{
  "title": "Equation of a line - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "📐 General form of line equation: 🎯", "options": {"A": "ax + by + c = 0", "B": "y = x²", "C": "x + y = xy", "D": "y = 1/x"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "📍 Slope-intercept form: ✏️", "options": {"A": "y = mx + c", "B": "ax + by = c", "C": "x/a + y/b = 1", "D": "y - y₁ = m(x - x₁)"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "📏 Horizontal line equation: 🌈", "options": {"A": "x = constant", "B": "y = constant", "C": "y = mx", "D": "x + y = constant"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "🎯 Vertical line equation: ⭐", "options": {"A": "x = constant", "B": "y = constant", "C": "y = x", "D": "y = -x"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "🔢 Line passing through origin: 📐", "options": {"A": "y = mx", "B": "y = mx + c, c≠0", "C": "x = a", "D": "y = b"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "✏️ Two-point form uses: 🔍", "options": {"A": "(x₁,y₁) and (x₂,y₂)", "B": "slope and intercept", "C": "intercepts only", "D": "one point only"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "📍 x-intercept is where line crosses: 📏", "options": {"A": "y-axis", "B": "x-axis", "C": "origin", "D": "both axes"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "📐 y-intercept is where line crosses: 🎯", "options": {"A": "x-axis", "B": "y-axis", "C": "origin", "D": "diagonal"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "🎨 Intercept form: x/a + y/b = ? ✏️", "options": {"A": "0", "B": "1", "C": "a+b", "D": "ab"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "🔍 Point-slope form: 🌈", "options": {"A": "y - y₁ = m(x - x₁)", "B": "y = mx + c", "C": "x/a + y/b = 1", "D": "ax + by + c = 0"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "📏 Line parallel to x-axis has slope: ⭐", "options": {"A": "0", "B": "∞", "C": "1", "D": "-1"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "🎯 Line parallel to y-axis has slope: 🔢", "options": {"A": "0", "B": "undefined", "C": "1", "D": "-1"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "📍 Line making 45° with x-axis has slope: 📐", "options": {"A": "0", "B": "1", "C": "-1", "D": "√3"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "✏️ If line equation is 2x + 3y = 6, x-intercept? 🔍", "options": {"A": "2", "B": "3", "C": "6", "D": "12"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "📐 Line through (1,2) with slope 3: 🎨", "options": {"A": "y=3x+2", "B": "y=3x-1", "C": "y=3x+1", "D": "y=3x-2"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "🔢 Two lines are parallel if: 🌈", "options": {"A": "slopes equal", "B": "slopes negative reciprocals", "C": "product of slopes = -1", "D": "slopes different"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "🎯 Two lines are perpendicular if: ⭐", "options": {"A": "slopes equal", "B": "product of slopes = -1", "C": "slopes reciprocals", "D": "slopes zero"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "📍 Line y = 2x + 5 has y-intercept: 📏", "options": {"A": "2", "B": "5", "C": "-5", "D": "-2"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "📐 Line 3x - 4y = 12, y-intercept? ✏️", "options": {"A": "3", "B": "-3", "C": "4", "D": "-4"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "🎨 x-axis equation: 🔍", "options": {"A": "x=0", "B": "y=0", "C": "x=y", "D": "x+y=0"}, "correct_answer": "B"},
    
