{
  "title": "Solution by Factorisation - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Solve by factorisation: x² + 5x + 6 = 0", "options": {"A": "-2, -3", "B": "2, 3", "C": "-2, 3", "D": "2, -3"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "Factors of x² - 7x + 12 = 0 are:", "options": {"A": "(x-3)(x-4)", "B": "(x+3)(x+4)", "C": "(x-2)(x-6)", "D": "(x+2)(x+6)"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Solve: x² - 3x + 2 = 0", "options": {"A": "1, 2", "B": "-1, -2", "C": "1, -2", "D": "-1, 2"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Factorise: x² - 8x + 15 = 0", "options": {"A": "(x-3)(x-5)", "B": "(x+3)(x+5)", "C": "(x-2)(x-7.5)", "D": "(x+2)(x+7.5)"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "Solve: x² + x - 6 = 0", "options": {"A": "2, -3", "B": "-2, 3", "C": "3, -2", "D": "-3, 2"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Factors of x² - 10x + 21 = 0:", "options": {"A": "(x-3)(x-7)", "B": "(x+3)(x+7)", "C": "(x-2)(x-10.5)", "D": "(x+2)(x+10.5)"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "Solve: x² - 4 = 0", "options": {"A": "2, -2", "B": "4, -4", "C": "1, -4", "D": "0, 4"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Factorise: x² + 8x + 15 = 0", "options": {"A": "(x+3)(x+5)", "B": "(x-3)(x-5)", "C": "(x+2)(x+7.5)", "D": "(x-2)(x-7.5)"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Solve: x² - 5x + 6 = 0", "options": {"A": "2, 3", "B": "-2, -3", "C": "2, -3", "D": "-2, 3"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Factors of x² + 2x - 8 = 0:", "options": {"A": "(x+4)(x-2)", "B": "(x-4)(x+2)", "C": "(x+8)(x-1)", "D": "(x-8)(x+1)"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Solve: x² - 9 = 0", "options": {"A": "3, -3", "B": "9, -9", "C": "0, 9", "D": "1, -9"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Factorise: x² - 6x + 8 = 0", "options": {"A": "(x-2)(x-4)", "B": "(x+2)(x+4)", "C": "(x-1)(x-8)", "D": "(x+1)(x+8)"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Solve: x² + 4x - 5 = 0", "options": {"A": "1, -5", "B": "-1, 5", "C": "2, -2.5", "D": "-2, 2.5"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Factors of x² - x - 12 = 0:", "options": {"A": "(x-4)(x+3)", "B": "(x+4)(x-3)", "C": "(x-6)(x+2)", "D": "(x+6)(x-2)"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Solve: x² + 6x + 9 = 0", "options": {"A": "-3, -3", "B": "3, 3", "C": "0, -6", "D": "3, -3"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Factorise: x² - 12x + 35 = 0", "options": {"A": "(x-5)(x-7)", "B": "(x+5)(x+7)", "C": "(x-3)(x-11.67)", "D": "(x+3)(x+11.67)"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Solve: x² - 2x - 15 = 0", "options": {"A": "5, -3", "B": "-5, 3", "C": "3, -5", "D": "-3, 5"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Factors of x² + 7x + 10 = 0:", "options": {"A": "(x+2)(x+5)", "B": "(x-2)(x-5)", "C": "(x+1)(x+10)", "D": "(x-1)(x-10)"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Solve: 2x² + 5x + 3 = 0", "options": {"A": "-1, -3/2", "B": "1, 3/2", "C": "-1, 3/2", "D": "1, -3/2"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Factorise: 3x² + 7x + 2 = 0", "options": {"A": "(3x+1)(x+2)", "B": "(3x-1)(x-2)", "C": "(x+1)(3x+2)", "D": "(x-1)(3x-2)"}, "correct_answer": "A"},

   
