{
  "title": "Properties of Cube Numbers - Grade 8 ICSE",
  "total_questions": 60,
  "questions": [
    {
      "id": 1,
      "difficulty": "easy",
      "question": "Cube of an even number is always? 🔢",
      "options": { "A": "Even", "B": "Odd", "C": "Can be both", "D": "Prime" },
      "correct_answer": "A"
    },
    {
      "id": 2,
      "difficulty": "easy",
      "question": "Cube of an odd number is always? ✨",
      "options": {
        "A": "Odd",
        "B": "Even",
        "C": "Can be both",
        "D": "Composite"
      },
      "correct_answer": "A"
    },
    {
      "id": 3,
      "difficulty": "easy",
      "question": "What is the cube of 1? 🎯",
      "options": { "A": "1", "B": "3", "C": "0", "D": "1/3" },
      "correct_answer": "A"
    },
    {
      "id": 4,
      "difficulty": "easy",
      "question": "Cube of a negative number is? ❄️",
      "options": { "A": "Negative", "B": "Positive", "C": "0", "D": "Depends" },
      "correct_answer": "A"
    },
    {
      "id": 5,
      "difficulty": "easy",
      "question": "The cube of 0 is? 🔘",
      "options": { "A": "0", "B": "1", "C": "Undefined", "D": "∞" },
      "correct_answer": "A"
    },
    {
      "id": 6,
      "difficulty": "easy",
      "question": "If n is integer, n³ - n is always divisible by? ➗",
      "options": { "A": "6", "B": "3", "C": "2", "D": "All of these" },
      "correct_answer": "D"
    },
    {
      "id": 7,
      "difficulty": "easy",
      "question": "How many perfect cubes are between 1 and 100? 📏",
      "options": { "A": "4", "B": "5", "C": "3", "D": "8" },
      "correct_answer": "A"
    },
    {
      "id": 8,
      "difficulty": "easy",
      "question": "Cube of a number ending in 3 ends in? 🧮",
      "options": { "A": "7", "B": "3", "C": "9", "D": "1" },
      "correct_answer": "A"
    },
    {
      "id": 9,
      "difficulty": "easy",
      "question": "Cube of a number ending in 7 ends in? 🔄",
      "options": { "A": "3", "B": "7", "C": "9", "D": "1" },
      "correct_answer": "A"
    },
    {
      "id": 10,
      "difficulty": "easy",
      "question": "Which is a perfect cube? 🧊",
      "options": { "A": "64", "B": "16", "C": "20", "D": "30" },
      "correct_answer": "A"
    },
    {
      "id": 11,
      "difficulty": "easy",
      "question": "Cube of 10 is? 🔟",
      "options": { "A": "1000", "B": "100", "C": "30", "D": "10000" },
      "correct_answer": "A"
    },
    {
      "id": 12,
      "difficulty": "easy",
      "question": "Which digit can a cube number end with? 🔢",
      "options": {
        "A": "0,1,8,7,4,5,6,3,2,9",
        "B": "Only 0,1,4,5,6,9",
        "C": "Any digit",
        "D": "Only odd digits"
      },
      "correct_answer": "C"
    },
    {
      "id": 13,
      "difficulty": "easy",
      "question": "Cube of 0.5 is? 🎲",
      "options": { "A": "0.125", "B": "1.5", "C": "0.25", "D": "1.25" },
      "correct_answer": "A"
    },
    {
      "id": 14,
      "difficulty": "easy",
      "question": "A perfect cube's prime factors have exponents that are? 📐",
      "options": {
        "A": "Multiples of 3",
        "B": "Even",
        "C": "Odd",
        "D": "Prime"
      },
      "correct_answer": "A"
    },
    {
      "id": 15,
      "difficulty": "easy",
      "question": "Which is NOT a perfect cube? 🚫",
      "options": { "A": "100", "B": "125", "C": "216", "D": "343" },
      "correct_answer": "A"
    },
    {
      "id": 16,
      "difficulty": "easy",
      "question": "Cube of (-2) is? ➖",
      "options": { "A": "-8", "B": "8", "C": "4", "D": "-4" },
      "correct_answer": "A"
    },
    {
      "id": 17,
      "difficulty": "easy",
      "question": "If n³ = 8, then (-n)³ = ? 🔄",
      "options": { "A": "-8", "B": "8", "C": "-2", "D": "2" },
      "correct_answer": "A"
    },
    {
      "id": 18,
      "difficulty": "easy",
      "question": "Cube of 1/2 is? 🍰",
      "options": { "A": "1/8", "B": "1/4", "C": "1/6", "D": "1/2" },
      "correct_answer": "A"
    },
    {
      "id": 19,
      "difficulty": "easy",
      "question": "How many perfect cubes from 1 to 500? 🧩",
      "options": { "A": "7", "B": "8", "C": "6", "D": "9" },
      "correct_answer": "A"
    },