    {"id": 21, "difficulty": "medium", "question": "📐 Line through (2,3) and (4,7): 🎯", "options": {"A": "y=2x-1", "B": "y=2x+1", "C": "y=3x-3", "D": "y=3x+1"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "📍 Line with x-intercept 3, y-intercept 4: ✏️", "options": {"A": "4x+3y=12", "B": "3x+4y=12", "C": "4x+3y=1", "D": "x/3+y/4=1"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "📏 Line parallel to 2x+3y=5 through (1,1): 🌈", "options": {"A": "2x+3y=5", "B": "2x+3y=7", "C": "2x+3y=1", "D": "2x+3y=3"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "🎯 Line perpendicular to 3x-4y=7 through (2,3): ⭐", "options": {"A": "4x+3y=17", "B": "4x+3y=11", "C": "3x+4y=18", "D": "4x-3y=-1"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "🔢 Point of intersection of x+y=5 and x-y=1: 📊", "options": {"A": "(2,3)", "B": "(3,2)", "C": "(1,4)", "D": "(4,1)"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "✏️ Line making equal intercepts through (3,4): 🎨", "options": {"A": "x+y=7", "B": "x-y=-1", "C": "x+y=1", "D": "x-y=7"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "📍 Angle between lines y=x and y=√3x: 📐", "options": {"A": "15°", "B": "30°", "C": "45°", "D": "60°"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "📐 Distance from (2,3) to line 3x+4y=5: 🔍", "options": {"A": "13/5", "B": "11/5", "C": "9/5", "D": "7/5"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "🎯 Line through intersection of x+y=4, x-y=2 and parallel to 3x+4y=5: ✏️", "options": {"A": "3x+4y=18", "B": "3x+4y=17", "C": "3x+4y=15", "D": "3x+4y=14"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "🔢 Equation of perpendicular bisector of (1,2) and (3,4): 📏", "options": {"A": "x+y=5", "B": "x-y=1", "C": "x+y=1", "D": "x-y=5"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "🎨 Line through (1,2) making angle 45° with x-axis: 🌈", "options": {"A": "y=x+1", "B": "y=x-1", "C": "y=-x+3", "D": "y=-x-1"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "📍 Reflection of point (2,3) in line y=x: ⭐", "options": {"A": "(3,2)", "B": "(-2,-3)", "C": "(-3,-2)", "D": "(2,-3)"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "📐 Family of lines through intersection of 2x+3y=5, x-y=2: 🔢", "options": {"A": "2x+3y-5+k(x-y-2)=0", "B": "2x+3y-5=0 only", "C": "x-y-2=0 only", "D": "(2x+3y-5)(x-y-2)=0"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "🎯 Line equally inclined to axes through (2,3): ✏️", "options": {"A": "x+y=5", "B": "x-y=-1", "C": "both A and B", "D": "neither"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "🔍 Distance between parallel lines 3x+4y=10 and 3x+4y=20: 📏", "options": {"A": "2", "B": "10/√25", "C": "10/5", "D": "2/5"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "✏️ Foot of perpendicular from (1,2) to line 3x+4y=5: 🎯", "options": {"A": "(11/25, 22/25)", "B": "(11/5, 2/5)", "C": "(1, 1/2)", "D": "(2/5, 11/5)"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "📍 Area of triangle formed by x=0, y=0, x/3+y/4=1: 📊", "options": {"A": "6", "B": "12", "C": "18", "D": "24"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "📐 Line through (a,0) and (0,b). If a+b=10, ab=21, equation: 🔍", "options": {"A": "7x+3y=21 or 3x+7y=21", "B": "x+y=10", "C": "xy=21", "D": "x/7+y/3=1"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "🎯 Equation of line with slope -3/4 and x-intercept 5: ⭐", "options": {"A": "3x+4y=15", "B": "4x+3y=20", "C": "3x+4y=20", "D": "4x+3y=15"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "🔢 Image of line x+y=5 in y-axis: ✏️", "options": {"A": "x-y=5", "B": "x+y=-5", "C": "-x+y=5", "D": "x-y=-5"}, "correct_answer": "B"},
    