  {"id": 21, "difficulty": "medium", "question": "Solve: 6x² - 7x - 3 = 0", "options": {"A": "3/2, -1/3", "B": "-3/2, 1/3", "C": "2/3, -3", "D": "-2/3, 3"}, "correct_answer": "A"},
  {"id": 22, "difficulty": "medium", "question": "Factorise: 2x² + √5x - 5 = 0", "options": {"A": "(2x - √5)(x + √5)", "B": "(2x + √5)(x - √5)", "C": "(√2x - 5)(√2x + 1)", "D": "(x - √5)(2x + √5)"}, "correct_answer": "B"},
  {"id": 23, "difficulty": "medium", "question": "Solve: √2x² + 7x + 5√2 = 0", "options": {"A": "-√2, -5/√2", "B": "√2, 5/√2", "C": "-2√2, -5/2", "D": "2√2, 5/2"}, "correct_answer": "A"},
  {"id": 24, "difficulty": "medium", "question": "Factorise: 4x² - 4a²x + (a⁴ - b⁴) = 0", "options": {"A": "(2x - a² - b²)(2x - a² + b²)", "B": "(2x - a²)² - b⁴", "C": "4(x - a²/2)² - b⁴", "D": "(2x - a²)² - (b²)²"}, "correct_answer": "A"},
  {"id": 25, "difficulty": "medium", "question": "Solve: 3x² - 2√6x + 2 = 0", "options": {"A": "√6/3, √6/3", "B": "-√6/3, -√6/3", "C": "√2, √3", "D": "2/√6, 2/√6"}, "correct_answer": "A"},
  {"id": 26, "difficulty": "medium", "question": "Factorise: x² + 4√3x + 9 = 0", "options": {"A": "(x + √3)(x + 3√3)", "B": "(x - √3)(x - 3√3)", "C": "(x + 2√3)² - 3", "D": "(x + 3)² - 12"}, "correct_answer": "A"},
  {"id": 27, "difficulty": "medium", "question": "Solve: 9x² - 9(a+b)x + (2a²+5ab+2b²) = 0", "options": {"A": "(2a+b)/3, (a+2b)/3", "B": "-(2a+b)/3, -(a+2b)/3", "C": "(a+2b)/3, (2a+b)/3", "D": "(3a+b)/9, (a+3b)/9"}, "correct_answer": "A"},
  {"id": 28, "difficulty": "medium", "question": "Factorise: abx² + (b² - ac)x - bc = 0", "options": {"A": "(bx - c)(ax + b)", "B": "(bx + c)(ax - b)", "C": "(abx - c)(x + b)", "D": "(abx + c)(x - b)"}, "correct_answer": "A"},
  {"id": 29, "difficulty": "medium", "question": "Solve: 4√3x² + 5x - 2√3 = 0", "options": {"A": "√3/4, -2/√3", "B": "-√3/4, 2/√3", "C": "√3/2, -1/√3", "D": "-√3/2, 1/√3"}, "correct_answer": "A"},
  {"id": 30, "difficulty": "medium", "question": "Factorise: 2x² + ax - a² = 0", "options": {"A": "(2x - a)(x + a)", "B": "(2x + a)(x - a)", "C": "(x - a)(2x + a)", "D": "(x + a)(2x - a)"}, "correct_answer": "A"},
  {"id": 31, "difficulty": "medium", "question": "Solve: x² - 2ax + a² - b² = 0", "options": {"A": "a+b, a-b", "B": "-a-b, -a+b", "C": "b+a, b-a", "D": "-b-a, -b+a"}, "correct_answer": "A"},
  {"id": 32, "difficulty": "medium", "question": "Factorise: x² - 2√5x + 3 = 0", "options": {"A": "(x - √5 - √2)(x - √5 + √2)", "B": "(x - √5)² - 2", "C": "(x - 3)(x - √5/3)", "D": "(x - 1)(x - 3)"}, "correct_answer": "A"},