    {
      "id": 20,
      "difficulty": "easy",
      "question": "Cube of an integer can end with digit 2? ✅",
      "options": {
        "A": "Yes (e.g., 8³=512)",
        "B": "No",
        "C": "Only for even",
        "D": "Only for odd"
      },
      "correct_answer": "A"
    },
    {
      "id": 21,
      "difficulty": "medium",
      "question": "If a number ends with 5, its cube ends with? 🎯",
      "options": { "A": "5", "B": "25", "C": "125", "D": "0" },
      "correct_answer": "A"
    },
    {
      "id": 22,
      "difficulty": "medium",
      "question": "The sum of cubes of first n natural numbers = [n(n+1)/2]²? ✅",
      "options": {
        "A": "True",
        "B": "False",
        "C": "Sometimes",
        "D": "Only for even n"
      },
      "correct_answer": "A"
    },
    {
      "id": 23,
      "difficulty": "medium",
      "question": "Cube of a number ending in 4 ends in? 🔢",
      "options": { "A": "4", "B": "6", "C": "8", "D": "2" },
      "correct_answer": "A"
    },
    {
      "id": 24,
      "difficulty": "medium",
      "question": "Which statement is true? 🧠",
      "options": {
        "A": "Cube of rational can be irrational",
        "B": "Cube of irrational is always irrational",
        "C": "Cube of integer is integer",
        "D": "Both B & C"
      },
      "correct_answer": "D"
    },
    {
      "id": 25,
      "difficulty": "medium",
      "question": "If a number's cube ends in 1, the number ends in? 🔍",
      "options": { "A": "1", "B": "3", "C": "7", "D": "9" },
      "correct_answer": "A"
    },
    {
      "id": 26,
      "difficulty": "medium",
      "question": "For integer n, n³ - n is divisible by 6. Proof uses? 📚",
      "options": {
        "A": "(n-1)n(n+1) product",
        "B": "Algebraic identity",
        "C": "Prime factors",
        "D": "All of these"
      },
      "correct_answer": "D"
    },
    {
      "id": 27,
      "difficulty": "medium",
      "question": "Smallest number by which 72 must be multiplied to get perfect cube? 🚀",
      "options": { "A": "3", "B": "2", "C": "6", "D": "12" },
      "correct_answer": "A"
    },
    {
      "id": 28,
      "difficulty": "medium",
      "question": "Cube of 11 is? 🔢",
      "options": { "A": "1331", "B": "121", "C": "14641", "D": "1111" },
      "correct_answer": "A"
    },
    {
      "id": 29,
      "difficulty": "medium",
      "question": "If x³ = 0.027, then x = ? 📐",
      "options": { "A": "0.3", "B": "0.03", "C": "0.003", "D": "3" },
      "correct_answer": "A"
    },
    {
      "id": 30,
      "difficulty": "medium",
      "question": "The cube of a two-digit number can be how many digits? 📏",
      "options": {
        "A": "4 to 6 digits",
        "B": "Always 6 digits",
        "C": "3 to 5 digits",
        "D": "Always 5 digits"
      },
      "correct_answer": "A"
    },
    {
      "id": 31,
      "difficulty": "medium",
      "question": "If n is even, n³ is divisible by? ➗",
      "options": { "A": "8", "B": "6", "C": "4", "D": "2" },
      "correct_answer": "A"
    },
    {
      "id": 32,
      "difficulty": "medium",
      "question": "Smallest perfect cube greater than 200? 🎯",
      "options": { "A": "216", "B": "125", "C": "343", "D": "512" },
      "correct_answer": "A"
    },
    {
      "id": 33,
      "difficulty": "medium",
      "question": "Cube of 1.1 is? 📈",
      "options": { "A": "1.331", "B": "1.21", "C": "1.1", "D": "1.4641" },
      "correct_answer": "A"
    },
    {
      "id": 34,
      "difficulty": "medium",
      "question": "Which number's cube is between 1000 and 2000? 🔢",
      "options": { "A": "12", "B": "11", "C": "13", "D": "14" },
      "correct_answer": "A"
    },
    {
      "id": 35,
      "difficulty": "medium",
      "question": "For any integer a, (-a)³ = ? ⚖️",
      "options": { "A": "-a³", "B": "a³", "C": "(-a)³", "D": "Both A & C" },
      "correct_answer": "D"
    },
    {
      "id": 36,
      "difficulty": "medium",
      "question": "Cube of a number ending in 6 ends in? 🔄",
      "options": { "A": "6", "B": "2", "C": "4", "D": "8" },
      "correct_answer": "A"
    },
    {
      "id": 37,
      "difficulty": "medium",
