{
  "title": "Real Numbers - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "The set of real numbers includes: 📊", "options": {"A": "Only rationals", "B": "Only irrationals", "C": "Both rationals and irrationals", "D": "Only integers"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "Which is a real number? ✅", "options": {"A": "√4", "B": "√5", "C": "3.14", "D": "All of these"}, "correct_answer": "D"},
    {"id": 3, "difficulty": "easy", "question": "Every rational number is a real number: 🔢", "options": {"A": "True", "B": "False", "C": "Sometimes", "D": "Never"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Every irrational number is a real number: 🔢", "options": {"A": "True", "B": "False", "C": "Sometimes", "D": "Never"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "Which is not a real number? ❌", "options": {"A": "√-1", "B": "π", "C": "0.5", "D": "√2"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Real numbers can be represented on a: 📏", "options": {"A": "Number line", "B": "Circle", "C": "Square", "D": "Graph"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "Between any two real numbers, there are: 🔍", "options": {"A": "No real numbers", "B": "Finitely many real numbers", "C": "Infinitely many real numbers", "D": "Exactly one real number"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "Decimal representation of a real number is: 🔢", "options": {"A": "Always terminating", "B": "Always non-terminating", "C": "Either terminating or non-terminating repeating", "D": "Either terminating or non-terminating non-repeating"}, "correct_answer": "D"},
    {"id": 9, "difficulty": "easy", "question": "Which is real but irrational? 🤔", "options": {"A": "√9", "B": "√10", "C": "0.75", "D": "-5"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "The sum of two real numbers is always: ➕", "options": {"A": "Real", "B": "Rational", "C": "Irrational", "D": "Integer"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Real numbers are closed under: 🔒", "options": {"A": "Addition", "B": "Subtraction", "C": "Multiplication", "D": "All of these"}, "correct_answer": "D"},
    {"id": 12, "difficulty": "easy", "question": "Which is an example of a real number that is not rational? 🧠", "options": {"A": "3", "B": "-2/3", "C": "√2", "D": "0"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "Is √16 a real number? 🔳", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Not sure"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "The number line is filled with: 📈", "options": {"A": "Only integers", "B": "Only rationals", "C": "Real numbers", "D": "Only fractions"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "Which of these sets is part of real numbers? 🔢", "options": {"A": "Natural numbers", "B": "Integers", "C": "Rational numbers", "D": "All of these"}, "correct_answer": "D"},
    {"id": 16, "difficulty": "easy", "question": "Real numbers include: ✅", "options": {"A": "Positive numbers", "B": "Negative numbers", "C": "Zero", "D": "All of these"}, "correct_answer": "D"},
    {"id": 17, "difficulty": "easy", "question": "The product of two real numbers is always: ✖️", "options": {"A": "Real", "B": "Rational", "C": "Irrational", "D": "Positive"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Zero is a real number: 0️⃣", "options": {"A": "True", "B": "False", "C": "Sometimes", "D": "Never"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Which of these is not a real number? 🚫", "options": {"A": "√(25)", "B": "√(-4)", "C": "1.5", "D": "π"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "Real numbers are used to measure: 📏", "options": {"A": "Length", "B": "Weight", "C": "Temperature", "D": "All of these"}, "correct_answer": "D"},

    {"id": 21, "difficulty": "medium", "question": "If a and b are real numbers, then a + b = b + a is: 🔄", "options": {"A": "Commutative property", "B": "Associative property", "C": "Closure property", "D": "Distributive property"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "The additive identity for real numbers is: ➕", "options": {"A": "1", "B": "0", "C": "-1", "D": "None"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "Multiplicative identity for real numbers is: ✖️", "options": {"A": "0", "B": "1", "C": "-1", "D": "None"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "Every real number has an additive inverse: 🔄", "options": {"A": "True", "B": "False", "C": "Only positives", "D": "Only negatives"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Every non-zero real number has a multiplicative inverse: 🔄", "options": {"A": "True", "B": "False", "C": "Only integers", "D": "Only fractions"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Which property: a(b + c) = ab + ac for reals? 📐", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Closure"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "If x is real and x² = 2, then x is: 🔲", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Natural"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "The set of real numbers is: 🔢", "options": {"A": "Finite", "B": "Countable", "C": "Uncountable", "D": "Empty"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "Between √2 and √3, there exists: 🔍", "options": {"A": "No real number", "B": "Only irrationals", "C": "Infinitely many rationals and irrationals", "D": "Only one rational"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "If a is irrational and b is rational, a + b is: ➕", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "If a is irrational and b is rational (b ≠ 0), a × b is: ✖️", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Zero"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "The real number √(0.09) is: 🔳", "options": {"A": "0.3 (Rational)", "B": "Irrational", "C": "0.03", "D": "0.9"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Which of these is always real? ✅", "options": {"A": "Square root of a positive real", "B": "Square root of a negative real", "C": "Division by zero", "D": "√(negative)"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "The number 0.101001000100001... is: 🔢", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Terminating"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "Real numbers satisfy the property of: 🔒", "options": {"A": "Trichotomy (exactly one: a>b, a=b, a<b)", "B": "Closure under addition", "C": "Associativity", "D": "All of these"}, "correct_answer": "D"},
