{
  "title": "Standard Form of Quadratic Equation - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "The standard form of a quadratic equation is:", "options": {"A": "ax² + bx + c = 0, a≠0", "B": "ax² + bx + c", "C": "ax + b = 0", "D": "ax² + bx = 0"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "In ax² + bx + c = 0, 'a' is called:", "options": {"A": "Quadratic coefficient", "B": "Linear coefficient", "C": "Constant term", "D": "Root"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Which is NOT a quadratic equation?", "options": {"A": "x² - 3x + 2 = 0", "B": "2x² + 5x - 3 = 0", "C": "x³ - 2x + 1 = 0", "D": "3x² - 7 = 0"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "The equation 3x - 5 = 0 is:", "options": {"A": "Quadratic", "B": "Linear", "C": "Cubic", "D": "Constant"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "In x² - 5x + 6 = 0, the coefficient of x is:", "options": {"A": "1", "B": "-5", "C": "6", "D": "0"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Which is in standard form?", "options": {"A": "2x² - 3x + 5 = 0", "B": "5 = 2x² - 3x", "C": "2x² = 3x - 5", "D": "2x² - 3x = -5"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "The constant term in 3x² - 7x + 2 = 0 is:", "options": {"A": "3", "B": "-7", "C": "2", "D": "0"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "x² = 9 can be written in standard form as:", "options": {"A": "x² - 9 = 0", "B": "x² + 0x - 9 = 0", "C": "Both A and B", "D": "x² = 9 only"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "Convert 2x(x-3) = 5 to standard form.", "options": {"A": "2x² - 6x - 5 = 0", "B": "2x² - 3x - 5 = 0", "C": "2x² - 6x + 5 = 0", "D": "2x² - 3x + 5 = 0"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "The degree of quadratic equation is:", "options": {"A": "1", "B": "2", "C": "3", "D": "0"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "In standard form, the right side is always:", "options": {"A": "0", "B": "1", "C": "x", "D": "any number"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "For x²/2 + 3x - 1 = 0, a, b, c are:", "options": {"A": "1/2, 3, -1", "B": "1, 3, -1", "C": "0.5, 3, 1", "D": "2, 3, -1"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Which represents a quadratic equation?", "options": {"A": "y = mx + c", "B": "y = ax² + bx + c", "C": "y = ax³ + bx² + c", "D": "y = k"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "The equation (x-2)(x+3) = 0 in standard form is:", "options": {"A": "x² + x - 6 = 0", "B": "x² - x - 6 = 0", "C": "x² + x + 6 = 0", "D": "x² - x + 6 = 0"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "If a=0 in ax² + bx + c = 0, it becomes:", "options": {"A": "Still quadratic", "B": "Linear", "C": "Cubic", "D": "Invalid"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "Write 3 - 2x² = 5x in standard form.", "options": {"A": "2x² + 5x - 3 = 0", "B": "-2x² - 5x + 3 = 0", "C": "2x² + 5x - 3 = 0 or -2x² - 5x + 3 = 0", "D": "2x² - 5x + 3 = 0"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "In 5x² - 3 = 0, b = ?", "options": {"A": "5", "B": "-3", "C": "0", "D": "1"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "The general form of quadratic equation is:", "options": {"A": "ax² + bx + c = 0, a≠0", "B": "ax + b = 0", "C": "ax² = 0", "D": "x² = k"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Convert (x+1)² = 4 to standard form.", "options": {"A": "x² + 2x - 3 = 0", "B": "x² + 2x + 1 = 4", "C": "x² + 2x - 3 = 0", "D": "x² + 2x + 5 = 0"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "For a pure quadratic equation:", "options": {"A": "b=0, c≠0", "B": "b≠0, c=0", "C": "b=0, c=0", "D": "a=0"}, "correct_answer": "A"},

