{
  "title": "Relationship between Zeros and Coefficients (Polynomials) - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "For quadratic polynomial ax² + bx + c, sum of zeros =", "options": {"A": "-b/a", "B": "b/a", "C": "c/a", "D": "-c/a"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "For quadratic polynomial ax² + bx + c, product of zeros =", "options": {"A": "c/a", "B": "-c/a", "C": "b/a", "D": "-b/a"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "For cubic polynomial ax³ + bx² + cx + d, sum of zeros =", "options": {"A": "-b/a", "B": "b/a", "C": "c/a", "D": "-c/a"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "For cubic polynomial ax³ + bx² + cx + d, sum of product of zeros taken two at a time =", "options": {"A": "c/a", "B": "-c/a", "C": "b/a", "D": "-b/a"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "For cubic polynomial ax³ + bx² + cx + d, product of zeros =", "options": {"A": "-d/a", "B": "d/a", "C": "-c/a", "D": "c/a"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "If α, β are zeros of x² - 5x + 6, then α + β =", "options": {"A": "5", "B": "-5", "C": "6", "D": "-6"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "If α, β are zeros of x² - 5x + 6, then αβ =", "options": {"A": "6", "B": "-6", "C": "5", "D": "-5"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "If zeros of x² + 3x + 2 are α and β, then α + β =", "options": {"A": "-3", "B": "3", "C": "2", "D": "-2"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "If zeros of x² + 3x + 2 are α and β, then αβ =", "options": {"A": "2", "B": "-2", "C": "3", "D": "-3"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "For 2x² - 3x + 1, sum of zeros =", "options": {"A": "3/2", "B": "-3/2", "C": "1/2", "D": "-1/2"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "For 2x² - 3x + 1, product of zeros =", "options": {"A": "1/2", "B": "-1/2", "C": "3/2", "D": "-3/2"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "If α, β, γ are zeros of x³ - 6x² + 11x - 6, then α + β + γ =", "options": {"A": "6", "B": "-6", "C": "11", "D": "-11"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "If α, β, γ are zeros of x³ - 6x² + 11x - 6, then αβ + βγ + γα =", "options": {"A": "11", "B": "-11", "C": "6", "D": "-6"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "If α, β, γ are zeros of x³ - 6x² + 11x - 6, then αβγ =", "options": {"A": "6", "B": "-6", "C": "11", "D": "-11"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "For cubic polynomial with zeros 1, 2, 3, the polynomial is:", "options": {"A": "x³ - 6x² + 11x - 6", "B": "x³ + 6x² + 11x + 6", "C": "x³ - 6x² - 11x - 6", "D": "x³ + 6x² - 11x + 6"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "If sum of zeros = 3 and product of zeros = 2, quadratic polynomial is:", "options": {"A": "x² - 3x + 2", "B": "x² + 3x + 2", "C": "x² - 3x - 2", "D": "x² + 3x - 2"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "If α + β = 4 and αβ = 3, then quadratic polynomial is:", "options": {"A": "x² - 4x + 3", "B": "x² + 4x + 3", "C": "x² - 4x - 3", "D": "x² + 4x - 3"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "For 3x² - 2x - 1, sum of zeros =", "options": {"A": "2/3", "B": "-2/3", "C": "1/3", "D": "-1/3"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "For 3x² - 2x - 1, product of zeros =", "options": {"A": "-1/3", "B": "1/3", "C": "2/3", "D": "-2/3"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "If zeros are reciprocals of each other in ax² + bx + c, then:", "options": {"A": "a = c", "B": "a = -c", "C": "b = c", "D": "b = -c"}, "correct_answer": "A"},

