{
  "title": "Properties of Rational Numbers - Grade 8 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Which property is shown: 2/3 + 4/5 = 4/5 + 2/3?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Identity"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "What is the additive inverse of 3/4?", "options": {"A": "4/3", "B": "-3/4", "C": "3/4", "D": "-4/3"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "Which property: (1/2 + 1/3) + 1/4 = 1/2 + (1/3 + 1/4)?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Closure"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "What is the multiplicative identity for rational numbers?", "options": {"A": "0", "B": "1", "C": "-1", "D": "The number itself"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "Find the reciprocal of 5/7.", "options": {"A": "5/7", "B": "-5/7", "C": "7/5", "D": "-7/5"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "Which property: 2/3 × (4/5 + 1/2) = (2/3 × 4/5) + (2/3 × 1/2)?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Identity"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "What is the additive identity for rational numbers?", "options": {"A": "0", "B": "1", "C": "-1", "D": "The number itself"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Find the multiplicative inverse of -3/8.", "options": {"A": "3/8", "B": "-3/8", "C": "8/3", "D": "-8/3"}, "correct_answer": "D"},
    {"id": 9, "difficulty": "easy", "question": "Which property: 5/6 × 6/5 = 1?", "options": {"A": "Commutative", "B": "Associative", "C": "Inverse", "D": "Identity"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "What is 3/4 + 0?", "options": {"A": "0", "B": "1", "C": "3/4", "D": "4/3"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "Find the additive inverse of -2/9.", "options": {"A": "2/9", "B": "-2/9", "C": "9/2", "D": "-9/2"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Which property: 7/8 × 1 = 7/8?", "options": {"A": "Commutative", "B": "Associative", "C": "Identity", "D": "Inverse"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "What is the reciprocal of 1/5?", "options": {"A": "1/5", "B": "-1/5", "C": "5", "D": "-5"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "Which property: 2/3 + (-2/3) = 0?", "options": {"A": "Commutative", "B": "Associative", "C": "Inverse", "D": "Identity"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "Find 4/5 × 1.", "options": {"A": "0", "B": "1", "C": "4/5", "D": "5/4"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "What is the additive inverse of 0?", "options": {"A": "0", "B": "1", "C": "-1", "D": "Does not exist"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Which property: (2/5 × 3/7) × 4/9 = 2/5 × (3/7 × 4/9)?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Identity"}, "correct_answer": "B"},
   {
  "id": 18,
  "difficulty": "easy",
  "question": "Find the multiplicative inverse of 1.",
  "options": {
    "A": "0",
    "B": "1",
    "C": "-1",
    "D": "Does not exist"
  },
  "correct_answer": "B"
}
, {"id": 19, "difficulty": "easy", "question": "What is 0 + (-3/4)?", "options": {"A": "0", "B": "1", "C": "-3/4", "D": "3/4"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "Which property: 3/4 × 4/3 = 1?", "options": {"A": "Commutative", "B": "Associative", "C": "Inverse", "D": "Identity"}, "correct_answer": "C"},
    {"id": 21, "difficulty": "medium", "question": "If a = 2/3, b = 4/5, c = 6/7, verify a × (b + c) = a×b + a×c. What property is this?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Closure"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "Find x if (3/4 + x) + 5/6 = 3/4 + (x + 5/6). Which property guarantees this equality?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Inverse"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "What is the product of a rational number and its reciprocal?", "options": {"A": "0", "B": "1", "C": "-1", "D": "The number itself"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "If p/q is a rational number, then p/q + (-p/q) = ?", "options": {"A": "0", "B": "1", "C": "p/q", "D": "-p/q"}, "correct_answer": "A"},
  {
  "id": 25,
  "difficulty": "medium",
  "question": "Which property ensures that rational numbers are closed under addition?",
  "options": {
    "A": "Sum of two rationals is always rational",
    "B": "Sum may be irrational",
    "C": "Sum is always integer",
    "D": "Sum is always positive"
  },
  "correct_answer": "A"
}