    {"id": 21, "difficulty": "medium", "question": "Write √2x² - 5x + 3√2 = 0 in standard form with integer coefficients if possible.", "options": {"A": "√2x² - 5x + 3√2 = 0 (already standard)", "B": "2x² - 5√2x + 6 = 0", "C": "x² - (5/√2)x + 3 = 0", "D": "Can't have integer coefficients"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Convert (x-√2)(x+√3) = 0 to standard form.", "options": {"A": "x² + (√3-√2)x - √6 = 0", "B": "x² - √6 = 0", "C": "x² - (√2-√3)x - √6 = 0", "D": "x² + √5x - √6 = 0"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "The equation (k-1)x² + 2x - 7 = 0 is quadratic when:", "options": {"A": "k ≠ 1", "B": "k = 1", "C": "k = 0", "D": "k any real"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Write 2/x + 3/(x+1) = 5 in standard quadratic form (x≠0,-1).", "options": {"A": "5x² - x - 2 = 0", "B": "5x² + x - 2 = 0", "C": "5x² - x + 2 = 0", "D": "5x² + x + 2 = 0"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "For what p is (p-3)x² + 2x - 1 = 0 not quadratic?", "options": {"A": "p = 3", "B": "p = 0", "C": "p = -3", "D": "p = 1"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Convert x + 1/x = 3, x≠0 to standard form.", "options": {"A": "x² - 3x + 1 = 0", "B": "x² + 3x + 1 = 0", "C": "x² - 3x - 1 = 0", "D": "x² + 3x - 1 = 0"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Write √(x+3) = x+1 in standard quadratic form.", "options": {"A": "x² + x - 2 = 0", "B": "x² + x + 2 = 0", "C": "x² - x - 2 = 0", "D": "x² - x + 2 = 0"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "The equation (m²-4)x² + (m-2)x + 3 = 0 is quadratic for:", "options": {"A": "m ≠ ±2", "B": "m ≠ 2", "C": "m ≠ -2", "D": "all m"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Convert (x²-1)/(x-1) = 3, x≠1 to standard form.", "options": {"A": "x - 2 = 0", "B": "x² - 3x + 2 = 0", "C": "x - 3 = 0", "D": "Not quadratic"}, "correct_answer": "D"},
    {"id": 30, "difficulty": "medium", "question": "Write |x-2| = 3 in standard quadratic form.", "options": {"A": "x² - 4x - 5 = 0", "B": "x² - 4x + 1 = 0", "C": "x² - 4x - 5 = 0 or x² - 4x + 1 = 0", "D": "Not always quadratic"}, "correct_answer": "D"},
    {"id": 31, "difficulty": "medium", "question": "For (k²-1)x² + kx + 1 = 0 to be quadratic:", "options": {"A": "k ≠ ±1", "B": "k ≠ 1", "C": "k ≠ -1", "D": "k ≠ 0"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Convert x/(x+1) + (x+1)/x = 25/12, x≠0,-1 to standard form.", "options": {"A": "12x² - 25x + 12 = 0", "B": "12x² + 25x + 12 = 0", "C": "12x² - 25x - 12 = 0", "D": "12x² + 25x - 12 = 0"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Write √(2x-1) = x-2 in standard quadratic form.", "options": {"A": "x² - 6x + 5 = 0", "B": "x² - 6x + 9 = 0", "C": "x² - 5x + 5 = 0", "D": "x² - 5x + 9 = 0"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "The equation ax² + bx + c = 0 where a,b,c are constants with a≠0 represents:", "options": {"A": "Always