    {"id": 36, "difficulty": "medium", "question": "If x is real and x² = 16, then x can be: 🔲", "options": {"A": "4", "B": "-4", "C": "Both 4 and -4", "D": "Only 4"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "The sum of a rational and an irrational is: ➕", "options": {"A": "Rational", "B": "Irrational", "C": "Either", "D": "None"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "The product of a non-zero rational and an irrational is: ✖️", "options": {"A": "Rational", "B": "Irrational", "C": "Zero", "D": "One"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "If a is real, then |a| is: 📏", "options": {"A": "Always real", "B": "Always positive", "C": "Both A and B", "D": "Always irrational"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "The decimal expansion of a real number is unique except for: 🔄", "options": {"A": "Terminating decimals", "B": "Non-terminating repeating", "C": "Both can have two representations", "D": "Only irrationals"}, "correct_answer": "A"},

    {"id": 41, "difficulty": "hard", "question": "If x and y are real numbers such that x + y = 0, then y is: ➕", "options": {"A": "Additive inverse of x", "B": "Reciprocal of x", "C": "Multiplicative inverse", "D": "Equal to x"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "For real numbers, division by zero is: 🚫", "options": {"A": "Defined", "B": "Not defined", "C": "Sometimes defined", "D": "Zero"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "hard", "question": "The set of real numbers is: 🔢", "options": {"A": "Dense", "B": "Complete", "C": "Uncountable", "D": "All of these"}, "correct_answer": "D"},
    {"id": 44, "difficulty": "hard", "question": "If a and b are irrational, can a × b be rational? 🤔", "options": {"A": "Never", "B": "Always", "C": "Sometimes (e.g., √2 × √2)", "D": "Only if a = b"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "hard", "question": "Which statement is false? ❌", "options": {"A": "Every integer is a real number", "B": "Every real number is rational", "C": "Every whole number is a real number", "D": "Every irrational is a real number"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "hard", "question": "If x = √2 + √3, then x is: ➕", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Natural"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "hard", "question": "The real numbers are closed under: 🔒", "options": {"A": "Taking square roots of positives", "B": "Taking square roots of negatives", "C": "Division", "D": "A and C only"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "If a is real and a ≠ 0, then a⁰ = ?", "options": {"A": "0", "B": "1", "C": "a", "D": "Undefined"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "hard", "question": "Which of these sets is not a subset of real numbers? 🚫", "options": {"A": "Imaginary numbers", "B": "Rational numbers", "C": "Integers", "D": "Natural numbers"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "If a real number x satisfies x² = x, then x can be: 🔲", "options": {"A": "0", "B": "1", "C": "Both 0 and 1", "D": "Any real"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "hard", "question": "For two distinct real numbers, there exists: 🔍", "options": {"A": "A rational between them", "B": "An irrational between them", "C": "Infinitely many reals between them", "D": "All of these"}, "correct_answer": "D"},
    {"id": 52, "difficulty": "hard", "question": "If √n is irrational, then n must be: 🔢", "options": {"A": "A non-perfect square", "B": "Prime", "C": "Odd", "D": "Even"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "Real numbers follow the Archimedean property: 📏", "options": {"A": "True", "B": "False", "C": "Only for integers", "D": "Only for positives"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "If a is real and a³ = 8, then a = ?", "options": {"A": "2", "B": "-2", "C": "2 only", "D": "2 or -2"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "The number √(3 + √5) is: 🔍", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "hard", "question": "Which of these operations is not always defined in real numbers? 🚫", "options": {"A": "Addition", "B": "Multiplication", "C": "Division by zero", "D": "Subtraction"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "hard", "question": "If x and y are real, x > y implies: ➕", "options": {"A": "x - y > 0", "B": "y - x < 0", "C": "Both A and B", "D": "x/y > 1"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "hard", "question": "For any real a, √(a²) = ?", "options": {"A": "a", "B": "|a|", "C": "-a", "D": "a²"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "hard", "question": "The number 0.9̅ (repeating 9) is equal to: 🔄", "options": {"A": "1", "B": "0.999...", "C": "Less than 1", "D": "A and B"}, "correct_answer": "D"},
    {"id": 60, "difficulty": "hard", "question": "Real numbers are ordered: 📊", "options": {"A": "Totally", "B": "Partially", "C": "Not ordered", "D": "Only positive ones"}, "correct_answer": "A"}
  ]
}