{
  "title": "Slope of line - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "📐 Slope of line through (1,2) and (3,4): 🎯", "options": {"A": "1", "B": "2", "C": "0", "D": "∞"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "📍 Slope formula m = ? 🔢", "options": {"A": "(y₂-y₁)/(x₂-x₁)", "B": "(x₂-x₁)/(y₂-y₁)", "C": "y₂/y₁", "D": "x₂/x₁"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "🎯 Slope of horizontal line: ⭐", "options": {"A": "0", "B": "∞", "C": "1", "D": "-1"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "📏 Slope of vertical line: 🌈", "options": {"A": "undefined", "B": "0", "C": "1", "D": "-1"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "🔢 Slope of line making 45° with x-axis: 📐", "options": {"A": "1", "B": "√3", "C": "1/√3", "D": "0"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "✏️ Slope of line parallel to x-axis: 🎨", "options": {"A": "0", "B": "∞", "C": "1", "D": "-1"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "📍 Slope of line parallel to y-axis: 🔍", "options": {"A": "undefined", "B": "0", "C": "1", "D": "-1"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "📐 If slope is positive, line makes ______ angle: ⚡", "options": {"A": "acute", "B": "obtuse", "C": "90°", "D": "180°"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "🎯 If slope is negative, line makes ______ angle: ⭐", "options": {"A": "obtuse", "B": "acute", "C": "90°", "D": "0°"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "📏 Slope of line through origin and (3,4): ✏️", "options": {"A": "4/3", "B": "3/4", "C": "1", "D": "0"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "🔢 Two lines parallel have ______ slopes: 📐", "options": {"A": "equal", "B": "negative reciprocals", "C": "product -1", "D": "different"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "📍 Two lines perpendicular have slopes: 🎯", "options": {"A": "product = -1", "B": "equal", "C": "sum = 0", "D": "ratio = 1"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "📐 Slope of line y = 2x + 3: 🌈", "options": {"A": "2", "B": "3", "C": "0", "D": "∞"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "🎯 Slope of line 3x + 4y = 7: ⚡", "options": {"A": "-3/4", "B": "3/4", "C": "-4/3", "D": "4/3"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "📏 Angle θ with x-axis, slope m = ? 🔢", "options": {"A": "tan θ", "B": "sin θ", "C": "cos θ", "D": "cot θ"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "🔢 Slope of line making 60° with x-axis: 📐", "options": {"A": "√3", "B": "1/√3", "C": "1", "D": "0"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "✏️ Slope of line making 30° with x-axis: 🎨", "options": {"A": "1/√3", "B": "√3", "C": "1", "D": "0"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "📍 If line has slope 0, it is ______ to x-axis: 🔍", "options": {"A": "parallel", "B": "perpendicular", "C": "at 45°", "D": "coincident"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "📐 If line has undefined slope, it is ______ to y-axis: ⭐", "options": {"A": "parallel", "B": "perpendicular", "C": "at 45°", "D": "coincident"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "🎯 Slope of line through (a,b) and (c,d): 📏", "options": {"A": "(d-b)/(c-a)", "B": "(c-a)/(d-b)", "C": "(a-c)/(b-d)", "D": "(b-d)/(a-c)"}, "correct_answer": "A"},
    