quadratic", "B": "Quadratic if b≠0", "C": "Quadratic if c≠0", "D": "May be linear"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Convert (x-1)³ - (x-2)³ = 1 to standard quadratic form.", "options": {"A": "3x² - 9x + 7 = 0", "B": "3x² - 9x + 8 = 0", "C": "3x² - 6x + 4 = 0", "D": "Not quadratic"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Write 2^(x+1) + 2^(1-x) = 5 in quadratic form by substitution.", "options": {"A": "2y² - 5y + 2 = 0 where y=2^x", "B": "y² - 5y + 4 = 0 where y=2^x", "C": "4y² - 5y + 1 = 0 where y=2^x", "D": "Not reducible to quadratic"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "For (sinθ)x² + (cosθ)x + tanθ = 0 to be quadratic:", "options": {"A": "sinθ ≠ 0", "B": "cosθ ≠ 0", "C": "tanθ ≠ 0", "D": "θ ≠ nπ"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Convert log(x+1) + log(x-1) = log 3 to standard quadratic form.", "options": {"A": "x² - 4 = 0", "B": "x² - 2 = 0", "C": "x² - 3 = 0", "D": "x² - 1 = 0"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Write x⁴ - 5x² + 4 = 0 in quadratic form by substitution.", "options": {"A": "y² - 5y + 4 = 0, y=x²", "B": "y² - 5y + 4 = 0, y=x", "C": "y² + 5y + 4 = 0, y=x²", "D": "y² - 4y + 5 = 0, y=x²"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "The equation (a-1)x² + 2ax + (a+1) = 0 is quadratic when:", "options": {"A": "a ≠ 1", "B": "a ≠ 0", "C": "a ≠ -1", "D": "a any real"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Convert 1/(x-2) + 1/(x-3) = 2/(x-4) to standard quadratic form.", "options": {"A": "x² - 9x + 20 = 0", "B": "x² - 9x + 18 = 0", "C": "x² - 8x + 15 = 0", "D": "x² - 8x + 16 = 0"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Write 3^(2x) - 10·3^x + 9 = 0 in quadratic form.", "options": {"A": "y² - 10y + 9 = 0, y=3^x", "B": "y² - 10y + 9 = 0, y=3x", "C": "y² - 9y + 10 = 0, y=3^x", "D": "y² + 10y - 9 = 0, y=3^x"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "For (k²-3k+2)x² + (k-1)x + 7 = 0 to be quadratic:", "options": {"A": "k ≠ 1,2", "B": "k ≠ 1", "C": "k ≠ 2", "D": "k ≠ 0"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Convert √(x+5) - √(x-3) = 2 to quadratic form after squaring.", "options": {"A": "x² - 8x + 16 = 0", "B": "x² - 4x + 4 = 0", "C": "x - 4 = 0", "D": "Not quadratic"}, "correct_answer": "D"},
    {"id": 45, "difficulty": "medium", "question": "Write sin²θ·x² - 2sinθ·cosθ·x + cos²θ = 0 in standard quadratic form.", "options": {"A": "Already in standard form", "B": "(sinθ·x - cosθ)² = 0", "C": "Both A and B", "D": "Not quadratic if sinθ=0"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "The equation (|a|-1)x² + 3x - 2 = 0 is quadratic when:", "options": {"A": "|a| ≠ 1", "B": "a ≠ 1", "C": "a ≠ -1", "D": "a ≠ ±1"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Convert (x+2)²/3 + (x-1)²/4 = 1 to standard quadratic form.", "options": {"A": "7x² + 20x - 5 = 0", "B": "7x² + 20x + 5 = 0", "C": "7x² - 20x - 5 = 0", "D": "7x² - 20x + 5 = 0"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Write 2cos²θ·x² - 3sinθ·x + 1 = 0 in standard quadratic form.", "options": {"A": "Already standard", "B": "(2cos²θ)x² - 3sinθ·x + 1 = 0", "C": "Both A and B", "D": "Not quadratic if cosθ=0"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "medium", "question": "For (t-√2)x² + √3x - π = 0 to be