  {"id": 33, "difficulty": "medium", "question": "Solve: 4x² - 2(a²+b²)x + a²b² = 0", "options": {"A": "a²/2, b²/2", "B": "-a²/2, -b²/2", "C": "a², b²", "D": "ab/2, ab/2"}, "correct_answer": "A"},
  {"id": 34, "difficulty": "medium", "question": "Factorise: √3x² + 10x - 8√3 = 0", "options": {"A": "(√3x - 2)(x + 4√3)", "B": "(√3x + 2)(x - 4√3)", "C": "(x - 2√3)(√3x + 4)", "D": "(x + 2√3)(√3x - 4)"}, "correct_answer": "A"},
  {"id": 35, "difficulty": "medium", "question": "Solve: x² - (√3+1)x + √3 = 0", "options": {"A": "1, √3", "B": "-1, -√3", "C": "1, -√3", "D": "-1, √3"}, "correct_answer": "A"},
  {"id": 36, "difficulty": "medium", "question": "Factorise: 2x² - 7x + 3 = 0", "options": {"A": "(2x - 1)(x - 3)", "B": "(2x + 1)(x + 3)", "C": "(x - 1)(2x - 3)", "D": "(x + 1)(2x + 3)"}, "correct_answer": "A"},
  {"id": 37, "difficulty": "medium", "question": "Solve: 3x² - 5x + 2 = 0", "options": {"A": "1, 2/3", "B": "-1, -2/3", "C": "2, 1/3", "D": "-2, -1/3"}, "correct_answer": "A"},
  {"id": 38, "difficulty": "medium", "question": "Factorise: 4x² - 12x + 9 = 0", "options": {"A": "(2x - 3)²", "B": "(2x + 3)²", "C": "(4x - 3)(x - 3)", "D": "(4x + 3)(x + 3)"}, "correct_answer": "A"},
  {"id": 39, "difficulty": "medium", "question": "Solve: 2x² + 5√3x + 6 = 0", "options": {"A": "-2√3, -√3/2", "B": "2√3, √3/2", "C": "-√3, -2√3", "D": "√3, 2√3"}, "correct_answer": "A"},
  {"id": 40, "difficulty": "medium", "question": "Factorise: x² + 2√2x - 6 = 0", "options": {"A": "(x + 3√2)(x - √2)", "B": "(x - 3√2)(x + √2)", "C": "(x + √2)² - 8", "D": "(x - √2)² - 4"}, "correct_answer": "A"},
  {"id": 41, "difficulty": "medium", "question": "Solve: 9x² - 6kx + 4 = 0 when it has equal roots", "options": {"A": "k = ±2", "B": "k = ±1", "C": "k = ±3", "D": "k = ±4"}, "correct_answer": "A"},
  {"id": 42, "difficulty": "medium", "question": "Factorise: (a-b+c)x² + 2(a-c)x + (a+b+c) = 0", "options": {"A": "[(a-b+c)x + (a+b+c)](x+1)", "B": "[(a-b+c)x + (a+b+c)](x-1)", "C": "(x+1)[(a-b+c)x + (a+b+c)]", "D": "Both A and C"}, "correct_answer": "D"},
  {"id": 43, "difficulty": "medium", "question": "Solve: x² - 4ax + 4a² - b² = 0", "options": {"A": "2a+b, 2a-b", "B": "-2a-b, -2a+b", "C": "a+2b, a-2b", "D": "-a-2b, -a+2b"}, "correct_answer": "A"},
  {"id": 44, "difficulty": "medium", "question": "Factorise: 12x² - 7x + 1 = 0", "options": {"A": "(3x-1)(4x-1)", "B": "(3x+1)(4x+1)", "C": "(6x-1)(2x-1)", "D": "(6x+1)(2x+1)"}, "correct_answer": "A"},
  {"id": 45, "difficulty": "medium", "question": "Solve: 8x² - 22x + 15 = 0", "options": {"A": "3/2, 5/4", "B": "-3/2, -5/4", "C": "2/3, 4/5", "D": "-2/3, -4/5"}, "correct_answer": "A"},
  {"id": 46, "difficulty": "medium", "question": "Factorise: 15x² - 16x + 4 = 0", "options": {"A": "(3x-2)(5x-2)", "B": "(3x+2)(5x+2)", "C": "(15x-4)(x-1)", "D": "(15x+4)(x+1)"}, "correct_answer": "A"},
