{
  "title": "Quadratic Formula - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "The quadratic formula for ax² + bx + c = 0 is:", "options": {"A": "x = [-b ± √(b² - 4ac)]/2", "B": "x = [b ± √(b² - 4ac)]/2a", "C": "x = [-b ± √(b² - 4ac)]/2a", "D": "x = [-b ± √(b² + 4ac)]/2a"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "Using quadratic formula, roots of x² - 3x + 2 = 0 are:", "options": {"A": "1, 2", "B": "-1, -2", "C": "1, -2", "D": "-1, 2"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Roots of x² - 5x + 6 = 0 by quadratic formula are:", "options": {"A": "2, 3", "B": "-2, -3", "C": "2, -3", "D": "-2, 3"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "For 2x² - 5x + 2 = 0, using formula, x = ?", "options": {"A": "2, 1/2", "B": "-2, -1/2", "C": "2, -1/2", "D": "-2, 1/2"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "Solve x² + x - 6 = 0 using formula.", "options": {"A": "2, -3", "B": "-2, 3", "C": "2, 3", "D": "-2, -3"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Roots of x² - 8x + 15 = 0 are:", "options": {"A": "3, 5", "B": "-3, -5", "C": "3, -5", "D": "-3, 5"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "Using quadratic formula, solve x² - 4 = 0.", "options": {"A": "±2", "B": "±4", "C": "±1", "D": "0, 4"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Solve 3x² - 7x + 2 = 0 by formula.", "options": {"A": "2, 1/3", "B": "-2, -1/3", "C": "2, -1/3", "D": "-2, 1/3"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Roots of 4x² - 12x + 9 = 0 are:", "options": {"A": "3/2, 3/2", "B": "-3/2, -3/2", "C": "3/2, -3/2", "D": "2/3, 2/3"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Solve x² - 7x + 12 = 0.", "options": {"A": "3, 4", "B": "-3, -4", "C": "3, -4", "D": "-3, 4"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Using formula, roots of 2x² + 5x - 3 = 0 are:", "options": {"A": "1/2, -3", "B": "-1/2, 3", "C": "1/2, 3", "D": "-1/2, -3"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Solve x² - x - 12 = 0.", "options": {"A": "4, -3", "B": "-4, 3", "C": "4, 3", "D": "-4, -3"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Roots of x² + 3x - 10 = 0 are:", "options": {"A": "2, -5", "B": "-2, 5", "C": "2, 5", "D": "-2, -5"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Solve 6x² - x - 1 = 0 by formula.", "options": {"A": "1/2, -1/3", "B": "-1/2, 1/3", "C": "1/2, 1/3", "D": "-1/2, -1/3"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Roots of x² - 2x - 8 = 0 are:", "options": {"A": "4, -2", "B": "-4, 2", "C": "4, 2", "D": "-4, -2"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Solve 9x² - 6x + 1 = 0.", "options": {"A": "1/3, 1/3", "B": "-1/3, -1/3", "C": "1/3, -1/3", "D": "3, 3"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Using formula, solve x² + 5x + 6 = 0.", "options": {"A": "-2, -3", "B": "2, 3", "C": "2, -3", "D": "-2, 3"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Roots of 2x² - 7x + 3 = 0 are:", "options": {"A": "3, 1/2", "B": "-3, -1/2", "C": "3, -1/2", "D": "-3, 1/2"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Solve x² - 9 = 0 using formula.", "options": {"A": "±3", "B": "±9", "C": "±1", "D": "0, 9"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Roots of x² + 7x + 12 = 0 are:", "options": {"A": "-3, -4", "B": "3, 4", "C": "3, -4", "D": "-3, 4"}, "correct_answer": "A"},

