{
  "title": "Properties of Rational Numbers - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Rational numbers are numbers that can be expressed as: 🧮", "options": {"A": "p/q where q≠0", "B": "p/q where q=0", "C": "only integers", "D": "decimals"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "Which property is shown: a + b = b + a? 🔄", "options": {"A": "Associative", "B": "Commutative", "C": "Distributive", "D": "Closure"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "The additive identity for rational numbers is: ➕", "options": {"A": "1", "B": "0", "C": "-1", "D": "a itself"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "Multiplicative identity for rational numbers is: ✖️", "options": {"A": "0", "B": "1", "C": "-1", "D": "a itself"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "Which is not a rational number? ❌", "options": {"A": "5", "B": "-3/4", "C": "0.6", "D": "√2"}, "correct_answer": "D"},
    {"id": 6, "difficulty": "easy", "question": "The additive inverse of 3/5 is: 🔄", "options": {"A": "5/3", "B": "-3/5", "C": "-5/3", "D": "3/5"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "Multiplicative inverse of -2/7 is: 🔄", "options": {"A": "7/2", "B": "-7/2", "C": "2/7", "D": "-2/7"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "Rational numbers are closed under: 🔒", "options": {"A": "Addition", "B": "Subtraction", "C": "Multiplication", "D": "All of these"}, "correct_answer": "D"},
    {"id": 9, "difficulty": "easy", "question": "For any rational a, a × 0 = ?", "options": {"A": "a", "B": "0", "C": "1", "D": "undefined"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "Which property: (a+b)+c = a+(b+c)? 🔗", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Inverse"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "Additive inverse of 0 is: 0️⃣", "options": {"A": "0", "B": "1", "C": "undefined", "D": "-0"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Multiplicative inverse of 1 is: 🔄", "options": {"A": "1", "B": "0", "C": "-1", "D": "undefined"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Is 0 a rational number? 🤔", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Never"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Rational numbers between 1 and 2 are: 🔍", "options": {"A": "Finite", "B": "Infinite", "C": "Only one", "D": "None"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "Which property: a(b+c) = ab + ac? 📐", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Closure"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "If a/b is rational, and b≠0, then -a/b is also rational. This is due to: 🔄", "options": {"A": "Closure", "B": "Inverse", "C": "Identity", "D": "Commutative"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Reciprocal of -5 is: 🔄", "options": {"A": "5", "B": "1/5", "C": "-1/5", "D": "-5"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "Is sum of two rationals always rational? ➕", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Never"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Zero has no: 🚫", "options": {"A": "Additive inverse", "B": "Multiplicative inverse", "C": "Reciprocal", "D": "B & C"}, "correct_answer": "D"},
    {"id": 20, "difficulty": "easy", "question": "Which is not closed for rational numbers? ❌", "options": {"A": "Addition", "B": "Subtraction", "C": "Division by zero", "D": "Multiplication"}, "correct_answer": "C"},

    {"id": 21, "difficulty": "medium", "question": "The rational number that is equal to its negative is: 🔄", "options": {"A": "1", "B": "-1", "C": "0", "D": "2"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "If x = -4/9, then -(-x) = ?", "options": {"A": "4/9", "B": "-4/9", "C": "9/4", "D": "0"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "Which property is used in: 3/5 + (-3/5) = 0? ➖", "options": {"A": "Additive inverse", "B": "Additive identity", "C": "Closure", "D": "Commutative"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "For rationals, division is not: 🚫", "options": {"A": "Commutative", "B": "Associative", "C": "Both A & B", "D": "Closed"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "If a × b = 1, then a and b are: 🔄", "options": {"A": "Additive inverses", "B": "Multiplicative inverses", "C": "Identities", "D": "Zero"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "(-7/8) × (8/-7) = ?", "options": {"A": "1", "B": "-1", "C": "0", "D": "49/64"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Which rational number has no reciprocal? 🚫", "options": {"A": "1", "B": "-1", "C": "0", "D": "2"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "Simplify using property: 2/3 × (4/5 + 1/2) = (2/3×4/5) + (2/3×1/2). Property? 📐", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Inverse"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "Product of a rational and its reciprocal is always: ✖️", "options": {"A": "0", "B": "1", "C": "-1", "D": "itself"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "If p/q is rational and q≠0, then (p/q)⁻¹ = ?", "options": {"A": "q/p", "B": "-p/q", "C": "-q/p", "D": "p/q"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Which is true? ✅", "options": {"A": "Subtraction is commutative", "B": "Division is associative", "C": "Addition is associative", "D": "Multiplication inverse of 0 is 0"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "If a, b, c are rational, a(b-c) = ab - ac due to: 📐", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Closure"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "A