{
  "title": "Ogive Curves - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Ogive is a graph of? 📈", "options": {"A": "Frequency", "B": "Cumulative frequency", "C": "Relative frequency", "D": "Class marks"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "The two types of ogives are? 2️⃣", "options": {"A": "Less than & More than", "B": "Greater than & Equal to", "C": "Upper & Lower", "D": "Simple & Weighted"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Ogive is also called? 📊", "options": {"A": "Frequency polygon", "B": "Cumulative frequency curve", "C": "Histogram", "D": "Bar chart"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "To draw 'less than' ogive, we plot? 📍", "options": {"A": "Upper limits vs cf", "B": "Lower limits vs cf", "C": "Midpoints vs cf", "D": "Class marks vs f"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "The point where both ogives intersect gives? ❌", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "Range"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "For 'more than' ogive, curve is? 📉", "options": {"A": "Increasing", "B": "Decreasing", "C": "Constant", "D": "U-shaped"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "To find median from ogive, draw horizontal at y=? ↔️", "options": {"A": "N/2", "B": "N/4", "C": "3N/4", "D": "N"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Ogive is always? 📈", "options": {"A": "Smooth curve", "B": "Step graph", "C": "Straight line", "D": "Zigzag"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "First quartile Q1 is found at y=? 1️⃣", "options": {"A": "N/4", "B": "N/2", "C": "3N/4", "D": "N"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Third quartile Q3 is at y=? 3️⃣", "options": {"A": "N/4", "B": "N/2", "C": "3N/4", "D": "N"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "The y-coordinate of intersection point of both ogives is? 📍", "options": {"A": "N/2", "B": "N", "C": "0", "D": "N/4"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Ogive can be used to find? 🎯", "options": {"A": "Median", "B": "Quartiles", "C": "Percentiles", "D": "All"}, "correct_answer": "D"},
    {"id": 13, "difficulty": "easy", "question": "For 'less than' ogive, first point is usually at? 🎯", "options": {"A": "(0,0)", "B": "(L1,0)", "C": "(U1,f1)", "D": "(L1,f1)"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "The total frequency N is the? Σ", "options": {"A": "First cf", "B": "Last cf", "C": "Middle cf", "D": "Highest f"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "Ogive is drawn on? 📄", "options": {"A": "Graph paper", "B": "Plain paper", "C": "Both", "D": "Neither"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "To find number of observations below a value, use? 🔽", "options": {"A": "Frequency table", "B": "Ogive", "C": "Histogram", "D": "Pie chart"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "For symmetric distribution, ogive is? ⚖️", "options": {"A": "S-shaped", "B": "Straight", "C": "J-shaped", "D": "U-shaped"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "The x-coordinate of intersection point gives? 📏", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "Variance"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "Ogive cannot give exact? ❌", "options": {"A": "Median", "B": "Quartiles", "C": "Mean", "D": "Percentiles"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "After plotting points, ogive is drawn by? ✏️", "options": {"A": "Joining by smooth curve", "B": "Joining by straight lines", "C": "Drawing bars", "D": "Drawing dots"}, "correct_answer": "A"},

    {"id": 21, "difficulty": "medium", "question": "Given less than cf: (10,5), (20,15), (30,35), (40,50). To draw ogive, we plot points? 📍", "options": {"A": "(10,5),(20,15),(30,35),(40,50)", "B": "(0,0),(10,5),(20,15),(30,35),(40,50)", "C": "(5,10),(15,20),(35,30),(50,40)", "D": "(10,0),(20,5),(30,15),(40,35)"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "If N=80, median from ogive is value at y=? 🎯", "options": {"A": "40", "B": "80", "C": "20", "D": "60"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "For 'more than' ogive, we plot? 📉", "options": {"A": "Lower limits vs cf", "B": "Upper limits vs cf", "C": "Midpoints vs cf", "D": "Class marks vs f"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "If ogive is steep, it indicates? 📈", "options": {"A": "Low frequency", "B": "High frequency", "C": "Zero frequency", "D": "Constant frequency"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "To find 60th percentile, draw horizontal at y=? 🎯", "options": {"A": "60", "B": "0.6N", "C": "N/60", "D": "60N"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "Given cf curve points: (0,0),(10,8),(20,25),(30,45),(40,60). Median? 📏", "options": {"A": "20", "B": "22", "C": "24", "D": "26"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "The difference between 'less than' and 'more than' ogives at any x is? ➖", "options": {"A": "N", "B": "N/2", "C": "Constant", "D": "Variable"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "If ogive has plateau, it means? ⏸️", "options": {"A": "Zero frequency class", "B": "High frequency", "C": "Missing data", "D": "Error"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "For data with total frequency 100, Q1 is at y=? 1️⃣", "options": {"A": "25", "B": "50", "C": "75", "D": "100"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "To find interquartile range from ogive, we need? 📐", "options": {"A": "Q3 & Q1", "B": "Median", "C": "Mean", "D": "Mode"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Given less than ogive points: (30,20),(40,45),(50,70),(60,85),(70,100). Number of observations in 40-50? 🔢", "options": {"A": "25", "B": "45", "C": "70", "D": "Cannot find"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Ogive is useful for? ✅", "options": {"A": "Large data", "B": "Grouped data", "C": "Continuous data", "D": "All"}, "correct_answer": "D"},
