{
  "title": "Mode - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Mode is the value that appears:", "options": {"A": "Least frequently", "B": "Most frequently", "C": "In the middle", "D": "First"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "For data: 2,3,4,2,5,2, the mode is:", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Data can have:", "options": {"A": "One mode", "B": "Multiple modes", "C": "No mode", "D": "All of these"}, "correct_answer": "D"},
    {"id": 4, "difficulty": "easy", "question": "If all values appear once, mode is:", "options": {"A": "First value", "B": "Last value", "C": "No mode", "D": "Middle value"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "For data: 5,6,7,8,9, mode is:", "options": {"A": "5", "B": "7", "C": "9", "D": "No mode"}, "correct_answer": "D"},
    {"id": 6, "difficulty": "easy", "question": "Mode is useful for:", "options": {"A": "Finding most common value", "B": "Finding average", "C": "Finding middle", "D": "Finding range"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "For data: 1,1,2,2,3,3, mode is:", "options": {"A": "1", "B": "2", "C": "3", "D": "1,2,3"}, "correct_answer": "D"},
    {"id": 8, "difficulty": "easy", "question": "Mode can be found for:", "options": {"A": "Numerical data", "B": "Categorical data", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "For grouped data, mode is in class with:", "options": {"A": "Lowest frequency", "B": "Highest frequency", "C": "Middle frequency", "D": "Any frequency"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "Data with two modes is called:", "options": {"A": "Unimodal", "B": "Bimodal", "C": "Trimodal", "D": "Multimodal"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "For shoe sizes: 7,8,8,9,9,9,10, mode is:", "options": {"A": "7", "B": "8", "C": "9", "D": "10"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "Mode is a measure of:", "options": {"A": "Central tendency", "B": "Dispersion", "C": "Correlation", "D": "Probability"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "For colors: Red,Blue,Red,Green,Red, mode is:", "options": {"A": "Red", "B": "Blue", "C": "Green", "D": "All"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "If one value appears 5 times and others once, mode is:", "options": {"A": "That value", "B": "First value", "C": "Last value", "D": "No mode"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Mode is not affected by:", "options": {"A": "Extreme values", "B": "Frequency", "C": "Most common value", "D": "All values"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "For data: 10,20,30,40,50, mode:", "options": {"A": "10", "B": "30", "C": "50", "D": "No mode"}, "correct_answer": "D"},
    {"id": 17, "difficulty": "easy", "question": "In frequency table, mode has:", "options": {"A": "Lowest frequency", "B": "Highest frequency", "C": "Zero frequency", "D": "Equal frequency"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "Mode can be found by:", "options": {"A": "Looking at data", "B": "Calculation", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "For test scores: 85,90,85,95,90,85, mode:", "options": {"A": "85", "B": "90", "C": "95", "D": "85 and 90"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Mode is always:", "options": {"A": "One of the data values", "B": "Not in data", "C": "Average of data", "D": "Middle value"}, "correct_answer": "A"},
    
    {"id": 21, "difficulty": "medium", "question": "Find mode: 12,15,12,18,15,12,20", "options": {"A": "12", "B": "15", "C": "18", "D": "20"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Find mode: 5,7,3,5,9,7,5,7,2", "options": {"A": "5", "B": "7", "C": "5 and 7", "D": "No mode"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "Data: 10,12,14,16,18,20. Mode?", "options": {"A": "10", "B": "14", "C": "18", "D": "No mode"}, "correct_answer": "D"},