quadratic:", "options": {"A": "t ≠ √2", "B": "t ≠ 0", "C": "t ≠ -√2", "D": "t any real"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Convert 1 + 1/(1+1/x) = 2, x≠0,-1 to standard quadratic form.", "options": {"A": "x² + x - 1 = 0", "B": "x² - x - 1 = 0", "C": "x² + x + 1 = 0", "D": "x² - x + 1 = 0"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Write (x²+1)/x + x/(x²+1) = 5/2, x≠0 in quadratic form by substitution y=x+1/x.", "options": {"A": "y² - (5/2)y - 1 = 0", "B": "y² - (5/2)y + 1 = 0", "C": "y² - 5y + 2 = 0", "D": "Not directly quadratic in x"}, "correct_answer": "D"},
    {"id": 52, "difficulty": "medium", "question": "The equation (a²+b²)x² + 2abx + (a²-b²) = 0 is always quadratic because:", "options": {"A": "a²+b² ≠ 0 for real a,b not both zero", "B": "a,b real", "C": "Coefficient of x² never zero", "D": "All of these"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "medium", "question": "Convert √(x+1) + √(x-1) = √(2x) to quadratic form after squaring.", "options": {"A": "x² - 2x + 1 = 0", "B": "x² - 1 = 0", "C": "x - 1 = 0", "D": "No quadratic formed"}, "correct_answer": "D"},
    {"id": 54, "difficulty": "medium", "question": "Write x + √(x) - 6 = 0 in quadratic form by substitution.", "options": {"A": "y² + y - 6 = 0, y=√x", "B": "y² + y - 6 = 0, y=x", "C": "y² - y - 6 = 0, y=√x", "D": "y² - y - 6 = 0, y=x"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "For (m-2)x² + √(m-1)x + 5 = 0 to be quadratic with real coefficients:", "options": {"A": "m ≠ 2 and m ≥ 1", "B": "m > 1", "C": "m ≥ 1 and m ≠ 2", "D": "m ≠ 2"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "Convert |x-3| + |x-4| = 1 to quadratic form.", "options": {"A": "Not reducible to single quadratic", "B": "x² - 7x + 12 = 0", "C": "2x² - 14x + 25 = 0", "D": "Depends on interval"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Write log(x²) - log(x) = log(3) in standard quadratic form.", "options": {"A": "x - 3 = 0", "B": "x² - 3x = 0", "C": "x² - 3 = 0", "D": "Not quadratic"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "The equation (p²+q²-1)x² + 2pqx + (p²+q²) = 0 is quadratic when:", "options": {"A": "p²+q² ≠ 1", "B": "p,q not both zero", "C": "Always quadratic for real p,q", "D": "p²+q² > 0"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "medium", "question": "Convert (x-1)^(1/3) + (x-1)^(-1/3) = 2 to quadratic form by substitution.", "options": {"A": "y² - 2y + 1 = 0, y=(x-1)^(1/3)", "B": "y² + 2y + 1 = 0, y=(x-1)^(1/3)", "C": "y² - 2y - 1 = 0, y=(x-1)^(1/3)", "D": "Not reducible to quadratic"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "Write 2sin²θ·x² - 3cosθ·x + 1 = 0 in standard quadratic form.", "options": {"A": "Already standard", "B": "2(1-cos²θ)x² - 3cosθ·x + 1 = 0", "C": "Both A and B", "D": "Not quadratic if sinθ=0"}, "correct_answer": "C"},