    {"id": 21, "difficulty": "medium", "question": "📐 Slope of line perpendicular to line with slope 2/3: 🎯", "options": {"A": "-3/2", "B": "3/2", "C": "-2/3", "D": "2/3"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "📍 Angle between lines with slopes m₁ and m₂: ✏️", "options": {"A": "tan⁻¹|(m₁-m₂)/(1+m₁m₂)|", "B": "tan⁻¹(m₁-m₂)", "C": "cos⁻¹(m₁m₂)", "D": "sin⁻¹(m₁-m₂)"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "📏 Lines with slopes 1/2 and 2 are: 🌈", "options": {"A": "perpendicular", "B": "parallel", "C": "at 45°", "D": "coincident"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "🎯 Slope of line making equal intercepts on axes: ⭐", "options": {"A": "-1", "B": "1", "C": "0", "D": "∞"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "🔢 Find slope of line through (2,3) making angle 60° with x-axis: 📐", "options": {"A": "√3", "B": "1/√3", "C": "1", "D": "-√3"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "✏️ If line passes through (1,2) and slope = 3, equation: 🎨", "options": {"A": "y=3x-1", "B": "y=3x+1", "C": "y=3x-2", "D": "y=3x+2"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "📍 Angle between lines y=√3x and y=1/√3 x: 🔍", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "📐 Slope of altitude from A(1,2) in triangle A(1,2), B(3,4), C(5,1): ⚡", "options": {"A": "-2/3", "B": "2/3", "C": "3/2", "D": "-3/2"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "🎯 If line makes intercepts a and b on axes, slope = ? 📏", "options": {"A": "-b/a", "B": "-a/b", "C": "b/a", "D": "a/b"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "🔢 Points (1,2), (3,4), (5,6) are collinear because slopes: 📐", "options": {"A": "equal", "B": "different", "C": "negative reciprocals", "D": "product -1"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "✏️ Slope of line parallel to 3x+4y=7: 🎯", "options": {"A": "-3/4", "B": "3/4", "C": "-4/3", "D": "4/3"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "📍 Slope of line perpendicular to 2x-3y=5: 🌈", "options": {"A": "-3/2", "B": "3/2", "C": "-2/3", "D": "2/3"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "📐 If slope of line joining (2,3) and (4,k) is 2, find k: 🔢", "options": {"A": "7", "B": "5", "C": "6", "D": "8"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "🎯 Acute angle between lines with slopes 2 and 1/3: ⭐", "options": {"A": "45°", "B": "30°", "C": "60°", "D": "75°"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "📏 Line through (1,2) perpendicular to line through (2,3) and (4,5). Its slope? ✏️", "options": {"A": "-1", "B": "1", "C": "0", "D": "∞"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "🔢 If line makes angle θ with x-axis, slope m. Then tan θ = ? 📐", "options": {"A": "m", "B": "1/m", "C": "√(1+m²)", "D": "1/√(1+m²)"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "📍 Slope of median from A(1,2) in triangle A(1,2), B(3,4), C(5,1): 🎨", "options": {"A": "-1/4", "B": "1/4", "C": "-4", "D": "4"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "📐 Lines equally inclined to axes have slopes: 🔍", "options": {"A": "1 or -1", "B": "0 or ∞", "C": "2 or 1/2", "D": "√3 or 1/√3"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "🎯 If three points (1,2), (3,4), (5,k) are collinear, k = ? ⚡", "options": {"A": "6", "B": "5", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "📏 Slope of line making intercepts whose sum is 5 and product is 6: ✏️", "options": {"A": "-2/3 or -3/2", "B": "2/3 or 3/2", "C": "1 or -1", "D": "0 or ∞"}, "correct_answer": "A"},
    
    {"id": 41, "difficulty": "hard", "question": "📐 Angle between lines (√3-1)x + (√3+1)y = 5 and (√3+1)x + (1-√3)y = 7: 🎯", "options": {"A": "60°", "B": "45°", "C": "30°", "D": "90°"}, "correct_answer": "D"},
    {"id": 42, "difficulty": "hard", "question": "📍 If line through (x₁,y₁) with slope m makes angle θ with line through (x₂,y₂) with slope m', condition for specific θ: ✏️", "options": {"A": "(m-m')/(1+mm') = ±tan θ", "B": "m-m' = tan θ", "C": "1+mm' = sec θ", "D": "mm' = cos θ"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "📏 Lines through (1,2) making angles π/4 with line 2x+3y=5. Their slopes: 🌈", "options": {"A": "-5 and 1/5", "B": "5 and -1/5", "C": "2 and -1/2", "D": "3 and -1/3"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "🎯 Product of slopes of lines equally inclined to axes through (h,k): ⭐", "options": {"A": "-1", "B": "1", "C": "0", "D": "∞"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "🔢 If slopes of lines represented by ax²+2hxy+by²=0 are m₁ and m₂, then m₁+m₂ = ? 