    {"id": 24, "difficulty": "medium", "question": "Ages: 14,15,16,14,17,15,14,18. Mode?", "options": {"A": "14", "B": "15", "C": "16", "D": "17"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Marks: 45,50,55,60,45,50,55,45,60,50. Mode?", "options": {"A": "45", "B": "50", "C": "45 and 50", "D": "55"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "Heights: 150,155,160,155,165,160,155. Mode?", "options": {"A": "150", "B": "155", "C": "160", "D": "165"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "Data: 2.5,3.0,2.5,3.5,3.0,2.5,4.0. Mode?", "options": {"A": "2.5", "B": "3.0", "C": "3.5", "D": "4.0"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "If mode is 25 and data has values 20,25,30,25,35, frequency of 25?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "Find mode: 100,120,150,100,130,120,150,100", "options": {"A": "100", "B": "120", "C": "150", "D": "100 and 150"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Data: A,B,C,A,B,D,A,B,C,A. Mode?", "options": {"A": "A", "B": "B", "C": "C", "D": "D"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Temperatures: 20,22,25,22,28,25,22,30. Mode?", "options": {"A": "20", "B": "22", "C": "25", "D": "28"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "If data has mode 15 and 20, it is:", "options": {"A": "Unimodal", "B": "Bimodal", "C": "Trimodal", "D": "No mode"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "Weights: 45,50,55,50,60,55,50,65. Mode?", "options": {"A": "45", "B": "50", "C": "55", "D": "60"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "Data: 7,8,9,10,11,12,13. Mode?", "options": {"A": "7", "B": "10", "C": "13", "D": "No mode"}, "correct_answer": "D"},
    {"id": 35, "difficulty": "medium", "question": "Scores: 75,80,85,90,75,85,80,75,90,85. Mode?", "options": {"A": "75", "B": "80", "C": "85", "D": "75 and 85"}, "correct_answer": "D"},
    {"id": 36, "difficulty": "medium", "question": "Find mode: 12,15,18,12,20,15,18,12,15,20", "options": {"A": "12", "B": "15", "C": "12 and 15", "D": "18"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "If all values appear equal times, mode:", "options": {"A": "First value", "B": "All values", "C": "No mode", "D": "Last value"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "Data: 3.2,4.5,3.2,5.1,4.5,3.2,6.0. Mode?", "options": {"A": "3.2", "B": "4.5", "C": "5.1", "D": "6.0"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Ages: 10,12,11,10,13,12,11,10,14. Mode?", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Find mode: 25,30,35,40,25,30,35,25,40,30,35", "options": {"A": "25", "B": "30", "C": "35", "D": "25,30,35"}, "correct_answer": "D"},
    {"id": 41, "difficulty": "medium", "question": "Data: X,Y,Z,X,Y,X,W,X,Y. Mode?", "options": {"A": "X", "B": "Y", "C": "Z", "D": "W"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "If mode is 42 and 48, data is:", "options": {"A": "Unimodal", "B": "Bimodal", "C": "Trimodal", "D": "No mode"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "Find mode: 18,22,25,30,18,25,22,30,18,25", "options": {"A": "18", "B": "22", "C": "25", "D": "18 and 25"}, "correct_answer": "D"},
    {"id": 44, "difficulty": "medium", "question": "Marks: 55,60,65,70,55,65,60,55,70,65. Mode?", "options": {"A": "55", "B": "60", "C": "65", "D": "55 and 65"}, "correct_answer": "D"},
    {"id": 45, "difficulty": "medium", "question": "Data: 1,3,2,1,4,3,2,1,4. Mode?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Heights: 160,165,170,165,175,170,165,180. Mode?", "options": {"A": "160", "B": "165", "C": "170", "D": "175"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "Find mode: 7,5,9,7,6,5,8,7,6,5", "options": {"A": "5", "B": "7", "C": "5 and 7", "D": "6"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "Data: 45,55,65,45,55,75,45,55. Mode?", "options": {"A": "45", "B": "55", "C": "45 and 55", "D": "65"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "medium", "question": "Temperatures: 18.5,20.0,22.5,20.0,25.0,22.5,20.0. Mode?", "options": {"A": "18.5", "B": "20.0", "C": "22.5", "D": "25.0"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "medium", "question": "If data has three modes, it is:", "options": {"A": "Unimodal", "B": "Bimodal", "C": "Trimodal", "D": "Multimodal"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "medium", "question": "Find mode: 12,18,24,30,12,18,24,36,12,18", "options": {"A": "12", "B": "18", "C": "12 and 18", "D": "24"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "medium", "question": "Data: 8,16,24,32,8,16,24,40,8,16,24. Mode?", "options": {"A": "8", "B": "16", "C": "24", "D": "8,16,24"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "medium", "question": "Ages: 13,15,17,19,13,15,17,21,13,15,17. Mode?", "options": {"A": "13", "B": "15", "C": "17", "D": "13,15,17"}, "correct_answer": "D"},
