{
  "title": "Distance formula - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "📐 Distance between points (0,0) and (3,4) is: 🎯", "options": {"A": "5", "B": "7", "C": "12", "D": "25"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "📍 Distance formula: √[(x₂-x₁)² + (____)²] 🔢", "options": {"A": "y₂-y₁", "B": "y₂+y₁", "C": "y₂×y₁", "D": "y₂/y₁"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "📏 Points (2,3) and (5,7). Distance = ? ✏️", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "🎯 Distance from origin to (6,8) is: ⭐", "options": {"A": "10", "B": "12", "C": "14", "D": "16"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "🔢 Points (1,1) and (4,5). Distance = ? 📊", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "📍 Points on x-axis have coordinates: 📐", "options": {"A": "(x,0)", "B": "(0,y)", "C": "(x,x)", "D": "(y,y)"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "📏 Distance between (a,0) and (0,b) is: 🔍", "options": {"A": "a+b", "B": "√(a²+b²)", "C": "a²+b²", "D": "|a-b|"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "🎯 Points (-3,0) and (3,0) are ____ units apart: 🔢", "options": {"A": "3", "B": "6", "C": "9", "D": "12"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "📍 Distance formula comes from: 📐", "options": {"A": "Pythagoras theorem", "B": "Euclid theorem", "C": "Thales theorem", "D": "Apollonius theorem"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "📏 Points (0,5) and (0,-5) distance: ⚡", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "🔢 For horizontal line, y-coordinates are: 📊", "options": {"A": "Different", "B": "Same", "C": "Zero", "D": "One"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "🎯 Distance between (-1,-1) and (2,3): ✏️", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "📍 If distance=0, points are: 🤔", "options": {"A": "Far apart", "B": "Same", "C": "Different", "D": "Opposite"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "📏 Points on same vertical line have same: 🔍", "options": {"A": "x-coordinate", "B": "y-coordinate", "C": "Both", "D": "Neither"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "🔢 Distance is always: ⭐", "options": {"A": "Positive", "B": "Negative", "C": "Zero", "D": "Fractional"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "🎯 (3,4) is ____ units from origin: 📐", "options": {"A": "3", "B": "4", "C": "5", "D": "7"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "📍 Points (x₁,y₁) and (x₂,y₂). Horizontal distance = ? 📏", "options": {"A": "|x₂-x₁|", "B": "|y₂-y₁|", "C": "x₂+x₁", "D": "y₂+y₁"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "📏 Distance formula works in: 🌈", "options": {"A": "1D only", "B": "2D only", "C": "3D only", "D": "Any dimension"}, "correct_answer": "D"},
    {"id": 19, "difficulty": "easy", "question": "🔢 If both coordinates double, distance: ⚡", "options": {"A": "Doubles", "B": "Halves", "C": "Quadruples", "D": "Same"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "🎯 Points (k,0) and (0,k). Distance = ? 📊", "options": {"A": "k", "B": "k√2", "C": "2k", "D": "k²"}, "correct_answer": "B"},
    
    {"id": 21, "difficulty": "medium", "question": "📐 Points A(2,3), B(5,7). Distance AB = ? 🔍", "options": {"A": "√13", "B": "5", "C": "√29", "D": "√34"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "📍 Points (-2,3) and (4,-1). Distance = ? ✏️", "options": {"A": "√52", "B": "2√13", "C": "√40", "D": "2√10"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "📏 Point equidistant from (0,0), (6,0), (0,8) is: 🎯", "options": {"A": "(3,4)", "B": "(4,3)", "C": "(2,2)", "D": "(6,8)"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "🔢 Point on x-axis 5 units from (2,3): 📐", "options": {"A": "(5,0) only", "B": "(-2,0) only", "C": "(6,0) or (-2,0)", "D": "(2,0) only"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "🎯 Distance between (a+b, a-b) and (a-b, a+b): ⭐", "options": {"A": "2√(a²+b²)", "B": "2√(ab)", "C": "b√2", "D": "2b√2"}, "correct_answer": "D"},
    {"id": 26, "difficulty": "medium", "question": "📍 Points (3,4), (-2,1), (x,y) collinear. Possible (x,y)? 🔍", "options": {"A": "(8,7)", "B": "(1,2)", "C": "(-7,-2)", "D": "(0,0)"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "📏 Vertices of right triangle at (0,0), (6,0), (0,8). Hypotenuse length? 📐", "options": {"A": "10", "B": "12", "C": "14", "D": "16"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "🔢 Point on y-axis 13 units from (5,12): 🎯", "options": {"A": "(0,0) only", "B": "(0,24) only", "C": "(0,0) or (0,24)", "D": "(0,12) only"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "🎯 Distance between parallel lines y=3x+4 and y=3x-2: 📏", "options": {"A": "6/√10", "B": "2/√10", "C": "4/√10", "D": "8/√10"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "📍 Points A(1,2), B(4,6), C(8,4). Which is largest distance? ✏️", "options": {"A": "AB", "B": "BC", "C": "AC", "D": "All equal"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "📐 Triangle vertices (0,0), (4,0), (0,3). Perimeter? 