,   {"id": 26, "difficulty": "medium", "question": "Find y if (2/3 × y) × 4/5 = 2/3 × (y × 4/5). What property allows this?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Identity"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "What is the result when a rational number is multiplied by 0?", "options": {"A": "The number itself", "B": "1", "C": "0", "D": "Reciprocal"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "If a = -5/6, what is a + (-a)?", "options": {"A": "5/6", "B": "-5/6", "C": "0", "D": "1"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "Which statement about rational numbers is FALSE?", "options": {"A": "They are closed under subtraction", "B": "They are closed under division", "C": "They are closed under addition", "D": "They are closed under multiplication"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "What is (-7/8) × (8/-7)?", "options": {"A": "-1", "B": "1", "C": "0", "D": "-49/64"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Find z if z × (3/4 + 2/5) = z×3/4 + z×2/5. Which property is illustrated?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Inverse"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "What is the sum of a rational number and its additive inverse?", "options": {"A": "0", "B": "1", "C": "The number itself", "D": "Reciprocal"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Which property says a + b = b + a for rational numbers a and b?", "options": {"A": "Associative", "B": "Commutative", "C": "Distributive", "D": "Closure"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "Find the value of (5/6 × 7/8) × 8/7.", "options": {"A": "5/6", "B": "7/8", "C": "1", "D": "0"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "What is true about division of rational numbers?", "options": {"A": "Always closed", "B": "Not closed (division by zero)", "C": "Always commutative", "D": "Always associative"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "If x = 2/3, what is x × (1/x)?", "options": {"A": "0", "B": "1", "C": "2/3", "D": "3/2"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "Which property: (a + b) + c = a + (b + c) for rationals a, b, c?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Inverse"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "What is (-9/10) + 9/10?", "options": {"A": "-9/10", "B": "9/10", "C": "0", "D": "1"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "Find the multiplicative inverse of -1.", "options": {"A": "1", "B": "-1", "C": "0", "D": "Does not exist"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "Which is NOT a property of rational numbers?", "options": {"A": "a + b = b + a", "B": "a × (b + c) = a×b + a×c", "C": "a ÷ b = b ÷ a", "D": "a + 0 = a"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "What is (3/4 × 5/6) × 6/5?", "options": {"A": "3/4", "B": "5/6", "C": "1", "D": "0"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "If a = -2/7, what is -a?", "options": {"A": "-2/7", "B": "2/7", "C": "7/2", "D": "-7/2"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "Which property allows us to write 2/3 + 4/5 as 4/5 + 2/3?", "options": {"A": "Associative", "B": "Commutative", "C": "Distributive", "D": "Identity"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "medium", "question": "What is the product of any rational number and 0?", "options": {"A": "The number itself", "B": "1", "C": "0", "D": "Undefined"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "Find the additive inverse of the multiplicative inverse of 3/5.", "options": {"A": "3/5", "B": "5/3", "C": "-3/5", "D": "-5/3"}, "correct_answer": "D"},
    {"id": 46, "difficulty": "medium", "question": "Which property: a × (b × c) = (a × b) × c for rationals?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Inverse"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "What is (1/2 + 3/4) + 1/4 without calculating?", "options": {"A": "1/2 + (3/4 + 1/4)", "B": "3/4 + (1/2 + 1/4)", "C": "1/4 + (1/2 + 3/4)", "D": "All of these"}, "correct_answer": "D"},
    {"id": 48, "difficulty": "medium", "question": "Find the reciprocal of the additive inverse of -4/9.", "options": {"A": "4/9", "B": "9/4", "C": "-4/9", "D": "-9/4"}, "correct_answer": "D"},
  {
  "id": 49,
  "difficulty": "medium",
  "question": "Which operation is NOT commutative for rational numbers?",
  "options": {
    "A": "Addition",
    "B": "Subtraction",
    "C": "Multiplication",
    "D": "All are commutative"
  },
  "correct_answer": "B"
}
,  {"id": 50, "difficulty": "medium", "question": "What is true about subtraction of rational numbers?", "options": {"A": "a - b = b - a", "B": "Not commutative", "C": "Always associative", "D": "Always closed"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "Find the value of (7/8 × 8/7) + (-7/8 + 7/8).", "options": {"A": "0", "B": "1", "C": "2", "D": "7/8"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "Which property ensures (2/3 × 4/5) × 5/4 = 2/3 × (4/5 × 5/4)?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Inverse"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "What is the additive inverse of the reciprocal of 2/7?", "options": {"A": "2/7", "B": "7/2", "C": "-2/7", "D": "-7/2"}, "correct_answer": "D"},