    {"id": 21, "difficulty": "medium", "question": "If α, β are zeros of 2x² + 5x + 2, then 1/α + 1/β =", "options": {"A": "-5/2", "B": "5/2", "C": "1/2", "D": "-1/2"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "If α, β are zeros of x² - x - 12, then α² + β² =", "options": {"A": "25", "B": "24", "C": "13", "D": "12"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "If α, β are zeros of 3x² - 4x + 1, then α³ + β³ =", "options": {"A": "28/27", "B": "37/27", "C": "19/27", "D": "10/27"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "If α, β are zeros of ax² + bx + c, then α² + β² =", "options": {"A": "(b² - 2ac)/a²", "B": "(b² + 2ac)/a²", "C": "(b² - 2ac)/a", "D": "(b² + 2ac)/a"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "If α, β are zeros of x² + px + q, then (α - β)² =", "options": {"A": "p² - 4q", "B": "p² + 4q", "C": "4q - p²", "D": "p² - q"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "If α, β are zeros of 2x² - 3x - 5, then α/β + β/α =", "options": {"A": "-29/10", "B": "29/10", "C": "-10/29", "D": "10/29"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "If α, β, γ are zeros of x³ - 3x² + 2x - 4, then α² + β² + γ² =", "options": {"A": "5", "B": "9", "C": "13", "D": "17"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "If α, β are zeros of x² - 6x + 8, then α³ + β³ =", "options": {"A": "72", "B": "144", "C": "216", "D": "288"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "If α, β are zeros of ax² + bx + c, then 1/α² + 1/β² =", "options": {"A": "(b² - 2ac)/c²", "B": "(b² + 2ac)/c²", "C": "(b² - 2ac)/a²", "D": "(b² + 2ac)/a²"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "If α, β, γ are zeros of 2x³ - x² - 7x + 6, then 1/α + 1/β + 1/γ =", "options": {"A": "7/6", "B": "-7/6", "C": "1/6", "D": "-1/6"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "If α, β are zeros of x² + 2x - 1, then (α+1)(β+1) =", "options": {"A": "0", "B": "1", "C": "2", "D": "-2"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "If α, β are zeros of 3x² - 5x + 2, then α²β + αβ² =", "options": {"A": "10/9", "B": "-10/9", "C": "9/10", "D": "-9/10"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "If α, β, γ are zeros of x³ - 12x² + 44x - 48, then αβγ =", "options": {"A": "48", "B": "-48", "C": "44", "D": "-44"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "If α, β are zeros of 2x² + 3x - 5, then (α-1)(β-1) =", "options": {"A": "-5", "B": "5", "C": "3", "D": "-3"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "If α, β are zeros of x² - (k+1)x + (k²+ k+1), then α² + β² =", "options": {"A": "k² - 2k - 1", "B": "k² + 2k - 1", "C": "k² - 2k + 1", "D": "k² + 2k + 1"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "If α, β are zeros of ax² + bx + c, then α/β + β/α =", "options": {"A": "(b² - 2ac)/ac", "B": "(b² + 2ac)/ac", "C": "(b² - 2ac)/a²", "D": "(b² + 2ac)/a²"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "If α, β, γ are zeros of x³ - 2x² - 5x + 6, then α² + β² + γ² =", "options": {"A": "14", "B": "18", "C": "22", "D": "26"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "If α, β are zeros of x² - 8x + 15, then α² + β² - αβ =", "options": {"A": "34", "B": "49", "C": "64", "D": "79"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "If α, β, γ are zeros of 2x³ - 5x² - 4x + 3, then αβ + βγ + γα =", "options": {"A": "-2", "B": "2", "C": "-5/2", "D": "5/2"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "If α, β are zeros of x² + px + q, then α²β + αβ² =", "options": {"A": "-pq", "B": "pq", "C": "-p²q", "D": "p²q"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "If α, β are zeros of 3x² - 4x + 7, then 1/(3α+1) + 