    {"id": 54, "difficulty": "medium", "question": "Find mode: 150,160,170,180,150,160,170,190,150,160", "options": {"A": "150", "B": "160", "C": "150 and 160", "D": "170"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "Data: 3.5,4.2,5.0,3.5,4.2,5.8,3.5,4.2. Mode?", "options": {"A": "3.5", "B": "4.2", "C": "3.5 and 4.2", "D": "5.0"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "If mode is only one value, data is:", "options": {"A": "Unimodal", "B": "Bimodal", "C": "Trimodal", "D": "No mode"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Find mode: 22,28,25,31,22,28,25,34,22,28", "options": {"A": "22", "B": "28", "C": "22 and 28", "D": "25"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "Data: 100,120,140,160,100,120,140,180,100,120. Mode?", "options": {"A": "100", "B": "120", "C": "100 and 120", "D": "140"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "medium", "question": "Scores: 85,90,95,100,85,90,95,105,85,90. Mode?", "options": {"A": "85", "B": "90", "C": "85 and 90", "D": "95"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "Find mode: 5,10,15,20,5,10,15,25,5,10,15", "options": {"A": "5", "B": "10", "C": "15", "D": "5,10,15"}, "correct_answer": "D"},
    {"id": 61, "difficulty": "medium", "question": "Data: 14,16,18,20,14,16,18,22,14,16. Mode?", "options": {"A": "14", "B": "16", "C": "14 and 16", "D": "18"}, "correct_answer": "C"},
    {"id": 62, "difficulty": "medium", "question": "If all frequencies are different, mode is:", "options": {"A": "Value with highest frequency", "B": "Value with lowest frequency", "C": "First value", "D": "No mode"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Find mode: 30,40,50,60,30,40,50,70,30,40", "options": {"A": "30", "B": "40", "C": "30 and 40", "D": "50"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "Data: 2,4,6,8,2,4,6,10,2,4,6. Mode?", "options": {"A": "2", "B": "4", "C": "6", "D": "2,4,6"}, "correct_answer": "D"},
    {"id": 65, "difficulty": "medium", "question": "Heights: 155,160,165,170,155,160,165,175,155,160. Mode?", "options": {"A": "155", "B": "160", "C": "155 and 160", "D": "165"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "Find mode: 11,22,33,44,11,22,33,55,11,22", "options": {"A": "11", "B": "22", "C": "11 and 22", "D": "33"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "Data: 6,12,18,24,6,12,18,30,6,12. Mode?", "options": {"A": "6", "B": "12", "C": "6 and 12", "D": "18"}, "correct_answer": "C"},
    {"id": 68, "difficulty": "medium", "question": "If two values have same highest frequency, data has:", "options": {"A": "One mode", "B": "Two modes", "C": "No mode", "D": "Three modes"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "Find mode: 9,18,27,36,9,18,27,45,9,18", "options": {"A": "9", "B": "18", "C": "9 and 18", "D": "27"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "Data: 20,25,30,35,20,25,30,40,20,25. Mode?", "options": {"A": "20", "B": "25", "C": "20 and 25", "D": "30"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "Marks: 65,70,75,80,65,70,75,85,65,70. Mode?", "options": {"A": "65", "B": "70", "C": "65 and 70", "D": "75"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "medium", "question": "Find mode: 4,8,12,16,4,8,12,20,4,8", "options": {"A": "4", "B": "8", "C": "4 and 8", "D": "12"}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "Data: 15,30,45,60,15,30,45,75,15,30. Mode?", "options": {"A": "15", "B": "30", "C": "15 and 30", "D": "45"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "If three values have same highest frequency, modes?", "options": {"A": "1", "B": "2", "C": "3", "D": "0"}, "correct_answer": "C"},
    {"id": 75, "difficulty": "medium", "question": "Find mode: 10,20,30,40,10,20,30,50,10,20", "options": {"A": "10", "B": "20", "C": "10 and 20", "D": "30"}, "correct_answer": "C"},
    {"id": 76, "difficulty": "medium", "question": "Data: 35,40,45,50,35,40,45,55,35,40. Mode?", "options": {"A": "35", "B": "40", "C": "35 and 40", "D": "45"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "Temperatures: 18,20,22,24,18,20,22,26,18,20. Mode?", "options": {"A": "18", "B": "20", "C": "18 and 20", "D": "22"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "Find mode: 50,60,70,80,50,60,70,90,50,60", "options": {"A": "50", "B": "60", "C": "50 and 60", "D": "70"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "Data: 25,35,45,55,25,35,45,65,25,35. Mode?", "options": {"A": "25", "B": "35", "C": "25 and 35", "D": "45"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "Mode is best for:", "options": {"A": "Categorical data", "B": "Finding average income", "C": "When extremes matter", "D": "All numerical data"}, "correct_answer": "A"},
    