rational number can be represented on a number line: 📏", "options": {"A": "True", "B": "False", "C": "Only integers", "D": "Only fractions"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "If x + 0 = x, 0 is called: ➕", "options": {"A": "Additive inverse", "B": "Additive identity", "C": "Multiplicative identity", "D": "Zero property"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "The reciprocal of a negative rational number is: 🔄", "options": {"A": "Positive", "B": "Negative", "C": "Zero", "D": "Undefined"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "For rational numbers, addition is: ➕", "options": {"A": "Not closed", "B": "Commutative but not associative", "C": "Both commutative and associative", "D": "Neither"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "Find x if (3/4) + x = 0.", "options": {"A": "3/4", "B": "-3/4", "C": "4/3", "D": "-4/3"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "The number 1 is the: ✖️", "options": {"A": "Additive identity", "B": "Multiplicative identity", "C": "Additive inverse", "D": "Multiplicative inverse of 0"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "If p/q = 0, then p must be: 🔢", "options": {"A": "0", "B": "1", "C": "q", "D": "any number"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Every integer is a rational number: 🤔", "options": {"A": "True", "B": "False", "C": "Sometimes", "D": "Never"}, "correct_answer": "A"},

    {"id": 41, "difficulty": "hard", "question": "If a/b and c/d are rationals, then (a/b) ÷ (c/d) = ?", "options": {"A": "ac/bd", "B": "ad/bc", "C": "ab/cd", "D": "bc/ad"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "Which statement is false? ❌", "options": {"A": "Rationals are closed under division", "B": "Rationals are closed under subtraction", "C": "Rationals are closed under multiplication", "D": "Rationals are closed under addition"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "For two rationals a and b, a - b = b - a only if: ➖", "options": {"A": "a = b", "B": "a = -b", "C": "a = 0", "D": "b = 0"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "If (x+y) is rational and x is rational, then y must be: 🔍", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Cannot say"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "The multiplicative inverse of -1 is: 🔄", "options": {"A": "1", "B": "-1", "C": "0", "D": "undefined"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "hard", "question": "If a × b = 0 and a ≠ 0, then b = ?", "options": {"A": "0", "B": "1", "C": "any number", "D": "undefined"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "The property a + (-a) = 0 is called: ➕", "options": {"A": "Additive identity", "B": "Additive inverse", "C": "Closure", "D": "Commutative"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "hard", "question": "A rational number p/q is in standard form if: 📝", "options": {"A": "q > 0 and HCF(p,q)=1", "B": "p > 0", "C": "q ≠ 0", "D": "p and q are integers"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "If a, b, c are rational, (a ÷ b) ÷ c = a ÷ (b ÷ c) is: ➗", "options": {"A": "Always true", "B": "Never true", "C": "True if c ≠ 0", "D": "True if b ≠ 0, c ≠ 0"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "hard", "question": "If x = 5/7, y = -3/4, then x + y = y + x illustrates: 🔄", "options": {"A": "Associative", "B": "Commutative", "C": "Closure", "D": "Inverse"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "hard", "question": "Every rational number has: 🔄", "options": {"A": "A unique additive inverse", "B": "A unique multiplicative inverse", "C": "Both", "D": "None"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "For a rational a, a × (1/a) = 1 holds if: ✖️", "options": {"A": "a ≠ 0", "B": "a > 0", "C": "a < 0", "D": "a is integer"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "If p/q is rational, then -p/q is its: 🔄", "options": {"A": "Reciprocal", "B": "Additive inverse", "C": "Multiplicative inverse", "D": "Negative reciprocal"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "hard", "question": "Which of the following is not a property of rational numbers? 🚫", "options": {"A": "Commutativity under addition", "B": "Associativity under multiplication", "C": "Existence of multiplicative inverse for 0", "D": "Distributivity of multiplication over addition"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "hard", "question": "If a/b and c/d are two rationals with b,d ≠ 0, their product is: ✖️", "options": {"A": "(a+c)/(b+d)", "B": "(ac)/(bd)", "C": "(ad)/(bc)", "D": "(ab)/(cd)"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "hard", "question": "Zero is the identity for: ➕", "options": {"A": "Addition", "B": "Multiplication", "C": "Both", "D": "None"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "A rational number between -1/3 and 1/2 is: 🔍", "options": {"A": "0", "B": "-1/6", "C": "1/4", "D": "All of these"}, "correct_answer": "D"},
    {"id": 58, "difficulty": "hard", "question": "If x = 2/3, y = 4/5, z = 6/7, then x(yz) = (xy)z illustrates: 🔗", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Closure"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "hard", "question": "The only rational number which is its own reciprocal is: 🔄", "options": {"A": "1", "B": "-1", "C": "Both 1 and -1", "D": "0"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "hard", "question": "If a and b are rational, then (a - b) is always: ➖", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Natural"}, "correct_answer": "A"}
  ]
}