    {"id": 61, "difficulty": "medium", "question": "For (√(k-1))x² + 3x - 2 = 0 to be quadratic with real coefficients:", "options": {"A": "k ≥ 1", "B": "k > 1", "C": "k ≥ 1 and k ≠ 2", "D": "k ≠ 1"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "Convert (x²-3x+2)/(x-1) = 5, x≠1 to standard form.", "options": {"A": "x - 7 = 0", "B": "x² - 8x + 7 = 0", "C": "x² - 3x - 3 = 0", "D": "Not quadratic"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Write 4^x - 6·2^x + 8 = 0 in quadratic form.", "options": {"A": "y² - 6y + 8 = 0, y=2^x", "B": "y² - 3y + 2 = 0, y=4^x", "C": "y² - 6y + 8 = 0, y=4^x", "D": "y² - 8y + 6 = 0, y=2^x"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "The equation (a+b)x² + (a-b)x + ab = 0 is quadratic when:", "options": {"A": "a+b ≠ 0", "B": "a ≠ -b", "C": "Both A and B", "D": "Always quadratic"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "Convert √(2x+3) - √(x+1) = 1 to quadratic form.", "options": {"A": "x² - 10x + 9 = 0", "B": "x² - 2x + 1 = 0", "C": "x² - 6x + 9 = 0", "D": "x - 3 = 0"}, "correct_answer": "B"},
    {"id": 66, "difficulty": "medium", "question": "Write sec²θ·x² - 2tanθ·x + 1 = 0 in standard quadratic form.", "options": {"A": "Already standard", "B": "(1+tan²θ)x² - 2tanθ·x + 1 = 0", "C": "Both A and B", "D": "Not quadratic if cosθ=0"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "For (|m|-2)x² + 5x - 3 = 0 to be quadratic:", "options": {"A": "|m| ≠ 2", "B": "m ≠ ±2", "C": "Both A and B", "D": "m ≠ 2"}, "correct_answer": "C"},
    {"id": 68, "difficulty": "medium", "question": "Convert (x+1)/(x-1) + (x-1)/(x+1) = 10/3, x≠±1 to standard quadratic form.", "options": {"A": "3x² - 25x + 3 = 0", "B": "3x² - 25x - 3 = 0", "C": "3x² + 25x + 3 = 0", "D": "3x² + 25x - 3 = 0"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Write (2x-3)^(2/3) + (2x-3)^(1/3) - 6 = 0 in quadratic form by substitution.", "options": {"A": "y² + y - 6 = 0, y=(2x-3)^(1/3)", "B": "y² + y - 6 = 0, y=2x-3", "C": "y² - y - 6 = 0, y=(2x-3)^(1/3)", "D": "y² - y - 6 = 0, y=2x-3"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "The equation (k²-4k+3)x² + (k-1)x + (k-2) = 0 is quadratic when:", "options": {"A": "k ≠ 1,3", "B": "k ≠ 1", "C": "k ≠ 3", "D": "k any real"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "Convert x/(x-1) + (x-1)/x = 2.5, x≠0,1 to standard quadratic form.", "options": {"A": "2x² - 9x + 2 = 0", "B": "2x² - 9x - 2 = 0", "C": "2x² + 9x + 2 = 0", "D": "2x² + 9x - 2 = 0"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Write √(x+4) + √(x-4) = √(2x+1) leads to which quadratic?", "options": {"A": "x² - 10x + 25 = 0", "B": "x² - 8x + 16 = 0", "C": "x² - 6x + 9 = 0", "D": "No quadratic"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "For (a-√3)x² + √2x - π = 0 to be quadratic:", "options": {"A": "a ≠ √3", "B": "a ≠ 0", "C": "a ≠ -√3", "D": "a any real"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "Convert (x²+3x+2)/(x+1) = 4, x≠-1 to standard form.", "options": {"A": "x - 2 = 0", "B": "x² - x - 2 = 0", "C": "x² + 3x - 2 = 0", "D": "Not quadratic"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Write 9^x - 4·3^(x+1) + 27 = 0 in quadratic form.", "options": {"A": "y² - 12y + 27 = 0, y=3^x", "B": "y² - 4y + 3 = 0, y=9^x", "C": "y² - 12y + 27 = 0, y=9^x", "D": "y² - 36y + 27 = 0, y=3^x"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "The equation (sin²θ-1)x² + cosθ·x + 1 = 0 is quadratic when:", "options": {"A": "sin²θ ≠ 1", "B": "θ ≠ nπ/2", "C": "Always quadratic", "D": "Never quadratic as sin²θ-1 ≤ 0"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "Convert 1/(x+2) + 2/(x+3) = 3/(x+4) to standard quadratic form.", "options": {"A": "x² + 5x + 6 = 0", "B": "x² + 9x + 18 = 0", "C": "x² + 7x + 12 = 0", "D": "x² + 