1/(3β+1) =", "options": {"A": "4/11", "B": "-4/11", "C": "11/4", "D": "-11/4"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "If α, β, γ are zeros of x³ - px² + qx - r, then α² + β² + γ² =", "options": {"A": "p² - 2q", "B": "p² + 2q", "C": "q² - 2p", "D": "q² + 2p"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "If α, β are zeros of 2x² - 6x + 3, then α³ + β³ =", "options": {"A": "27/4", "B": "9/2", "C": "27/2", "D": "9/4"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "If α, β, γ are zeros of x³ - 6x² + 3x + 10, then αβγ =", "options": {"A": "-10", "B": "10", "C": "-3", "D": "3"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "If α, β are zeros of x² - √2x + 1, then α² + β² =", "options": {"A": "0", "B": "2", "C": "4", "D": "√2"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "If α, β, γ are zeros of 2x³ + 3x² - 11x - 6, then α + β + γ =", "options": {"A": "-3/2", "B": "3/2", "C": "-11/2", "D": "11/2"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "If α, β are zeros of ax² + bx + c, then (α+1)(β+1) =", "options": {"A": "(a - b + c)/a", "B": "(a + b + c)/a", "C": "(a - b - c)/a", "D": "(a + b - c)/a"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "If α, β are zeros of x² + 5x + 6, then α²β + αβ² =", "options": {"A": "-30", "B": "30", "C": "-11", "D": "11"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "If α, β, γ are zeros of x³ - 3x² + 4, then αβ + βγ + γα =", "options": {"A": "0", "B": "3", "C": "4", "D": "-3"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "If α, β are zeros of 4x² - 8x + 3, then 1/α² + 1/β² =", "options": {"A": "40/9", "B": "9/40", "C": "16/9", "D": "9/16"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "If α, β, γ are zeros of x³ + 2x² - 5x - 6, then αβγ =", "options": {"A": "6", "B": "-6", "C": "5", "D": "-5"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "If α, β are zeros of x² - 2√5x + 3, then α/β + β/α =", "options": {"A": "14/3", "B": "-14/3", "C": "3/14", "D": "-3/14"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "If α, β, γ are zeros of 3x³ - 5x² - 11x - 3, then 1/α + 1/β + 1/γ =", "options": {"A": "-11/3", "B": "11/3", "C": "-5/3", "D": "5/3"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "If α, β are zeros of 2x² + 4x - 6, then (α+2)(β+2) =", "options": {"A": "3", "B": "-3", "C": "5", "D": "-5"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "If α, β, γ are zeros of x³ - 4x² + x + 6, then α² + β² + γ² =", "options": {"A": "14", "B": "18", "C": "22", "D": "26"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "If α, β are zeros of x² - (k+2)x + 2k, then α² + β² =", "options": {"A": "k² + 4", "B": "k² - 4", "C": "k² + 4k + 4", "D": "k² - 4k + 4"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "If α, β, γ are zeros of 2x³ - 3x² - 12x + 20, then αβ + βγ + γα =", "options": {"A": "-6", "B": "6", "C": "-3", "D": "3"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "If α, β are zeros of 3x² - 6x + 4, then α³ + β³ =", "options": {"A": "0", "B": "8", "C": "16", "D": "24"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "If α, β, γ are zeros of x³ - 9x² + 26x - 24, then α + β + γ =", "options": {"A": "9", "B": "-9", "C": "26", "D": "-26"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "If α, β are zeros of ax² + bx + c, then α²β + αβ² =", "options": {"A": "-bc/a²", "B": "bc/a²", "C": "-bc/a", "D": "bc/a"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "If α, β, γ are zeros of 3x³ + 2x² - 7x + 2, then 1/αβ + 1/βγ + 1/γα =", "options": {"A": "-7/2", "B": "7/2", "C": "-2/7", "D": "2/7"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "If α, β are