    {"id": 21, "difficulty": "medium", "question": "Solve 2x² + √5x - 5 = 0 by quadratic formula.", "options": {"A": "√5/2, -√5", "B": "-√5/2, √5", "C": "√5, -√5", "D": "√5/2, √5"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Using formula, solve √2x² + 7x + 5√2 = 0.", "options": {"A": "-√2, -5/√2", "B": "√2, 5/√2", "C": "√2, -5/√2", "D": "-√2, 5/√2"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Roots of 3x² - 2√6x + 2 = 0 are:", "options": {"A": "√6/3, √6/3", "B": "-√6/3, -√6/3", "C": "√6/3, -√6/3", "D": "√2, √3"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Solve x² - 2√2x + 2 = 0.", "options": {"A": "√2, √2", "B": "-√2, -√2", "C": "√2, -√2", "D": "2, √2"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Using formula, solve 4x² - 4a²x + (a⁴ - b⁴) = 0.", "options": {"A": "(a²+b²)/2, (a²-b²)/2", "B": "(a²-b²)/2, (a²+b²)/2", "C": "a²/2, b²/2", "D": "a², b²"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Solve 1/(x+4) - 1/(x-7) = 11/30, x≠-4,7.", "options": {"A": "1, 2", "B": "2, 3", "C": "1, 3", "D": "2, 5"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Roots of x² + 4√3x + 9 = 0 are:", "options": {"A": "-√3, -3√3", "B": "√3, 3√3", "C": "√3, -3√3", "D": "-√3, 3√3"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Solve (x²+1)/x = 34/15, x≠0.", "options": {"A": "3/5, 5/3", "B": "-3/5, -5/3", "C": "3/5, -5/3", "D": "-3/5, 5/3"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Using quadratic formula, solve abx² + (b² - ac)x - bc = 0.", "options": {"A": "c/b, -b/a", "B": "-c/b, b/a", "C": "c/b, b/a", "D": "-c/b, -b/a"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Solve √3x² + 10x - 8√3 = 0.", "options": {"A": "2√3/3, -4√3", "B": "-2√3/3, 4√3", "C": "2√3/3, 4√3", "D": "-2√3/3, -4√3"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Roots of x² - (√2+1)x + √2 = 0 are:", "options": {"A": "1, √2", "B": "-1, -√2", "C": "1, -√2", "D": "-1, √2"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Solve 4x² - 2(a²+b²)x + a²b² = 0.", "options": {"A": "a²/2, b²/2", "B": "-a²/2, -b²/2", "C": "a²/2, -b²/2", "D": "-a²/2, b²/2"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Using formula, solve x² - 3√5x + 10 = 0.", "options": {"A": "2√5, √5", "B": "-2√5, -√5", "C": "2√5, -√5", "D": "-2√5, √5"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Solve 2x² + ax - a² = 0.", "options": {"A": "a/2, -a", "B": "-a/2, a", "C": "a/2, a", "D": "-a/2, -a"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Roots of 9x² - 9(a+b)x + (2a²+5ab+2b²)=0 are:", "options": {"A": "(2a+b)/3, (a+2b)/3", "B": "-(2a+b)/3, -(a+2b)/3", "C": "(2a+b)/3, -(a+2b)/3", "D": "-(2a+b)/3, (a+2b)/3"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Solve x + 1/x = 25/12, x≠0.", "options": {"A": "4/3, 3/4", "B": "-4/3, -3/4", "C": "4/3, -3/4", "D": "-4/3, 3/4"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Using formula, solve 3x² - 2x + 1/3 = 0.", "options": {"A": "1/3, 1/3", "B": "-1/3, -1/3", "C": "1/3, -1/3", "D": "1, 1/3"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Solve 1/(x-1)(x-2) + 1/(x-2)(x-3) = 2/3, x≠1,2,3.", "options": {"A": "0, 4", "B": "1, 3", "C": "2, 4", "D": "0, 3"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Roots of x² - 2ax + (a² - b²) = 0 are:", "options": {"A": "a+b, a-b", "B": "-a-b, -a+b", "C": "a+b, -a+b", "D": "-a-b, a-b"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Solve 4x² + 