11x + 30 = 0"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Write tan²θ·x² - 2secθ·x + 1 = 0 in standard quadratic form.", "options": {"A": "Already standard", "B": "(sec²θ-1)x² - 2secθ·x + 1 = 0", "C": "Both A and B", "D": "Not quadratic if cosθ=0"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "For (√(k)+1)x² + (√(k)-1)x + k = 0 to be quadratic with real coefficients:", "options": {"A": "k ≥ 0", "B": "k > 0", "C": "k ≥ 0 and k ≠ 1", "D": "k any non-negative"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "Convert (x²-4)/(x-2) = 3, x≠2 to standard form.", "options": {"A": "x - 5 = 0", "B": "x² - 3x - 10 = 0", "C": "x² - 5x + 6 = 0", "D": "Not quadratic"}, "correct_answer": "A"},

    {"id": 81, "difficulty": "hard", "question": "Write the equation (a²+b²)x² - 2(ac+bd)x + (c²+d²) = 0 in standard quadratic form and state condition for it to be pure quadratic.", "options": {"A": "Standard as given; pure quadratic when ac+bd=0", "B": "Standard as given; never pure quadratic", "C": "Needs rearrangement; pure when c=d=0", "D": "Not necessarily quadratic"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "Convert the system x+y=a, xy=b to a single quadratic equation in standard form.", "options": {"A": "t² - at + b = 0", "B": "t² + at + b = 0", "C": "t² - at - b = 0", "D": "t² + at - b = 0"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "Write the equation √(x+3-4√(x-1)) + √(x+8-6√(x-1)) = 1 after substitution y=√(x-1) in quadratic form.", "options": {"A": "|y-2| + |y-3| = 1 leads to cases, not single quadratic", "B": "y² - 5y + 6 = 0", "C": "2y² - 10y + 12 = 0", "D": "No quadratic form"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Convert the equation (x²+1)² = 4x(x²-1) to standard quadratic form after simplification.", "options": {"A": "x⁴ - 4x³ + 2x² + 4x + 1 = 0, not quadratic", "B": "Leads to (x²-2x-1)(x²+2x-1)=0", "C": "Two quadratics: x²-2x-1=0 and x²+2x-1=0", "D": "Both B and C"}, "correct_answer": "D"},
    {"id": 85, "difficulty": "hard", "question": "Write the equation (x²-5x+5)^(x²-9x+20) = 1 as combination of quadratic equations.", "options": {"A": "x²-5x+5=1 or x²-9x+20=0 or (x²-5x+5=-1 with even exponent)", "B": "Three quadratic equations possible", "C": "Both A and B", "D": "Not reducible to quadratics"}, "correct_answer": "C"},
    {"id": 86, "difficulty": "hard", "question": "Convert the parametric equations x = at², y = 2at to a quadratic in x and y.", "options": {"A": "y² = 4ax", "B": "x² = 4ay", "C": "y² - 4ax = 0", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 87, "difficulty": "hard", "question": "Write the equation (x-1)(x-2)(x-3)(x-4) = 15 in quadratic form after substitution y=x²-5x.", "options": {"A": "y² + 4y - 15 = 0", "B": "y² + 4y - 12 = 0", "C": "y² - 4y - 15 = 0", "D": "y² - 4y - 12 = 0"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "Convert the equation sin²θ·x² - 2sin(θ+π/4)·x + √2 = 0 to standard quadratic form.", "options": {"A": "Already standard", "B": "sin²θ·x² - √2(sinθ+cosθ)x + √2 = 0", "C": "Both A and B", "D": "Can't simplify further"}, "correct_answer": "C"},