    {"id": 33, "difficulty": "medium", "question": "If both ogives intersect at (55,50), and N=100, median is? ❌", "options": {"A": "55", "B": "50", "C": "105", "D": "5"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "For 'less than' ogive, curve is? 📈", "options": {"A": "Non-decreasing", "B": "Non-increasing", "C": "Constant", "D": "Decreasing"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "To estimate median graphically, accuracy depends on? 🎯", "options": {"A": "Scale", "B": "Plotting", "C": "Curve smoothing", "D": "All"}, "correct_answer": "D"},
    {"id": 36, "difficulty": "medium", "question": "Given more than ogive: (10,100),(20,85),(30,60),(40,30),(50,10). Frequency of 20-30? 📊", "options": {"A": "25", "B": "30", "C": "35", "D": "40"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Ogive cannot be used for? ❌", "options": {"A": "Discrete ungrouped data", "B": "Grouped data", "C": "Continuous data", "D": "It can be used for all"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "If ogive is S-shaped, distribution is? 📊", "options": {"A": "Normal", "B": "Skewed", "C": "Uniform", "D": "Exponential"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "To find value below which 75% observations lie, use? 📈", "options": {"A": "Q1", "B": "Median", "C": "Q3", "D": "P75"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "Given N=120, from ogive median=35, Q1=25, Q3=45. IQR? 📐", "options": {"A": "10", "B": "20", "C": "30", "D": "40"}, "correct_answer": "B"},

    {"id": 41, "difficulty": "hard", "question": "For data with classes 0-10,10-20,... and less than cf: 5,20,45,70,85,100. Draw ogive and estimate median. 📏", "options": {"A": "27.5", "B": "30", "C": "32.5", "D": "35"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "If 'less than' ogive is y=L(x) and 'more than' ogive is y=M(x), then L(x)+M(x)=? ➕", "options": {"A": "N", "B": "N/2", "C": "2N", "D": "0"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "Given ogive points: (0,0),(10,12),(20,35),(30,65),(40,85),(50,100). Find number in 25-35. 🔢", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "hard", "question": "For a normal distribution, ogive is symmetrical about? ⚖️", "options": {"A": "Mean", "B": "Median", "C": "Both", "D": "Mode"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "hard", "question": "If ogive is concave up, distribution is? 📈", "options": {"A": "Positively skewed", "B": "Negatively skewed", "C": "Symmetric", "D": "Uniform"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "hard", "question": "To find percentile P_k, we solve L(x)=kN/100. This gives approximate? 🎯", "options": {"A": "True value", "B": "Interpolated value", "C": "Exact value", "D": "Rounded value"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "hard", "question": "Given less than cf curve equation y=0.01x²+2x for x in [0,50], N=100. Estimate median. 🧮", "options": {"A": "30", "B": "35", "C": "40", "D": "45"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "hard", "question": "For exponential distribution, ogive shape is? 📈", "options": {"A": "Rapidly rising", "B": "Linear", "C": "S-shaped", "D": "U-shaped"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "If ogive is piecewise linear, distribution has? 📊", "options": {"A": "Uniform frequencies", "B": "Varying frequencies", "C": "Zero frequencies", "D": "Outliers"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "The intersection point of less than and more than ogives has coordinates (m, N/2). Then m is? 📍", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "Midrange"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "hard", "question": "Given N=200, from ogive: 30% observations below 25, 70% below 45. Estimate number between 25-45. 🔢", "options": {"A": "80", "B": "100", "C": "120", "D": "140"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "For grouped data with open ends, ogive can be drawn if we assume? 🤔", "options": {"A": "Class boundaries", "B": "Class marks", "C": "Class widths", "D": "Frequencies"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "If ogive has point of inflection, it corresponds to? 📊", "options": {"A": "Mean", "B": "Median", "C": "Mode", "D": "Quartile"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "hard", "question": "To compare two distributions, we can use? 📈", "options": {"A": "Histograms", "B": "Ogive", "C": "Both", "D": "Neither"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "hard", "question": "Given less than ogive passes through (20,30),(30,65),(40,100). If N=100, frequency of 30-40? 📊", "options": {"A": "35", "B": "40", "C": "45", "D": "50"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "For a J-shaped distribution, ogive is? 📈", "options": {"A": "S-shaped", "B": "Concave", "C": "Convex", "D": "Linear"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "hard", "question": "If ogive is straight line, distribution is? 📏", "options": {"A": "Uniform", "B": "Normal", "C": "Exponential", "D": "Binomial"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "The median from ogive and from formula may differ due to? 🤔", "options": {"A": "Grouping", "B": "Interpolation", "C": "Plotting error", "D": "All"}, "correct_answer": "D"},
    {"id": 59, "difficulty": "hard", "question": "Given cf curve: y=0.02x² for 0≤x≤50, N=50. Find Q1. 🧮", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "hard", "question": "For cumulative frequency polygon, points are joined by? 📈", "options": {"A": "Straight lines", "B": "Curves", "C": "Dots", "D": "Bars"}, "correct_answer": "A"}
  ]
}