    {"id": 54, "difficulty": "medium", "question": "Find x if (x + 3/5) + 2/7 = x + (3/5 + 2/7). Which property?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Identity"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "What is (5/6 × 0) + (5/6 × 1)?", "options": {"A": "0", "B": "1", "C": "5/6", "D": "11/6"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "Find the multiplicative inverse of the additive inverse of -3/4.", "options": {"A": "3/4", "B": "4/3", "C": "-3/4", "D": "-4/3"}, "correct_answer": "D"},
    {"id": 57, "difficulty": "medium", "question": "Which property: a + (b + c) = (a + b) + c?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Closure"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "medium", "question": "What is (-11/12) × 12/(-11)?", "options": {"A": "-1", "B": "1", "C": "0", "D": "-121/144"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "medium", "question": "Find y if y × (2/3 + 1/4) = y×2/3 + y×1/4. This illustrates which property?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Inverse"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "What is the sum of a number and its negative?", "options": {"A": "0", "B": "1", "C": "The number", "D": "Negative of number"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "Which is true for rational numbers a, b, c: a×(b+c) = ?", "options": {"A": "a×b + c", "B": "a×b + a×c", "C": "b×a + c×a", "D": "Both B and C"}, "correct_answer": "D"},
    {"id": 62, "difficulty": "medium", "question": "Find the additive inverse of the multiplicative inverse of -5/8.", "options": {"A": "5/8", "B": "8/5", "C": "-5/8", "D": "-8/5"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "What property allows 3/4 × (5/6 × 7/8) = (3/4 × 5/6) × 7/8?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Identity"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "Find z if (z + 2/5) = 2/5 + z. Which property?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Identity"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "What is (7/9 × 1) + (7/9 × 0)?", "options": {"A": "0", "B": "1", "C": "7/9", "D": "14/9"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "Find the reciprocal of the additive inverse of 3/11.", "options": {"A": "3/11", "B": "11/3", "C": "-3/11", "D": "-11/3"}, "correct_answer": "D"},
    {"id": 67, "difficulty": "medium", "question": "Which property: (a × b) × c = a × (b × c)?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Inverse"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "What is (-13/14) + 13/14?", "options": {"A": "-13/14", "B": "13/14", "C": "0", "D": "1"}, "correct_answer": "C"},
    {"id": 69, "difficulty": "medium", "question": "Find x if x × (3/7 + 4/9) = x×3/7 + x×4/9. Property?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Inverse"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "What is the product of a number and its reciprocal?", "options": {"A": "0", "B": "1", "C": "The number", "D": "-1"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "hard", "question": "If a, b, c are rationals, which is always true?", "options": {"A": "a ÷ (b ÷ c) = (a ÷ b) ÷ c", "B": "a - (b - c) = (a - b) - c", "C": "a × (b + c) = a×b + a×c", "D": "a ÷ b = b ÷ a"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "hard", "question": "Find the value of [(-2/3) + (4/5)] + (-4/5) using properties.", "options": {"A": "-2/3", "B": "4/5", "C": "0", "D": "1"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "hard", "question": "Which statement about rational numbers is correct?", "options": {"A": "Division is associative", "B": "Subtraction is commutative", "C": "Multiplication distributes over addition", "D": "Addition distributes over multiplication"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "hard", "question": "Simplify using properties: (3/4 × 5/6) + (3/4 × 1/6)", "options": {"A": "3/4", "B": "5/6", "C": "1/2", "D": "2/3"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "hard", "question": "If a = -5/7, b = 3/8, c = 2/5, verify a×(b-c) = a×b - a×c. Which property?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Inverse"}, "correct_answer": "C"},
