A) The graph of a linear equation in two variables is always a straight line.
(R) A straight line represents the relationship where the rate of change is constant.

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Category: Plotting given data points.

82. The cost of petrol is directly proportional to the number of litres purchased. If 12 litres of petrol cost \$144, how much will 18 litres cost?

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Category: Drawing a line or curve based on the data.

83. A patient's temperature is recorded every 4 hours as follows: (6 a.m., 37°C), (10 a.m., 40°C), (2 p.m., 38°C), (6 p.m., 35°C). What was the patient's temperature at 12 p.m. if the trend continues linearly?

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Category: Drawing a line or curve based on the data.

84. (A) The graph of the distance travelled by a car versus time is a linear graph.
(R) The speed of the car remains constant throughout the journey.

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Category: Examples of Graphs

85. What is the shape of the graph of the equation $y = x^2$?

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Category: Examples of Graphs

86. A bank offers 8\% simple interest on deposits. If a deposit of \$500 earns \$40 in interest, how much would a deposit of \$1000 earn in interest according to the linear graph representing this relationship?

87 / 100

Category: Cost of Apples vs. Number of Apples

87. A graph is plotted with the number of apples on the x-axis and the cost in rupees on the y-axis. The equation of the line is $y = 5x$. If the cost of 7 apples is to be determined, what will be the cost?

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Category: Cost of Apples vs. Number of Apples

88. A graph is plotted with the number of apples on the x-axis and the cost in rupees on the y-axis. The graph passes through the points (2,10) and (4,20). If the cost per apple remains constant, what will be the cost of 6 apples?

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Category: Distance Travelled by a Car vs. Time

89. A car travels at a constant speed. If it covers 30 km in 1 hour, how much distance will it cover in 3 hours?

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Category: Distance Travelled by a Car vs. Time

90. On a graph of distance travelled by a car vs. time, if the car has covered 75 km, what time corresponds to this distance on the graph?

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Category: Distance Travelled by a Car vs. Time

91. (A) The slope of the distance-time graph for a car moving with uniform acceleration increases linearly with time.
(R) The velocity of the car increases uniformly with time when the acceleration is constant.

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Category: Interest on Deposits for a Year

92. A deposit of \$3000 earns an annual interest of \$240. If the bank offers the same rate of interest, what will be the interest earned on a deposit of \$5000?

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Category: Interest on Deposits for a Year

93. A bank offers 10\% simple interest on deposits for a year. If the graph of deposit (x-axis) vs. simple interest earned (y-axis) is plotted, what will be the slope of the line?

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Category: Interest on Deposits for a Year

94. (A) The graph of interest earned on a fixed deposit over one year is a straight line.
(R) The interest earned on a fixed deposit for one year is calculated using simple interest, which is linear.

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Category: Side of a Square vs. Perimeter

95. Which graph correctly represents the relationship between the side and perimeter of a square?

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Category: Side of a Square vs. Perimeter

96. (A) The graph of the side of a square versus its perimeter is a straight line.
(R) The perimeter of a square is directly proportional to its side length.

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Category: Side of a Square vs. Perimeter

97. A square has a perimeter of 16 cm. If each side of the square is doubled, what will be the new perimeter?

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Category: Side of a Square vs. Area

98. (A) The graph of side of a square vs. its area is a straight line passing through the origin.
(R) The relationship between the side of a square and its area is linear.

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Category: Side of a Square vs. Area

99. If the side of a square is increased by 50\%, what will be the percentage increase in its area?

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Category: Side of a Square vs. Area

100. For a square with side length 5 cm, what is its area?

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