4bx - (a² - b²) = 0.", "options": {"A": "(a-b)/2, -(a+b)/2", "B": "-(a-b)/2, (a+b)/2", "C": "(a-b)/2, (a+b)/2", "D": "-(a-b)/2, -(a+b)/2"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Using quadratic formula, solve x² - (√3+1)x + √3 = 0.", "options": {"A": "1, √3", "B": "-1, -√3", "C": "1, -√3", "D": "-1, √3"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Solve (x-1)/(x+1) + (x+1)/(x-1) = 34/15, x≠±1.", "options": {"A": "4, 1/4", "B": "-4, -1/4", "C": "4, -1/4", "D": "-4, 1/4"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Roots of √2x² + 7x + 5√2 = 0 are:", "options": {"A": "-√2, -5/√2", "B": "√2, 5/√2", "C": "√2, -5/√2", "D": "-√2, 5/√2"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Solve x² - 4√2x + 6 = 0.", "options": {"A": "3√2, √2", "B": "-3√2, -√2", "C": "3√2, -√2", "D": "-3√2, √2"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Using formula, 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": "(2a+b)/3, -(a+2b)/3", "D": "-(2a+b)/3, (a+2b)/3"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Solve (x-2)/(x+2) + (x+2)/(x-2) = 34/15, x≠±2.", "options": {"A": "7, 1/7", "B": "-7, -1/7", "C": "7, -1/7", "D": "-7, 1/7"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Roots of x² - (2b-1)x + (b²-b-20)=0 are:", "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": 48, "difficulty": "medium", "question": "Solve 3x² - 2√6x + 2 = 0.", "options": {"A": "√6/3, √6/3", "B": "-√6/3, -√6/3", "C": "√6/3, -√6/3", "D": "√2, √3"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Using formula, solve 4/x - 3 = 5/(2x+3), x≠0,-3/2.", "options": {"A": "3, -1/2", "B": "-3, 1/2", "C": "3, 1/2", "D": "-3, -1/2"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Solve x² - (√3+√2)x + √6 = 0.", "options": {"A": "√3, √2", "B": "-√3, -√2", "C": "√3, -√2", "D": "-√3, √2"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Roots of (a-b+c)x² + 2(a-c)x + (a+b+c)=0 are:", "options": {"A": "-(a+b)/(a-b+c), -1", "B": "(a+b)/(a-b+c), 1", "C": "-(a+b)/(a-b+c), 1", "D": "(a+b)/(a-b+c), -1"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Solve √2x² - 3x - 2√2 = 0.", "options": {"A": "2√2, -1/√2", "B": "-2√2, 1/√2", "C": "2√2, 1/√2", "D": "-2√2, -1/√2"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "Using quadratic formula, solve x² - 2ax + a² - b² = 0.", "options": {"A": "a+b, a-b", "B": "-a-b, -a+b", "C": "a+b, -a+b", "D": "-a-b, a-b"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Solve 4√3x² + 5x - 2√3 = 0.", "options": {"A": "√3/4, -2/√3", "B": "-√3/4, 2/√3", "C": "√3/4, 2/√3", "D": "-√3/4, -2/√3"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "Roots of x² + 2√3x - 9 = 0 are:", "options": {"A": "√3, -3√3", "B": "-√3, 3√3", "C": "√3, 3√3", "D": "-√3, -3√3"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Solve 3x² - 5x + 2 = 0 by formula.", "options": {"A": "1, 2/3", "B": "-1, -2/3", "C": "1, -2/3", "D": "-1, 2/3"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Using formula, solve 2x² - 2√2x + 1 = 0.", "options": {"A": "1/√2, 1/√2", "B": "-1/√2, -1/√2", "C": "1/√2, -1/√2", "D": "√2, √2"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "Solve abx² - (a²+b²)x + ab = 0.", "options": {"A": "a/b, b/a", "B": "-a/b, -b/a", "C": "a/b, -b/a", "D": "-a/b, b/a"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Roots of x² - 2√5x + 3 = 0 