📐", "options": {"A": "-2h/b", "B": "2h/b", "C": "-a/b", "D": "a/b"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "✏️ Angle between lines joining origin to points of intersection of y=mx and curve: 🎨", "options": {"A": "depends on m", "B": "always 90°", "C": "always 45°", "D": "always 60°"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "📍 Slope of line making angle α with line of slope m is: 🔍", "options": {"A": "(m ± tan α)/(1 ∓ m tan α)", "B": "m ± tan α", "C": "m tan α", "D": "tan α/m"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "📐 If line through (1,2) with slope m makes area 5 with axes, possible m: ⚡", "options": {"A": "2 or 1/2", "B": "3 or 1/3", "C": "4 or 1/4", "D": "5 or 1/5"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "🎯 Lines represented by (tan²θ)x² - (2 tan θ sec θ)xy + (sec²θ)y² = 0 have slopes: 📏", "options": {"A": "tan θ and tan θ", "B": "tan θ and cot θ", "C": "sin θ and cos θ", "D": "sec θ and cosec θ"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "🔢 Angle between lines ax²+2hxy+by²=0 is tan⁻¹[2√(h²-ab)/(a+b)]. If lines are perpendicular, condition: 📐", "options": {"A": "a+b=0", "B": "h²=ab", "C": "h²>ab", "D": "a=b"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "✏️ Slope of line bisecting angle between lines with slopes m₁ and m₂: 🎯", "options": {"A": "(m₁+m₂)/(1-m₁m₂) or -(1+m₁m₂)/(m₁+m₂)", "B": "√(m₁m₂)", "C": "(m₁-m₂)/2", "D": "2/(m₁+m₂)"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "📍 If line through (h,k) with slope m makes intercepts on axes whose sum is constant, then m satisfies: 🌈", "options": {"A": "m² + (something)m + 1 = 0", "B": "m = constant", "C": "m = 0", "D": "m = ∞"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "📐 Lines through (x₁,y₁) at fixed distance d from origin have slopes given by: ✏️", "options": {"A": "quadratic in m", "B": "linear in m", "C": "constant", "D": "no solution"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "🎯 Combined equation of lines with slopes m₁ and m₂ passing through origin: ⭐", "options": {"A": "y² - (m₁+m₂)xy + m₁m₂x² = 0", "B": "x² - (m₁+m₂)xy + m₁m₂y² = 0", "C": "y² + (m₁+m₂)xy + m₁m₂x² = 0", "D": "x² + (m₁+m₂)xy + m₁m₂y² = 0"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "📏 If line makes intercepts on axes such that their sum is constant, locus of foot of perpendicular from origin: 🔢", "options": {"A": "circle", "B": "line", "C": "parabola", "D": "ellipse"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "🔢 Angle between lines joining (0,0) to intersection of line y=mx+c and curve: 📐", "options": {"A": "tan⁻¹[2√(h²-ab)/(a+b)]", "B": "constant", "C": "depends on c", "D": "depends on m"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "✏️ If slopes of lines represented by ax²+2hxy+by²+2gx+2fy+c=0 satisfy m₁+m₂=2 and m₁m₂=3, then: 🎨", "options": {"A": "h/b = -1, a/b = 3", "B": "h/b = 1, a/b = 3", "C": "h/b = -2, a/b = 3", "D": "h/b = 2, a/b = 3"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "📍 Line through point (α,β) with slope m. If it makes triangle area T with axes, then: 🔍", "options": {"A": "m satisfies T m² + 2(α m - β) m + T = 0", "B": "m = T/(αβ)", "C": "m = constant", "D": "m = α/β"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "📐 If line through (1,2) makes equal angles with lines through (2,3) and (3,4), slope = ? ⚡", "options": {"A": "1", "B": "-1", "C": "0", "D": "∞"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "🎯 Lines joining origin to points of intersection of curve and line are perpendicular if: 📏", "options": {"A": "sum of coefficients of x² and y² = 0", "B": "h = 0", "C": "a = b", "D": "ab = 0"}, "correct_answer": "A"}
  ]
}