{
  "title": "Irrational Numbers - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Which of these is an irrational number? 🤔", "options": {"A": "√9", "B": "√2", "C": "3/4", "D": "0.5"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "π (pi) is: 🔵", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Natural"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "√16 is: 🔲", "options": {"A": "Irrational", "B": "Rational", "C": "Neither", "D": "Both"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "Which is irrational? 🚫", "options": {"A": "0.333...", "B": "√25", "C": "√3", "D": "-5"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "Irrational numbers have decimal expansion that is: 📊", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Ending"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "Which is not irrational? ✅", "options": {"A": "√7", "B": "√100", "C": "√11", "D": "π"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "Is 1.010010001... rational? 🔄", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "0.75 is: 📉", "options": {"A": "Irrational", "B": "Rational", "C": "Both", "D": "None"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "√(49) is rational because it equals: 🔢", "options": {"A": "7", "B": "√7", "C": "49", "D": "14"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Which of these is irrational? ❌", "options": {"A": "22/7", "B": "3.14", "C": "√5", "D": "0.125"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "Decimal form of √2 is: 🔍", "options": {"A": "1.41421356...", "B": "1.5", "C": "1.414", "D": "1.414141..."}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Is 0 an irrational number? 0️⃣", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Depends"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "√(64) = ?", "options": {"A": "Irrational", "B": "Rational", "C": "Neither", "D": "Undefined"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Which is a rational number? ✅", "options": {"A": "√10", "B": "√1", "C": "√13", "D": "√17"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "Irrational numbers can be written as fraction p/q where q≠0? 🤨", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Only if p=0"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "√(0.04) = 0.2, which type of number? 📏", "options": {"A": "Irrational", "B": "Rational", "C": "Neither", "D": "Imaginary"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "1/3 = 0.333... is: 🔄", "options": {"A": "Irrational", "B": "Rational", "C": "Both", "D": "None"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "Which is irrational? ❓", "options": {"A": "√36", "B": "√50", "C": "√81", "D": "√100"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "A number whose square is 2: 🔲", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Natural"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "The value of π is approximately: 🥧", "options": {"A": "3.14", "B": "22/7", "C": "3.14159265...", "D": "All of these"}, "correct_answer": "D"},

    {"id": 21, "difficulty": "medium", "question": "Which of these is irrational? 🧠", "options": {"A": "√(4/9)", "B": "√(9/16)", "C": "√(8/18)", "D": "√(27/3)"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "Sum of √2 and √2 is: ➕", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Zero"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "Product of √3 and √3 is: ✖️", "options": {"A": "Irrational", "B": "Rational", "C": "Both", "D": "None"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "Decimal expansion of √17 is: 🔢", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "None"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "Which is rational? ✅", "options": {"A": "0.101101110...", "B": "√(0.09)", "C": "√15", "D": "π - 3"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "√(2.25) is: 📐", "options": {"A": "1.5 (Rational)", "B": "Irrational", "C": "Neither", "D": "1.5 (Irrational)"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "If a is irrational, 1/a is: 🔄", "options": {"A": "Always rational", "B": "Always irrational", "C": "Can be rational", "D": "None"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "Between 3 and 4, there are: ➗", "options": {"A": "No irrationals", "B": "Finitely many irrationals", "C": "Infinitely many irrationals", "D": "Only one irrational"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "√(12)/√(3) simplifies to: ✂️", "options": {"A": "√4 = 2 (Rational)", "B": "√15 (Irrational)", "C": "√36 (Rational)", "D": "√9 (Rational)"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "The number (√5 + 1)(√5 - 1) is: 🧮", "options": {"A": "Irrational", "B": "Rational", "C": "5", "D": "4"}, "correct_answer": "D"},
    {"id": 31, "difficulty": "medium", "question": "Which expression gives irrational? 🤔", "options": {"A": "√8 × √2", "B": "√27 / √3", "C": "√12 - √3", "D": "√50 + √2"}, "correct_answer": "D"},