are:", "options": {"A": "√5+√2, √5-√2", "B": "-√5-√2, -√5+√2", "C": "√5+√2, -√5+√2", "D": "-√5-√2, √5-√2"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "Solve 2x² - 7x + 5 = 0.", "options": {"A": "5/2, 1", "B": "-5/2, -1", "C": "5/2, -1", "D": "-5/2, 1"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "Using quadratic formula, solve x² - (p+q)x + pq = 0.", "options": {"A": "p, q", "B": "-p, -q", "C": "p, -q", "D": "-p, q"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "Solve 3x² + 5√5x - 10 = 0.", "options": {"A": "√5/3, -2√5", "B": "-√5/3, 2√5", "C": "√5/3, 2√5", "D": "-√5/3, -2√5"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Roots of 2x² + 3√3x + 3 = 0 are:", "options": {"A": "-√3/2, -√3", "B": "√3/2, √3", "C": "√3/2, -√3", "D": "-√3/2, √3"}, "correct_answer": "A"},
    {"id": 64, "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": 65, "difficulty": "medium", "question": "Using formula, solve 4x² - 4a²x + a⁴ - b⁴ = 0.", "options": {"A": "(a²+b²)/2, (a²-b²)/2", "B": "-(a²+b²)/2, -(a²-b²)/2", "C": "(a²+b²)/2, -(a²-b²)/2", "D": "-(a²+b²)/2, (a²-b²)/2"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "Solve 1/(x-3) + 2/(x-2) = 8/x, x≠0,2,3.", "options": {"A": "6, 1", "B": "-6, -1", "C": "6, -1", "D": "-6, 1"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "Roots of x² - 2√3x + 3 = 0 are:", "options": {"A": "√3, √3", "B": "-√3, -√3", "C": "√3, -√3", "D": "3, 1"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "Solve (x²+3)/x = 4, x≠0.", "options": {"A": "1, 3", "B": "-1, -3", "C": "1, -3", "D": "-1, 3"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Using quadratic formula, solve x² - 2mx + m² - n² = 0.", "options": {"A": "m+n, m-n", "B": "-m-n, -m+n", "C": "m+n, -m+n", "D": "-m-n, m-n"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "Solve √5x² + 9x + 4√5 = 0.", "options": {"A": "-√5, -4/√5", "B": "√5, 4/√5", "C": "√5, -4/√5", "D": "-√5, 4/√5"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "Roots of x² - (a+b)x + ab = 0 are:", "options": {"A": "a, b", "B": "-a, -b", "C": "a, -b", "D": "-a, b"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Solve 3x² - 2√6x + 2 = 0.", "options": {"A": "√6/3, √6/3", "B": "-√6/3, -√6/3", "C": "√6/3, -√6/3", "D": "√2, √3"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "Using formula, solve 2x² + 3√3x + 3 = 0.", "options": {"A": "-√3/2, -√3", "B": "√3/2, √3", "C": "√3/2, -√3", "D": "-√3/2, √3"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "Solve x² - (√5+1)x + √5 = 0.", "options": {"A": "1, √5", "B": "-1, -√5", "C": "1, -√5", "D": "-1, √5"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Roots of 4x² - 4a²x + (a⁴-b⁴)=0 are:", "options": {"A": "(a²+b²)/2, (a²-b²)/2", "B": "-(a²+b²)/2, -(a²-b²)/2", "C": "(a²+b²)/2, -(a²-b²)/2", "D": "-(a²+b²)/2, (a²-b²)/2"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Solve x + 1/x = 10/3, x≠0.", "options": {"A": "3, 1/3", "B": "-3, -1/3", "C": "3, -1/3", "D": "-3, 1/3"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "Using quadratic formula, solve 3x² - 2√6x + 2 = 0.", "options": {"A": "√6/3, √6/3", "B": "-√6/3, -√6/3", "C": "√6/3, -√6/3", "D": "√2, √3"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Solve 1/(x+3) + 1/(x+4) = 1/(x+6) + 1/(x+7), x≠-3,-4,-6,-7.", "options": {"A": "-5", "B": "5", "C": "-5/2", "D": "5/2"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "Roots of x² - 2√3x + 2 = 0 are:", "options": {"A": "√3+1, √3-1", "B": "-√3-1, -√3+1", "C": "√3+1, -√3+1", "D": "-√3-1, √3-1"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "Solve 2x² + 5√3x + 6 = 0.", "options": {"A": "-2√3, -√3/2", "B": "2√3, √3/2", "C": "2√3, -√3/2", "D": "-2√3, √3/2"}, "correct_answer": "A"},