    {"id": 81, "difficulty": "hard", "question": "For grouped data with modal class 20-30, f1=15, f0=10, f2=12, h=10. Mode = ?", "options": {"A": "23.33", "B": "24.44", "C": "25.55", "D": "26.66"}, "correct_answer": "D"},
    {"id": 82, "difficulty": "hard", "question": "Data: 12,15,18,12,20,15,18,12,15,20,18,12. Find mode(s).", "options": {"A": "12", "B": "15", "C": "12 and 15", "D": "12,15,18"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "For frequency distribution: Value:10 Freq:3, Value:20 Freq:5, Value:30 Freq:5, Value:40 Freq:2. Mode?", "options": {"A": "20", "B": "30", "C": "20 and 30", "D": "10"}, "correct_answer": "C"},
    {"id": 84, "difficulty": "hard", "question": "Modal class has frequency 25, previous class 18, next class 20, class width 10, lower limit 30. Mode?", "options": {"A": "34.44", "B": "35.55", "C": "36.66", "D": "37.77"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "Data has three values with frequency 7 each, others less. Number of modes?", "options": {"A": "0", "B": "1", "C": "3", "D": "7"}, "correct_answer": "C"},
    {"id": 86, "difficulty": "hard", "question": "For grouped data: 10-20:5,20-30:12,30-40:18,40-50:10,50-60:5. Modal class?", "options": {"A": "20-30", "B": "30-40", "C": "40-50", "D": "50-60"}, "correct_answer": "B"},
    {"id": 87, "difficulty": "hard", "question": "If mode=25 and mean=30, distribution is likely:", "options": {"A": "Symmetric", "B": "Positively skewed", "C": "Negatively skewed", "D": "Bimodal"}, "correct_answer": "C"},
    {"id": 88, "difficulty": "hard", "question": "For data with values 5,10,15,20,25 each appearing 4 times, mode?", "options": {"A": "5", "B": "15", "C": "All values", "D": "No mode"}, "correct_answer": "C"},
    {"id": 89, "difficulty": "hard", "question": "Modal class: 40-50, f1=28, f0=20, f2=24, h=10. Mode?", "options": {"A": "43.33", "B": "44.44", "C": "45.55", "D": "46.66"}, "correct_answer": "D"},
    {"id": 90, "difficulty": "hard", "question": "Data: 18,22,25,30,18,25,22,30,18,25,22,18. Which has highest frequency?", "options": {"A": "18", "B": "22", "C": "25", "D": "30"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "For grouped data with equal class widths, mode formula uses:", "options": {"A": "Only frequencies", "B": "Frequencies and class limits", "C": "Only class marks", "D": "Only total frequency"}, "correct_answer": "B"},
    {"id": 92, "difficulty": "hard", "question": "If in grouped data, two classes have same highest frequency, mode:", "options": {"A": "Does not exist", "B": "Is average of class marks", "C": "Can be calculated for each", "D": "Is undefined"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "Data has mean=35, median=33, mode=30. Distribution is:", "options": {"A": "Symmetric", "B": "Positively skewed", "C": "Negatively skewed", "D": "Bimodal"}, "correct_answer": "C"},
    {"id": 94, "difficulty": "hard", "question": "For continuous data, mode is point where:", "options": {"A": "Frequency is maximum", "B": "Curve has peak", "C": "Both A and B", "D": "Neither"}, "correct_answer": "C"},
    {"id": 95, "difficulty": "hard", "question": "If mode < median < mean, distribution is:", "options": {"A": "Symmetric", "B": "Positively skewed", "C": "Negatively skewed", "D": "Uniform"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "For bimodal data, there are:", "options": {"A": "Two peaks", "B": "One peak", "C": "No peaks", "D": "Flat distribution"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "Mode for grouped data formula: Mode = L + [(f1-f0)/(2f1-f0-f2)]×h. L is:", "options": {"A": "Lower limit of modal class", "B": "Upper limit", "C": "Class mark", "D": "Class width"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "If all classes have same frequency, mode:", "options": {"A": "First class", "B": "Last class", "C": "All classes", "D": "Cannot determine"}, "correct_answer": "D"},
    {"id": 99, "difficulty": "hard", "question": "Data with no mode is called:", "options": {"A": "Unimodal", "B": "Bimodal", "C": "Amodal", "D": "Uniform"}, "correct_answer": "C"},
    {"id": 100, "difficulty": "hard", "question": "For perfectly symmetric distribution, mode, median, mean:", "options": {"A": "Are equal", "B": "Mode<median<mean", "C": "Mean<median<mode", "D": "All different"}, "correct_answer": "A"}
  ]
}