zeros of x² - 4x + 1, then α³ + β³ =", "options": {"A": "52", "B": "40", "C": "36", "D": "28"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "If α, β, γ are zeros of x³ - 12x² + 39x - 28, then αβγ =", "options": {"A": "28", "B": "-28", "C": "39", "D": "-39"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "If α, β are zeros of 2x² + 3x - 5, then (2α+1)(2β+1) =", "options": {"A": "-15", "B": "15", "C": "-5", "D": "5"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "If α, β, γ are zeros of 2x³ - 7x² + 8x - 3, then α² + β² + γ² =", "options": {"A": "17/4", "B": "9/4", "C": "25/4", "D": "33/4"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "If α, β are zeros of x² - 2x + 3, then α² + β² =", "options": {"A": "-2", "B": "2", "C": "4", "D": "6"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "If α, β, γ are zeros of x³ - 6x² + 11x - 6, then 1/α + 1/β + 1/γ =", "options": {"A": "11/6", "B": "-11/6", "C": "6/11", "D": "-6/11"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "If α, β are zeros of 3x² - 5x + 7, then α/β + β/α =", "options": {"A": "-17/21", "B": "17/21", "C": "-21/17", "D": "21/17"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "If α, β, γ are zeros of 4x³ - 8x² - 11x + 5, then α + β + γ =", "options": {"A": "2", "B": "-2", "C": "11/4", "D": "-11/4"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "If α, β are zeros of x² + 4x + 3, then α²β + αβ² =", "options": {"A": "-12", "B": "12", "C": "-4", "D": "4"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "If α, β, γ are zeros of x³ - 3x² - 6x + 8, then αβ + βγ + γα =", "options": {"A": "-6", "B": "6", "C": "-3", "D": "3"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "If α, β are zeros of 2x² - 4x + 1, then α³ + β³ =", "options": {"A": "5", "B": "13/4", "C": "17/4", "D": "21/4"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "If α, β, γ are zeros of x³ - 2x² - 5x + 6, then 1/αβ + 1/βγ + 1/γα =", "options": {"A": "-5/6", "B": "5/6", "C": "-6/5", "D": "6/5"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "If α, β are zeros of x² - 8x + 7, then (α-1)(β-1) =", "options": {"A": "0", "B": "6", "C": "-6", "D": "8"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "If α, β, γ are zeros of 3x³ - 4x² - 5x + 2, then α² + β² + γ² =", "options": {"A": "46/9", "B": "34/9", "C": "22/9", "D": "10/9"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "If α, β are zeros of x² - 6x + 2, then α² + β² =", "options": {"A": "32", "B": "36", "C": "40", "D": "44"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "If α, β, γ are zeros of x³ - x² - 4x + 4, then αβγ =", "options": {"A": "-4", "B": "4", "C": "-1", "D": "1"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "If α, β are zeros of 4x² - 9x + 2, then 1/(2α-1) + 1/(2β-1) =", "options": {"A": "9/2", "B": "-9/2", "C": "2/9", "D": "-2/9"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "If α, β, γ are zeros of 2x³ + 5x² - 9x - 18, then α + β + γ =", "options": {"A": "-5/2", "B": "5/2", "C": "-9/2", "D": "9/2"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "If α, β are zeros of x² + 2x - 8, then α²β + αβ² =", "options": {"A": "-16", "B": "16", "C": "-8", "D": "8"}, "correct_answer": "A"},