  {"id": 47, "difficulty": "medium", "question": "Solve: 6x² + 11x + 4 = 0", "options": {"A": "-1/2, -4/3", "B": "1/2, 4/3", "C": "-2/3, -1", "D": "2/3, 1"}, "correct_answer": "A"},
  {"id": 48, "difficulty": "medium", "question": "Factorise: 10x² - 9x - 7 = 0", "options": {"A": "(5x-7)(2x+1)", "B": "(5x+7)(2x-1)", "C": "(10x-7)(x+1)", "D": "(10x+7)(x-1)"}, "correct_answer": "A"},
  {"id": 49, "difficulty": "medium", "question": "Solve: 4x² + 4√3x + 3 = 0", "options": {"A": "-√3/2, -√3/2", "B": "√3/2, √3/2", "C": "-√3, -√3", "D": "√3, √3"}, "correct_answer": "A"},
  {"id": 50, "difficulty": "medium", "question": "Factorise: x² - 2x(a²+b²)/(a²-b²) + 1 = 0", "options": {"A": "[x - (a+b)/(a-b)][x - (a-b)/(a+b)]", "B": "[x - a/(a-b)][x - b/(a+b)]", "C": "[x - 1][x - (a²+b²)/(a²-b²)]", "D": "Not factorisable simply"}, "correct_answer": "A"},
  {"id": 51, "difficulty": "medium", "question": "Solve: 16x² - 40x + 25 = 0", "options": {"A": "5/4, 5/4", "B": "-5/4, -5/4", "C": "5/2, 5/2", "D": "-5/2, -5/2"}, "correct_answer": "A"},
  {"id": 52, "difficulty": "medium", "question": "Factorise: 25x² - 30x + 9 = 0", "options": {"A": "(5x-3)²", "B": "(5x+3)²", "C": "(25x-9)(x-1)", "D": "(25x+9)(x+1)"}, "correct_answer": "A"},
  {"id": 53, "difficulty": "medium", "question": "Solve: 2√2x² + 7x + 5√2 = 0", "options": {"A": "-√2, -5/√2", "B": "√2, 5/√2", "C": "-5/2, -√2/2", "D": "5/2, √2/2"}, "correct_answer": "A"},
  {"id": 54, "difficulty": "medium", "question": "Factorise: x² + 2(a-3)x + a²-6a+8 = 0", "options": {"A": "(x + a-4)(x + a-2)", "B": "(x - a+4)(x - a+2)", "C": "(x + a-3)² - 1", "D": "(x - a+3)² - 1"}, "correct_answer": "A"},
  {"id": 55, "difficulty": "medium", "question": "Solve: 9x² + 18x + 8 = 0", "options": {"A": "-2/3, -4/3", "B": "2/3, 4/3", "C": "-1/3, -8/3", "D": "1/3, 8/3"}, "correct_answer": "A"},
  {"id": 56, "difficulty": "medium", "question": "Factorise: 4x² - 4a²x + a⁴ - b⁴ = 0", "options": {"A": "(2x - a² - b²)(2x - a² + b²)", "B": "(2x - a²)² - (b²)²", "C": "4(x - a²/2)² - b⁴", "D": "All of these"}, "correct_answer": "D"},
  {"id": 57, "difficulty": "medium", "question": "Solve: abx² - (a²+b²)x + ab = 0", "options": {"A": "a/b, b/a", "B": "-a/b, -b/a", "C": "b/a, a/b", "D": "-b/a, -a/b"}, "correct_answer": "A"},
  {"id": 58, "difficulty": "medium", "question": "Factorise: x² - 2x sinθ + sin²θ - cos²θ = 0", "options": {"A": "(x - sinθ - cosθ)(x - sinθ + cosθ)", "B": "(x - 1)² - cos²θ", "C": "(x - sinθ)² - cos²θ", "D": "Both A and C"}, "correct_answer": "D"},
  {"id": 59, "difficulty": "medium", "question": "(p+q)²x² - 2(p²-q²)x + (p-q)² = 0", "options": {"A": "(p-q)/(p+q), (p-q)/(p+q)", "B": "(p+q)/(p-q), (p+q)/(p-q)", "C": "1, (p-q)²/(p+q)²", "D": "1, 1"}, "correct_answer": "A"},
  {"id": 60, "difficulty": "medium", "question": "Factorise: x² - 2ax + a² - b² - c² + 2bc = 0", "options": {"A": "[x - (a+b-c)][x - (a-b+c)]", "B": "[x - (a+b+c)][x - (a-b-c)]", "C": "(x-a)² - (b-c)²", "D": "Both A and C"}, "correct_answer": "D"},