    {"id": 89, "difficulty": "hard", "question": "Write the equation √(x²+3x+2) + √(x²+7x+12) = √(4x²+40x+90) in quadratic form after squaring.", "options": {"A": "Leads to x²+5x+6=0", "B": "Leads to linear equation", "C": "Leads to 2x²+10x+12=0", "D": "No quadratic form"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "Convert the equation (a+b-2c)x² + (b+c-2a)x + (c+a-2b) = 0 to factored quadratic form.", "options": {"A": "(x-1)[(a+b-2c)x - (c+a-2b)] = 0", "B": "(x-1)[(a+b-2c)x + (c+a-2b)] = 0", "C": "Already in standard form", "D": "Can't factor generally"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Write the equation x = √(6+√(6+√(6+...))) in standard quadratic form.", "options": {"A": "x² - x - 6 = 0", "B": "x² - 6 = 0", "C": "x² - √6x - 6 = 0", "D": "x² - 6x + 6 = 0"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "Convert the equation (x²+3x+2)(x²+7x+12) = 24 to quadratic form after substitution.", "options": {"A": "y² + 10y = 0 where y=x²+5x", "B": "y² + 10y - 24 = 0 where y=x²+5x", "C": "y² + 10y + 24 = 0 where y=x²+5x", "D": "Not reducible to single quadratic"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Write the equation 2^(2x+1) + 2^(x+2) = 2^(x+3) + 4 in quadratic form by substitution.", "options": {"A": "2y² + 4y = 8y + 4 where y=2^x", "B": "2y² - 4y - 4 = 0 where y=2^x", "C": "y² - 2y - 2 = 0 where y=2^x", "D": "y² - 4y + 4 = 0 where y=2^x"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "Convert the equation √(x+1) + √(2x+3) = √(3x+4) to quadratic form after squaring.", "options": {"A": "x² + 2x + 1 = 0", "B": "x² - 2x + 1 = 0", "C": "4x² - 4x + 1 = 0", "D": "No quadratic form"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "Write the equation (cos²θ-sin²θ)x² - 2cosθ·sinθ·x + (cos²θ-sin²θ) = 0 in standard quadratic form.", "options": {"A": "cos2θ·x² - sin2θ·x + cos2θ = 0", "B": "Already standard", "C": "Both A and B", "D": "Not quadratic if θ=π/4"}, "correct_answer": "C"},
    {"id": 96, "difficulty": "hard", "question": "Convert the equation (x²+1)/x² + (x²-1)/x = 5/2 to quadratic form by substitution y=x+1/x.", "options": {"A": "y² + y - 6 = 0", "B": "y² + y - 6.5 = 0", "C": "Not directly quadratic in y", "D": "Leads to y² - (5/2)y - 2 = 0"}, "correct_answer": "D"},
    {"id": 97, "difficulty": "hard", "question": "Write the equation |x-1| + |x-2| = 3 as combination of quadratic equations.", "options": {"A": "Leads to three cases with linear equations only", "B": "Can produce x²-3x+2=0 in one case", "C": "No quadratic equations involved", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 98, "difficulty": "hard", "question": "Convert the equation x√x + (x-6)√(x-6) = 6√(x(x-6)) to quadratic form by substitution y=√x - √(x-6).", "options": {"A": "y³ - 6y = 0", "B": "y(y²-6) = 0", "C": "Leads to quadratic in y²", "D": "Not reducible to quadratic"}, "correct_answer": "B"},
    {"id": 99, "difficulty": "hard", "question": "Write the equation (x²-1)² + 8x² = 4x(x²+1) in standard quadratic form after simplification.", "options": {"A": "x⁴ - 4x³ + 6x² - 4x + 1 = 0", "B": "(x²-2x+1)² = 0", "C": "x² - 2x + 1 = 0", "D": "Both B and C"}, "correct_answer": "D"},
    {"id": 100, "difficulty": "hard", "question": "Convert the equation √(3x²-7x-30) - √(2x²-7x-5) = x-5 to quadratic form.", "options": {"A": "Leads to (x-6)(3x+5) = 0 after squaring", "B": "x² - 12x + 36 = 0", "C": "Both A and B possible depending on domain", "D": "No quadratic form"}, "correct_answer": "C"}
  ]
}