    {"id": 81, "difficulty": "hard", "question": "If α, β are zeros of ax² + bx + c and α+β, α²+β², α³+β³ are in GP, then:", "options": {"A": "b² = ac", "B": "b² = 2ac", "C": "b² = 3ac", "D": "b² = 4ac"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "If α, β, γ are zeros of x³ - 3x² + 2x - 4 and S_n = αⁿ + βⁿ + γⁿ, then S₅ - 3S₄ + 2S₃ - 4S₂ =", "options": {"A": "0", "B": "4", "C": "8", "D": "12"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "If α, β are zeros of x² - 6x + 1, then for n≥1, αⁿ + βⁿ is always:", "options": {"A": "An integer", "B": "A rational number", "C": "An irrational number", "D": "A complex number"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "If α, β, γ are zeros of x³ + px² + qx + r and α+β=0, then:", "options": {"A": "γ = -p", "B": "γ = p", "C": "γ = -q", "D": "γ = q"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "If α, β are zeros of x² - 2x + 3 and S_n = αⁿ + βⁿ, then Sₙ₊₂ =", "options": {"A": "2Sₙ₊₁ - 3Sₙ", "B": "2Sₙ₊₁ + 3Sₙ", "C": "3Sₙ₊₁ - 2Sₙ", "D": "3Sₙ₊₁ + 2Sₙ"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "If α, β, γ are zeros of x³ - 12x² + 44x - 48 and they are in AP, then the common difference is:", "options": {"A": "2", "B": "3", "C": "4", "D": "6"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "If α, β are zeros of x² - x - 1 and T_n = αⁿ + βⁿ, then Tₙ₊₂ =", "options": {"A": "Tₙ₊₁ + Tₙ", "B": "Tₙ₊₁ - Tₙ", "C": "Tₙ₊₁ × Tₙ", "D": "Tₙ₊₁ / Tₙ"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "If α, β, γ are zeros of x³ - 6x² + 11x - 6 and they are in GP, then the common ratio is:", "options": {"A": "2", "B": "3", "C": "1/2", "D": "1/3"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "If α, β are zeros of ax² + bx + c and α+2, β+2 are zeros of x² + 3x + 2, then a:b:c =", "options": {"A": "1:1:1", "B": "1:2:3", "C": "2:3:4", "D": "1:3:2"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "If α, β, γ are zeros of x³ + qx + r and S_n = αⁿ + βⁿ + γⁿ, then S₅ =", "options": {"A": "-5qr", "B": "5qr", "C": "-5q²r", "D": "5q²r"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "If α, β are zeros of x² - 2x - 1 and U_n = αⁿ - βⁿ, then Uₙ₊₂ =", "options": {"A": "2Uₙ₊₁ + Uₙ", "B": "2Uₙ₊₁ - Uₙ", "C": "Uₙ₊₁ + 2Uₙ", "D": "Uₙ₊₁ - 2Uₙ"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "If α, β, γ are zeros of x³ - x² - 4 and they are in HP, then the middle term is:", "options": {"A": "1", "B": "-1", "C": "2", "D": "-2"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "If α, β are zeros of x² + px + q and α², β² are zeros of x² + rx + s, then:", "options": {"A": "r = p² - 2q, s = q²", "B": "r = p² + 2q, s = q²", "C": "r = 2p - q, s = q²", "D": "r = 2p + q, s = q²"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "If α, β, γ are zeros of x³ - 3x + 1 and S_n = αⁿ + βⁿ + γⁿ, then S₆ =", "options": {"A": "6", "B": "9", "C": "12", "D": "18"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "If α, β are zeros of ax² + bx + c and α+β = αβ, then:", "options": {"A": "a + b + c = 0", "B": "a - b + c = 0", "C": "a + b - c = 0", "D": "a - b - c = 0"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "If α, β, γ are zeros of x³ - 3x² + 2 and they are in AP, then the zeros are:", "options": {"A": "1, 2, 0", "B": "1, 2, -1", "C": "1, 1, 1", "D": "2, 2, -1"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "If α, β are zeros of x² - 2x cosθ + 1, then αⁿ + βⁿ =", "options": {"A": "2cos(nθ)", "B": "2sin(nθ)", "C": "cos(nθ)", "D": "sin(nθ)"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "If α, β, γ are zeros of x³ - 2x² + 3x - 4 and S_n = αⁿ + βⁿ + γⁿ, then S₄ =", "options": {"A": "-4", "B": "4", "C": "8", "D": "-8"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "If α, β are zeros of x² - √2x + 1 and n is odd, then αⁿ + βⁿ =", "options": {"A": "√2", "B": "-√2", "C": "2", "D": "-2"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "If α, β, γ are zeros of x³ + 2x² + 3x + 4 and S_n = αⁿ + βⁿ + γⁿ, then S₃ =", "options": {"A": "-6", "B": "6", "C": "-18", "D": "18"}, "correct_answer": "A"}
  ]
}