  {"id": 61, "difficulty": "medium", "question": "Solve: 4x² - 12x + 5 = 0", "options": {"A": "1/2, 5/2", "B": "-1/2, -5/2", "C": "2/3, 5/3", "D": "-2/3, -5/3"}, "correct_answer": "A"},
  {"id": 62, "difficulty": "medium", "question": "Factorise: 3x² + 4√3x + 4 = 0", "options": {"A": "(√3x + 2)²", "B": "(3x + 2√3)²", "C": "(x√3 + 2)²", "D": "All represent same"}, "correct_answer": "D"},
  {"id": 63, "difficulty": "medium", "question": "Solve: x² - (2b-1)x + (b²-b-20) = 0", "options": {"A": "b+4, b-5", "B": "-b-4, -b+5", "C": "b-4, b+5", "D": "-b+4, -b-5"}, "correct_answer": "A"},
  {"id": 64, "difficulty": "medium", "question": "Factorise: (a²+b²)x² - 2(ac+bd)x + (c²+d²) = 0 when ad=bc", "options": {"A": "[√(a²+b²)x - √(c²+d²)]²", "B": "(a²+b²)[x - (ac+bd)/(a²+b²)]²", "C": "Perfect square", "D": "All of these"}, "correct_answer": "D"},
  {"id": 65, "difficulty": "medium", "question": "Solve: 2x² - 2√2x + 1 = 0", "options": {"A": "1/√2, 1/√2", "B": "-1/√2, -1/√2", "C": "√2, √2", "D": "-√2, -√2"}, "correct_answer": "A"},
  {"id": 66, "difficulty": "medium", "question": "Factorise: x² + 2√3x - 9 = 0", "options": {"A": "(x + 3√3)(x - √3)", "B": "(x - 3√3)(x + √3)", "C": "(x + √3)² - 12", "D": "(x - √3)² - 6"}, "correct_answer": "A"},
  {"id": 67, "difficulty": "medium", "question": "Solve: 3x² + 5√5x - 10 = 0", "options": {"A": "√5/3, -2√5", "B": "-√5/3, 2√5", "C": "√5, -2√5/3", "D": "-√5, 2√5/3"}, "correct_answer": "A"},
  {"id": 68, "difficulty": "medium", "question": "Factorise: x² - (p+q)x + pq = 0", "options": {"A": "(x-p)(x-q)", "B": "(x+p)(x+q)", "C": "(x-p)(x+q)", "D": "(x+p)(x-q)"}, "correct_answer": "A"},
  {"id": 69, "difficulty": "medium", "question": "Solve: 2x² + 3√3x + 3 = 0", "options": {"A": "-√3/2, -√3", "B": "√3/2, √3", "C": "-√3, -√3/2", "D": "√3, √3/2"}, "correct_answer": "A"},
  {"id": 70, "difficulty": "medium", "question": "Factorise: 4x² + 4√2x + 2 = 0", "options": {"A": "(2x + √2)²", "B": "(√2x + 1)²", "C": "2(√2x + 1)²", "D": "All of these"}, "correct_answer": "D"},
  {"id": 71, "difficulty": "medium", "question": "Solve: x² - 3√2x + 4 = 0", "options": {"A": "2√2, √2", "B": "-2√2, -√2", "C": "√2, 2√2", "D": "-√2, -2√2"}, "correct_answer": "A"},
  {"id": 72, "difficulty": "medium", "question": "Factorise: 9x² - 12x + 4 = 0", "options": {"A": "(3x-2)²", "B": "(3x+2)²", "C": "(9x-4)(x-1)", "D": "(9x+4)(x+1)"}, "correct_answer": "A"},
  {"id": 73, "difficulty": "medium", "question": "Solve: 10x² - 11x + 3 = 0", "options": {"A": "3/5, 1/2", "B": "-3/5, -1/2", "C": "5/3, 2", "D": "-5/3, -2"}, "correct_answer": "A"},
  {"id": 74, "difficulty": "medium", "question": "Factorise: x² - 2√2x + 2 = 0", "options": {"A": "(x - √2)²", "B": "(x + √2)²", "C": "(x - 2)(x - √2)", "D": "(x + 2)(x + √2)"}, "correct_answer": "A"},
  {"id": 75, "difficulty": "medium", "question": "Solve: 7x² - 10x + 3 = 0", "options": {"A": "1, 3/7", "B": "-1, -3/7", "C": "7/3, 1", "D": "-7/3, -1"}, "correct_answer": "A"},