    {"id": 41, "difficulty": "hard", "question": "📐 Line through (1,2) cutting intercepts whose sum is 6: 🎯", "options": {"A": "2x+y=4 or x+2y=5", "B": "x+y=3 only", "C": "3x+2y=7", "D": "x+3y=7"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "📍 Distance between lines (3x+4y+5)/√(3²+4²)=±2: 📏", "options": {"A": "4", "B": "2", "C": "2√(3²+4²)", "D": "4/5"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "🎯 Lines ax+by+c=0 and a'x+b'y+c'=0 perpendicular if: ⭐", "options": {"A": "aa'+bb'=0", "B": "ab'+a'b=0", "C": "ab-a'b'=0", "D": "aa'-bb'=0"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "🔢 Equation of line through (2,3) making area 3 with axes: 📊", "options": {"A": "3x+2y=12 or x+6y=20", "B": "2x+3y=13", "C": "x+y=5", "D": "2x-y=1"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "✏️ Foot of perpendicular from origin to line 3x+4y=25: 🎨", "options": {"A": "(3,4)", "B": "(4,3)", "C": "(15/5,20/5)", "D": "(75/25,100/25)"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "📐 Equation of altitude from A(1,2) in triangle A(1,2), B(3,4), C(5,1): 🔍", "options": {"A": "2x-3y+4=0", "B": "3x+2y-7=0", "C": "x-2y+3=0", "D": "2x+y-4=0"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "🎯 Line through (α,β) making angle θ with x-axis: 📏", "options": {"A": "(x-α)/cosθ = (y-β)/sinθ", "B": "y-β = tanθ(x-α)", "C": "xcosθ+ysinθ=αcosθ+βsinθ", "D": "all of these"}, "correct_answer": "D"},
    {"id": 48, "difficulty": "hard", "question": "📍 Combined equation of lines x=0 and y=0: ✏️", "options": {"A": "xy=0", "B": "x²+y²=0", "C": "x+y=0", "D": "x²-y²=0"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "📐 Equation of line through (2,3) dividing (1,1) and (4,5) in ratio k:1: 🔢", "options": {"A": "(3k-1)x+(4k-2)y=11k-5", "B": "2x+3y=13", "C": "x+y=5", "D": "varies with k"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "🎯 Distance between lines y=mx+c₁ and y=mx+c₂: 🌈", "options": {"A": "|c₁-c₂|/√(1+m²)", "B": "|c₁-c₂|", "C": "|c₁-c₂|√(1+m²)", "D": "|c₁+c₂|/√(1+m²)"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "🔢 Line through (1,2) with intercepts in ratio 2:3: 📊", "options": {"A": "2x+3y=8", "B": "3x+2y=7", "C": "2x/3+3y/2=1", "D": "x/2+y/3=1"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "✏️ Equation of line making triangle area 24 with axes and passing through (3,4): 🎯", "options": {"A": "4x+3y=24", "B": "4x-3y=0", "C": "3x+4y=25", "D": "8x+3y=36 or 3x+8y=36"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "hard", "question": "📐 Orthocenter of triangle (0,0), (3,0), (0,4): 🔍", "options": {"A": "(0,0)", "B": "(3,0)", "C": "(0,4)", "D": "(1,1)"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "🎯 Equation of line through point of intersection of 2x+3y=5, x-y=2 and equidistant from (1,2), (3,4): ⭐", "options": {"A": "2x+y=7", "B": "x+2y=7", "C": "x-2y=1", "D": "2x-y=3"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "📍 Equation of line cutting intercepts a,b such that 1/a + 1/b = constant: ✏️", "options": {"A": "x/a + y/b = 1", "B": "bx + ay = ab", "C": "both A and B", "D": "neither"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "hard", "question": "📐 Lines (a+b)x + (a-b)y = 2ab and (a-b)x + (a+b)y = 2ab intersect at: 🔢", "options": {"A": "(a,b)", "B": "(b,a)", "C": "(ab, ab)", "D": "(a+b, a-b)"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "🎯 Equation of line through (2,3) making equal angles with lines 3x=4y+7, 5y=12x+6: 📏", "options": {"A": "9x-7y=3 or 7x+9y=41", "B": "x+y=5", "C": "x-y=-1", "D": "3x+4y=18"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "🔢 Point dividing distance between lines 3x+4y=5 and 3x+4y=20 in ratio 2:3: 🎨", "options": {"A": "on line 3x+4y=11", "B": "on line 3x+4y=14", "C": "on line 3x+4y=17", "D": "on line 3x+4y=8"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "hard", "question": "✏️ Equation of line through origin dividing segment between (1,2), (3,4) in ratio 1:2: 📐", "options": {"A": "y=4x/3", "B": "y=3x/2", "C": "y=5x/4", "D": "y=6x/5"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "📐 Lines x/a + y/b = 1 and x/b + y/a = 1 intersect at: 🎯", "options": {"A": "(ab/(a+b), ab/(a+b))", "B": "((a+b)/ab, (a+b)/ab)", "C": "(1,1)", "D": "(a,b)"}, "correct_answer": "A"}
  ]
}