🔢", "options": {"A": "12", "B": "13", "C": "14", "D": "15"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "⚡ Points (2,3), (5,7), (8,11) are: 🔍", "options": {"A": "Collinear", "B": "Right triangle", "C": "Equilateral", "D": "Isosceles"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "🎨 Distance from (3,4) to line x=7: 📏", "options": {"A": "3", "B": "4", "C": "5", "D": "7"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "🔺 Points (k,3), (4,5), (6,k) collinear. Find k: 📊", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "📏 Quadrilateral vertices (0,0), (4,0), (4,3), (0,3). Perimeter? 🎯", "options": {"A": "12", "B": "14", "C": "16", "D": "18"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "📍 Point P(x,y) equidistant from (0,0) and (6,8). Condition: ✏️", "options": {"A": "3x+4y=25", "B": "6x+8y=25", "C": "3x+4y=50", "D": "6x+8y=100"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "🔢 Distance between (sinθ, cosθ) and (cosθ, sinθ): ⭐", "options": {"A": "√2|sinθ-cosθ|", "B": "|sinθ-cosθ|", "C": "√2", "D": "1"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "🎯 Points A(-1,0), B(3,0), C(0,4). Type of triangle? 📐", "options": {"A": "Equilateral", "B": "Right", "C": "Isosceles", "D": "Scalene"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "📏 Origin is ____ from (12,5) and (5,12): 🔍", "options": {"A": "Different distances", "B": "Same distance", "C": "Twice distance", "D": "Half distance"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "📍 Point dividing (2,3) and (5,7) in ratio 2:1. Distance from origin? ✏️", "options": {"A": "5", "B": "√29", "C": "√34", "D": "√41"}, "correct_answer": "D"},
    
    {"id": 41, "difficulty": "hard", "question": "📐 Points A(1,1), B(4,4), C(4,8), D(1,5). Shape? 🔍", "options": {"A": "Square", "B": "Rectangle", "C": "Parallelogram", "D": "Rhombus"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "hard", "question": "🎯 Point on line y=2x+3 closest to origin: 📏", "options": {"A": "(-6/5, 3/5)", "B": "(-3/5, 9/5)", "C": "(0,3)", "D": "(-1,1)"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "📍 Points (at₁², 2at₁) and (at₂², 2at₂) distance: ⚡", "options": {"A": "a|t₁-t₂|√(t₁²+t₂²)", "B": "a|t₁-t₂|√(1+t₁t₂)", "C": "a|t₁-t₂|√[(t₁+t₂)²+4]", "D": "a(t₁-t₂)²"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "hard", "question": "📏 Locus of point equidistant from (3,4) and (5,2): ✏️", "options": {"A": "x-y=1", "B": "x+y=7", "C": "x-y=3", "D": "x+y=9"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "🔢 Distance between lines 3x+4y=10 and 3x+4y=20: 📐", "options": {"A": "2", "B": "10/√25", "C": "10/5", "D": "2/5"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "🎯 Point on y-axis equidistant from (2,3) and (-4,1): 🎨", "options": {"A": "(0,-3)", "B": "(0,3)", "C": "(0,-4)", "D": "(0,4)"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "📐 Triangle vertices (0,6), (8,0), (0,0). Distance from centroid to origin? 🔍", "options": {"A": "10/3", "B": "√(100/9)", "C": "√(136/9)", "D": "√(164/9)"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "📍 Points A(1,2), B(2,3), C(3,4). Area of triangle? 📊", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "📏 Distance between (a cosθ, a sinθ) and (a cosφ, a sinφ): ⭐", "options": {"A": "2a|sin((θ-φ)/2)|", "B": "a|θ-φ|", "C": "2a sin((θ-φ)/2)", "D": "a|sinθ-sinφ|"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "🔢 Triangle vertices (0,0), (6,0), (3,4). Circumradius? 🎯", "options": {"A": "3", "B": "3.125", "C": "3.25", "D": "3.5"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "hard", "question": "🎯 Points (x,y) where |x|+|y|=4. Maximum distance from origin? 📏", "options": {"A": "2", "B": "2√2", "C": "4", "D": "4√2"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "hard", "question": "📐 Points (k+1, 2k), (3k, 2k+3), (5k-1, 5k) collinear. Find k: 🔢", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "hard", "question": "📍 Distance from point (2,3) to line through (1,1) and (4,5): ✏️", "options": {"A": "1/√5", "B": "2/√5", "C": "3/√5", "D": "4/√5"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "📏 Locus of point whose distance from (1,2) is twice distance from (3,4): 🎨", "options": {"A": "Circle", "B": "Line", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "🔢 Points A(0,0), B(3,4), C(7,7). Length of median from A? 📐", "options": {"A": "√29", "B": "√34", "C": "√37", "D": "√40"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "hard", "question": "🎯 Minimum distance between point (2,3) and line y=mx where m>0? ⚡", "options": {"A": "√13", "B": "√(13/2)", "C": "√(26)", "D": "13/√(1+m²)"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "hard", "question": "📐 Distance between orthocenter and circumcenter of triangle (0,0), (6,0), (0,8): 🔍", "options": {"A": "5", "B": "√29", "C": "√34", "D": "√41"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "hard", "question": "📍 Points on x-axis at distance 5 from (2,3). Sum of x-coordinates? ✏️", "options": {"A": "4", "B": "6", "C": "8", "D": "10"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "📏 Four points (0,0), (a,0), (a,b), (0,b). Distance between midpoints of diagonals? 🎯", "options": {"A": "0", "B": "√(a²+b²)/2", "C": "√(a²+b²)", "D": "(a+b)/2"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "🔢 Point divides (1,2) and (3,4) externally in ratio 2:1. Distance from (0,0)? 📊", "options": {"A": "√29", "B": "√34", "C": "√41", "D": "√45"}, "correct_answer": "C"}
  ]
}