  {"id": 76, "difficulty": "medium", "question": "Factorise: 8x² - 14x + 5 = 0", "options": {"A": "(4x-5)(2x-1)", "B": "(4x+5)(2x+1)", "C": "(8x-5)(x-1)", "D": "(8x+5)(x+1)"}, "correct_answer": "A"},
  {"id": 77, "difficulty": "medium", "question": "Solve: 12x² - 13x + 3 = 0", "options": {"A": "3/4, 1/3", "B": "-3/4, -1/3", "C": "4/3, 3", "D": "-4/3, -3"}, "correct_answer": "A"},
  {"id": 78, "difficulty": "medium", "question": "Factorise: 15x² - x - 6 = 0", "options": {"A": "(3x-2)(5x+3)", "B": "(3x+2)(5x-3)", "C": "(15x-6)(x+1)", "D": "(15x+6)(x-1)"}, "correct_answer": "B"},
  {"id": 79, "difficulty": "medium", "question": "Solve: 4x² - 4√3x + 3 = 0", "options": {"A": "√3/2, √3/2", "B": "-√3/2, -√3/2", "C": "√3, √3", "D": "-√3, -√3"}, "correct_answer": "A"},
  {"id": 80, "difficulty": "medium", "question": "Factorise: x² - (a+b)x + ab - c² = 0", "options": {"A": "[x - (a+c)][x - (b-c)]", "B": "[x - (a-c)][x - (b+c)]", "C": "(x-a)(x-b) - c²", "D": "All of these if rearranged"}, "correct_answer": "D"},

  {"id": 81, "difficulty": "hard", "question": "Solve by factorisation: a²b²x² + b²x - a²x - 1 = 0", "options": {"A": "1/a², -1/b²", "B": "-1/a², 1/b²", "C": "1/a², 1/b²", "D": "-1/a², -1/b²"}, "correct_answer": "A"},
  {"id": 82, "difficulty": "hard", "question": "Factorise: (x²+1)² - x² = 0", "options": {"A": "(x²+x+1)(x²-x+1)", "B": "(x²+√2x+1)(x²-√2x+1)", "C": "(x²+2x+1)(x²-2x+1)", "D": "Not factorisable into real linear factors"}, "correct_answer": "D"},
  {"id": 83, "difficulty": "hard", "question": "Solve: (a-b+c)x² + 2(a-c)x + (a+b+c) = 0", "options": {"A": "-1, -(a+b+c)/(a-b+c)", "B": "1, -(a+b+c)/(a-b+c)", "C": "-1, (a+b+c)/(a-b+c)", "D": "1, (a+b+c)/(a-b+c)"}, "correct_answer": "A"},
  {"id": 84, "difficulty": "hard", "question": "Factorise: (a²+b²+c²)x² - 2(ab+bc+ca)x + (a²+b²+c²) = 0 when a=b=c", "options": {"A": "(a²+b²+c²)(x-1)²", "B": "3a²(x-1)²", "C": "Perfect square", "D": "All of these"}, "correct_answer": "D"},
  {"id": 85, "difficulty": "hard", "question": "Solve: (a+b-2c)x² + (b+c-2a)x + (c+a-2b) = 0", "options": {"A": "1, (c+a-2b)/(a+b-2c)", "B": "-1, (2b-c-a)/(a+b-2c)", "C": "1, (2b-c-a)/(a+b-2c)", "D": "-1, (c+a-2b)/(a+b-2c)"}, "correct_answer": "A"},
  {"id": 86, "difficulty": "hard", "question": "Factorise: (sin²A)x² - 2sinA·cosA·x + cos²A = 0", "options": {"A": "(sinA · x - cosA)²", "B": "sin²A(x - cotA)²", "C": "(x sinA - cosA)²", "D": "All of these"}, "correct_answer": "D"},
  {"id": 87, "difficulty": "hard", "question": "Solve: x⁴ - 5x² + 4 = 0 by factorisation", "options": {"A": "±1, ±2", "B": "±i, ±2i", "C": "±1, ±√2", "D": "±2, ±√2"}, "correct_answer": "A"},
  {"id": 88, "difficulty": "hard", "question": "Factorise: (x-1)(x-2)(x-3)(x-4) - 15 = 0 (find factors after substitution)", "options": {"A": "(x²-5x+5)(x²-5x+6) - 15", "B": "(x²-5x+7)(x²-5x+4) after solving", "C": "Not easily factorisable", "D": "Leads to quadratic in y=x²-5x"}, "correct_answer": "D"},