    {"id": 81, "difficulty": "hard", "question": "Using quadratic formula, solve for x: 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": "Solve: (x²+1)² - x² = 0.", "options": {"A": "±i√((√5-1)/2), ±i√((√5+1)/2)", "B": "±√((√5-1)/2), ±√((√5+1)/2)", "C": "±i, ±1", "D": "No real roots"}, "correct_answer": "D"},
    {"id": 83, "difficulty": "hard", "question": "Using formula, solve: x⁴ - 5x² + 4 = 0.", "options": {"A": "±1, ±2", "B": "±i, ±2i", "C": "±1, ±√2", "D": "±2, ±√2"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Solve: √(x+4) + √(x-4) = √(2x+1).", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "Using quadratic formula in substitution, solve: 2(x²+1/x²) - 9(x+1/x) + 14 = 0.", "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": 86, "difficulty": "hard", "question": "Solve: (x² - 5x + 5)^(x² - 9x + 20) = 1.", "options": {"A": "2, 3, 4, 5", "B": "1, 4, 5", "C": "2, 3, 5", "D": "1, 2, 3, 4, 5"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Using formula after substitution, solve: 3^(2x) - 10·3^x + 9 = 0.", "options": {"A": "0, 2", "B": "1, 2", "C": "0, 1", "D": "1, 3"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "Solve: √(3x² - 7x - 30) - √(2x² - 7x - 5) = x - 5.", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "Using quadratic formula, solve for x: (a-b)x² + (b-c)x + (c-a) = 0.", "options": {"A": "1, (c-a)/(a-b)", "B": "-1, (a-c)/(a-b)", "C": "1, (a-c)/(a-b)", "D": "-1, (c-a)/(a-b)"}, "correct_answer": "A"},
    {"id": 90, "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": 91, "difficulty": "hard", "question": "Using formula, solve: x = √(6 + √(6 + √(6 + ... ∞))).", "options": {"A": "3", "B": "2", "C": "1", "D": "0"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "Solve: |x² - x - 6| = x + 2.", "options": {"A": "-2, 2, 4", "B": "-2, 2, 3", "C": "-2, 4", "D": "2, 4"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Using quadratic formula after substitution, solve: 2^2x - 3·2^(x+2) + 32 = 0.", "options": {"A": "2, 3", "B": "1, 2", "C": "3, 4", "D": "0, 1"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "Solve: √(x+3 - 4√(x-1)) + √(x+8 - 6√(x-1)) = 1.", "options": {"A": "[5,10]", "B": "[1,5]", "C": "[5,8]", "D": "[2,7]"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Using formula, 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": 96, "difficulty": "hard", "question": "Solve: (x²+1/x²) - 3(x-1/x) - 2 = 0.", "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": 97, "difficulty": "hard", "question": "Using quadratic formula in disguised form, solve: (x-a)/(x-b) + (x-b)/(x-a) = a/b + b/a, a≠0,b≠0.", "options": {"A": "0, a+b", "B": "a, b", "C": "0, ab", "D": "a+b, ab"}, "correct_answer": "A"},
    {"id": 98, "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": 99, "difficulty": "hard", "question": "Using formula, 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": 100, "difficulty": "hard", "question": "Solve: x√x + (x-6)√(x-6) = 6√(x(x-6)).", "options": {"A": "4, 9", "B": "0, 6", "C": "1, 9", "D": "4, 6"}, "correct_answer": "A"}
  ]
}