    {"id": 76, "difficulty": "hard", "question": "Find x using properties: (x × 2/3) × 3/2 = 5/4", "options": {"A": "5/4", "B": "3/2", "C": "2/3", "D": "15/8"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "hard", "question": "Which is NOT a field property of rational numbers?", "options": {"A": "Existence of additive inverse", "B": "Existence of multiplicative inverse", "C": "Commutativity of division", "D": "Distributivity"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "hard", "question": "Simplify: [(-7/8) + (5/6)] + (-5/6) using inverse property.", "options": {"A": "-7/8", "B": "5/6", "C": "0", "D": "1"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "hard", "question": "If p/q and r/s are rationals with q,s ≠ 0, then (p/q) ÷ (r/s) = ?", "options": {"A": "(p×s)/(q×r)", "B": "(p×r)/(q×s)", "C": "(q×s)/(p×r)", "D": "(q×r)/(p×s)"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "hard", "question": "Using distributive property, find: 2/3 × (1/4 + 1/5 + 1/6)", "options": {"A": "2/3 × 1/4 + 2/3 × 1/5 + 2/3 × 1/6", "B": "1/4 + 1/5 + 1/6 × 2/3", "C": "2/3 + 1/4 + 1/5 + 1/6", "D": "(2/3 × 1/4) × (2/3 × 1/5) × (2/3 × 1/6)"}, "correct_answer": "A"},
    {"id": 81, "difficulty": "hard", "question": "Find y if (y + 3/7) × 7/3 = 1 using properties.", "options": {"A": "-3/7", "B": "3/7", "C": "0", "D": "4/7"}, "correct_answer": "C"},
    {"id": 82, "difficulty": "hard", "question": "Which property ensures rational numbers form an abelian group under addition?", "options": {"A": "Closure, associativity, identity, inverse, commutativity", "B": "Closure, associativity, identity only", "C": "Closure, commutativity only", "D": "Identity and inverse only"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "Simplify: (5/6 × 4/7) × 7/4 + (5/6 × 3/7) × 7/3", "options": {"A": "5/3", "B": "5/6", "C": "5/7", "D": "10/7"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "If a, b, c ∈ Q, and a ≠ 0, which is always true?", "options": {"A": "a ÷ (b ÷ c) = (a ÷ b) ÷ c", "B": "a × (b - c) = a×b - a×c", "C": "(a - b) - c = a - (b - c)", "D": "a ÷ b = b ÷ a"}, "correct_answer": "B"},
    {"id": 85, "difficulty": "hard", "question": "Find the value of [(2/3 × 3/4) + (2/3 × 1/4)] × 6 using properties.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 86, "difficulty": "hard", "question": "Which is a field axiom for rational numbers?", "options": {"A": "For every a ≠ 0, ∃ a⁻¹ such that a × a⁻¹ = 1", "B": "a + b = b - a", "C": "a × (b × c) = (a × b) × (a × c)", "D": "a ÷ (b + c) = a÷b + a÷c"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Simplify using properties: [(-5/8) × (3/7)] × 7/3 + [(-5/8) × (4/7)] × 7/4", "options": {"A": "-5/4", "B": "-5/8", "C": "-5/2", "D": "-5/16"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "If x, y, z ∈ Q, which statement is correct?", "options": {"A": "x × (y ÷ z) = (x × y) ÷ (x × z)", "B": "x - (y - z) = (x - y) - z", "C": "x ÷ (y + z) = x÷y + x÷z", "D": "x × (y + z) = x×y + x×z"}, "correct_answer": "D"},
    {"id": 89, "difficulty": "hard", "question": "Find the value of (3/4 × 8/9 × 9/8 × 4/3) using inverse properties.", "options": {"A": "0", "B": "1", "C": "3/4", "D": "8/9"}, "correct_answer": "B"},
    {"id": 90, "difficulty": "hard", "question": "Which property distinguishes rational numbers from integers regarding division?", "options": {"A": "Closure under division (except by zero)", "B": "Commutativity of division", "C": "Associativity of division", "D": "Identity for division"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Simplify: [(7/9 × 3/14) + (7/9 × 11/14)] × 18/7", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "If a, b ∈ Q and a × b = 0, then what must be true?", "options": {"A": "a = 0 or b = 0", "B": "Both a and b must be 0", "C": "a = b", "D": "a = -b"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Find x using properties: (x + 5/8) - 5/8 = 3/4", "options": {"A": "3/4", "B": "5/8", "C": "11/8", "D": "1/2"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "Which is true about the set of rational numbers?", "options": {"A": "Dense but not complete", "B": "Complete but not dense", "C": "Neither dense nor complete", "D": "Both dense and complete"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Simplify: (2/5 × 10/3 × 3/10 × 5/2) + (2/5 + 3/5 - 1)", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "If a/b and c/d are rationals, their sum is:", "options": {"A": "(a+c)/(b+d)", "B": "(ad+bc)/(bd)", "C": "(ac)/(bd)", "D": "(a+b)/(c+d)"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "Find the value of [(11/12 × 24/33) × (13/14 × 28/39)] using properties.", "options": {"A": "1/3", "B": "2/3", "C": "3/4", "D": "4/5"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "Which property is used in: a × (1/a) = 1 for a ≠ 0?", "options": {"A": "Multiplicative inverse", "B": "Multiplicative identity", "C": "Commutative", "D": "Associative"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "Simplify: (3/7 × 14/9) + (3/7 × 5/9) + (3/7 × 2/9)", "options": {"A": "1", "B": "3/7", "C": "9/7", "D": "7/9"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "If Q is the set of rational numbers, which is NOT a property of (Q, +, ×)?", "options": {"A": "Commutative ring with unity", "B": "Field", "C": "Integral domain", "D": "Division ring but not field"}, "correct_answer": "D"}
  ]
}