  {"id": 89, "difficulty": "hard", "question": "Solve: (x²+3x+2)(x²+7x+12) = 24", "options": {"A": "0, -5, (-5±√17)/2", "B": "0, -5, (-5±√15)/2", "C": "0, -4, (-5±√17)/2", "D": "1, -5, (-5±√17)/2"}, "correct_answer": "A"},
  {"id": 90, "difficulty": "hard", "question": "Factorise: √(x+4) + √(x-4) = √(2x+1) after squaring and rearranging", "options": {"A": "Leads to x²-10x+25=0", "B": "(x-5)²=0", "C": "x=5", "D": "All of these"}, "correct_answer": "D"},
  {"id": 91, "difficulty": "hard", "question": "Solve: 2(x²+1/x²) - 9(x+1/x) + 14 = 0 by substitution y=x+1/x", "options": {"A": "2, 1/2, 3, 1/3", "B": "1, 2, 3, 1/3", "C": "2, 1/2, 1, 1", "D": "1, 1/2, 2, 3"}, "correct_answer": "A"},
  {"id": 92, "difficulty": "hard", "question": "Factorise: |x² - x - 6| = x+2 gives equations that factorise to", "options": {"A": "(x-4)(x+2)=0 and (x-2)(x+2)=0", "B": "(x-4)(x+2)=0 and x²-4=0", "C": "x²-4x-4=0 and x²-4=0", "D": "(x-2)(x-4)=0 and (x+2)²=0"}, "correct_answer": "B"},
  {"id": 93, "difficulty": "hard", "question": "Solve: 3^(2x) - 10·3^x + 9 = 0 by substitution y=3^x", "options": {"A": "0, 2", "B": "1, 2", "C": "0, 1", "D": "1, 3"}, "correct_answer": "A"},
  {"id": 94, "difficulty": "hard", "question": "Factorise: √(3x²-7x-30) - √(2x²-7x-5) = x-5 leads to factorisable form", "options": {"A": "(x-6)(...)=0", "B": "x=6 only", "C": "(x-6) factor", "D": "All of these"}, "correct_answer": "D"},
  {"id": 95, "difficulty": "hard", "question": "Solve: (x-1)(x-2)(x-3)(x-4) = 15", "options": {"A": "(5±√5)/2, (5±√21)/2", "B": "(5±√3)/2, (5±√17)/2", "C": "(5±√2)/2, (5±√19)/2", "D": "No real roots"}, "correct_answer": "A"},
  {"id": 96, "difficulty": "hard", "question": "Factorise: x = √(6+√(6+√(6+...))) leads to x²-x-6=0", "options": {"A": "(x-3)(x+2)=0", "B": "x=3 only", "C": "Positive root is 3", "D": "All of these"}, "correct_answer": "D"},
  {"id": 97, "difficulty": "hard", "question": "Solve: (x²+1/x²) - 3(x-1/x) - 2 = 0 by substitution", "options": {"A": "(3±√5)/2, (1±√5)/2", "B": "(3±√13)/2, (1±√5)/2", "C": "(3±√5)/2, (1±√3)/2", "D": "(5±√13)/2, (1±√5)/2"}, "correct_answer": "A"},
  {"id": 98, "difficulty": "hard", "question": "Factorise: (x-a)/(x-b) + (x-b)/(x-a) = a/b + b/a leads to", "options": {"A": "x(x-(a+b))=0", "B": "x(x-a-b)=0", "C": "x=0 or x=a+b", "D": "All of these"}, "correct_answer": "D"},
  {"id": 99, "difficulty": "hard", "question": "Solve: √(x+2√(x-1)) + √(x-2√(x-1)) = √(x-1)", "options": {"A": "x ≥ 5", "B": "x ≥ 2", "C": "x ≥ 1", "D": "x ≥ 3"}, "correct_answer": "A"},
  {"id": 100, "difficulty": "hard", "question": "Factorise: x√x + (x-6)√(x-6) = 6√(x(x-6)) leads to", "options": {"A": "(√x - √(x-6))²(√x + √(x-6)) = 0", "B": "(√x - √(x-6))² = 0 for x=9", "C": "x=4,9", "D": "All of these"}, "correct_answer": "D"}
   ]
}