    {"id": 32, "difficulty": "medium", "question": "0.2020020002... is: 🔢", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Whole"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "If x² = 7, then x is: 🔲", "options": {"A": "Rational", "B": "Irrational", "C": "Natural", "D": "None"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "Is (√2)² irrational? ❌", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Depends"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "√(0.49) is: 📏", "options": {"A": "0.7 rational", "B": "0.7 irrational", "C": "0.07 rational", "D": "Irrational"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "A rational number between √2 and √3 is: 🔍", "options": {"A": "1.5", "B": "1.414...", "C": "1.732...", "D": "1.8"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Which is not irrational? ✅", "options": {"A": "√(6.25)", "B": "√10", "C": "√(1/3)", "D": "√(0.5)"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "The sum of a rational and irrational is: ➕", "options": {"A": "Rational", "B": "Irrational", "C": "Either", "D": "Zero"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "Reciprocal of √2 is: 🔄", "options": {"A": "Rational", "B": "Irrational", "C": "1/2", "D": "0.5"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "√(144/169) is: 📊", "options": {"A": "Irrational", "B": "12/13 (Rational)", "C": "13/12", "D": "1.2"}, "correct_answer": "B"},

    {"id": 41, "difficulty": "hard", "question": "Prove √5 is irrational. Which step is correct? 🧠", "options": {"A": "Assume √5 = p/q in lowest terms", "B": "Then 5 = p²/q²", "C": "p² = 5q² so p² divisible by 5", "D": "All of these"}, "correct_answer": "D"},
    {"id": 42, "difficulty": "hard", "question": "The product of √8 and √18 is: ✖️", "options": {"A": "√26", "B": "12 (Rational)", "C": "√144", "D": "144"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "hard", "question": "If p is prime, √p is: 🔢", "options": {"A": "Always rational", "B": "Always irrational", "C": "Sometimes rational", "D": "Never irrational"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "hard", "question": "Which of these could be rational? 🤔", "options": {"A": "√2 + √3", "B": "√2 × √3", "C": "√6 / √2", "D": "√2 - √2"}, "correct_answer": "D"},
    {"id": 45, "difficulty": "hard", "question": "The decimal 0.123456789101112... is: 🔢", "options": {"A": "Rational", "B": "Irrational", "C": "Terminating", "D": "Repeating"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "hard", "question": "If a and b are irrational, a×b can be rational. Example? 🔄", "options": {"A": "√2 × √2", "B": "√3 × √2", "C": "π × π", "D": "√5 × √7"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "Is (√3 + √2)(√3 - √2) rational? ➖", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Cannot say"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "Classify: (√50 - √2) / √2", "options": {"A": "Rational", "B": "Irrational", "C": "2", "D": "4"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "hard", "question": "√(10 + √25) is: 🔍", "options": {"A": "√15 (Irrational)", "B": "√35 (Irrational)", "C": "√(10+5) = √15 (Irrational)", "D": "√15 = irrational"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "hard", "question": "If m = √7 - √5 and n = √7 + √5, then m×n = ? ✖️", "options": {"A": "2", "B": "12", "C": "√2", "D": "√35"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "Which is irrational? ❌", "options": {"A": "∛27", "B": "∛64", "C": "∛16", "D": "∛8"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "hard", "question": "The number (√12 + √3)² simplifies to: 🔲", "options": {"A": "27", "B": "15+6√3", "C": "12+3", "D": "15"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "Between any two rational numbers, there is: 🔍", "options": {"A": "No irrational", "B": "Exactly one irrational", "C": "Infinitely many irrationals", "D": "Finitely many irrationals"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "hard", "question": "If x = 1 + √2, then x² - 2x = ? 🔢", "options": {"A": "1", "B": "-1", "C": "2", "D": "√2"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "Which sum is rational? ➕", "options": {"A": "√2 + √8", "B": "√5 + √20", "C": "√3 + √12", "D": "√7 + √28"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "hard", "question": "Simplify √(98) - √(50) + √(8). Result is? ✂️", "options": {"A": "6√2", "B": "5√2", "C": "4√2", "D": "√2"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "If √n is irrational, n must be: 🔢", "options": {"A": "Non-perfect square", "B": "Perfect square", "C": "Prime", "D": "Even"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "The expression (√a + √b)(√a - √b) is always: ➖", "options": {"A": "Irrational", "B": "Rational", "C": "a-b (Rational)", "D": "Depends"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "hard", "question": "∛(125) is: 🔳", "options": {"A": "Irrational", "B": "Rational", "C": "5 (Rational)", "D": "B & C"}, "correct_answer": "D"},
    {"id": 60, "difficulty": "hard", "question": "Choose the irrational number: ❓", "options": {"A": "log₁₀100", "B": "sin 30°", "C": "cos 60°", "D": "sin 45°"}, "correct_answer": "D"}
  ]
}