      "question": "If a perfect cube ends with three zeros, it must have at least how many zeros? 🚀",
      "options": { "A": "3", "B": "6", "C": "9", "D": "12" },
      "correct_answer": "A"
    },
    {
      "id": 38,
      "difficulty": "medium",
      "question": "The cube of a fraction less than 1 is? 🍰",
      "options": {
        "A": "Less than the fraction",
        "B": "Greater than fraction",
        "C": "Equal",
        "D": "Can't say"
      },
      "correct_answer": "A"
    },
    {
      "id": 39,
      "difficulty": "medium",
      "question": "If n³ is odd, then n is? 🔢",
      "options": { "A": "Odd", "B": "Even", "C": "Can be both", "D": "Prime" },
      "correct_answer": "A"
    },
    {
      "id": 40,
      "difficulty": "medium",
      "question": "Smallest number to divide 108 to get perfect cube? ➗",
      "options": { "A": "4", "B": "2", "C": "3", "D": "6" },
      "correct_answer": "A"
    },
    {
      "id": 41,
      "difficulty": "hard",
      "question": "The cube of a number ending in 9 ends in? 🎲",
      "options": { "A": "9", "B": "1", "C": "3", "D": "7" },
      "correct_answer": "A"
    },
    {
      "id": 42,
      "difficulty": "hard",
      "question": "Prove that difference of cubes of two consecutive integers is odd. Example: 2³-1³=? 🔥",
      "options": {
        "A": "7",
        "B": "Always odd",
        "C": "Both A & B",
        "D": "Always even"
      },
      "correct_answer": "C"
    },
    {
      "id": 43,
      "difficulty": "hard",
      "question": "If a number has prime factorization 2³×3³×5⁶, is it a perfect cube? ✅",
      "options": {
        "A": "Yes",
        "B": "No",
        "C": "Maybe",
        "D": "Only if exponents even"
      },
      "correct_answer": "A"
    },
    {
      "id": 44,
      "difficulty": "hard",
      "question": "For integer n, n³ and (n+1)³ differ by? 📊",
      "options": {
        "A": "3n²+3n+1",
        "B": "n³+1",
        "C": "3n³+3n+1",
        "D": "n²+n+1"
      },
      "correct_answer": "A"
    },
    {
      "id": 45,
      "difficulty": "hard",
      "question": "Cube root of a perfect cube ending in 2 ends in? 🔢",
      "options": { "A": "8", "B": "2", "C": "4", "D": "6" },
      "correct_answer": "A"
    },
    {
      "id": 46,
      "difficulty": "hard",
      "question": "Which can be cube of a rational number? 🧮",
      "options": {
        "A": "0.008",
        "B": "0.04",
        "C": "0.009",
        "D": "All of these"
      },
      "correct_answer": "D"
    },
    {
      "id": 47,
      "difficulty": "hard",
      "question": "If a perfect cube is even, its cube root is? 🔄",
      "options": { "A": "Even", "B": "Odd", "C": "Can be both", "D": "Prime" },
      "correct_answer": "A"
    },
    {
      "id": 48,
      "difficulty": "hard",
      "question": "For n>1, n³ is always greater than n² + n? ⚖️",
      "options": { "A": "Yes", "B": "No", "C": "For n≥2", "D": "For n>2" },
      "correct_answer": "C"
    },
    {
      "id": 49,
      "difficulty": "hard",
      "question": "Smallest natural number by which 392 must be multiplied for perfect cube? 🚀",
      "options": { "A": "7", "B": "14", "C": "21", "D": "28" },
      "correct_answer": "A"
    },
    {
      "id": 50,
      "difficulty": "hard",
      "question": "Cube of 0.01 is? 🌟",
      "options": {
        "A": "0.000001",
        "B": "0.001",
        "C": "0.0001",
        "D": "0.00001"
      },
      "correct_answer": "A"
    },
    {
      "id": 51,
      "difficulty": "hard",
      "question": "If a number's cube ends in 8, the number ends in? 🔍",
      "options": { "A": "2", "B": "4", "C": "6", "D": "8" },
      "correct_answer": "A"
    },
    {
      "id": 52,
      "difficulty": "hard",
      "question": "The sum of cubes of first 5 natural numbers? 📈",
      "options": { "A": "225", "B": "100", "C": "325", "D": "125" },
      "correct_answer": "A"
    },
    {
      "id": 53,
      "difficulty": "hard",
      "question": "For integer n, n³ + (n+1)³ + (n+2)³ is divisible by? ➗",
      "options": { "A": "9", "B": "3", "C": "6", "D": "All of these" },
      "correct_answer": "D"
    },
    {
      "id": 54,
      "difficulty": "hard",
      "question": "If a³ + b³ = 72 and a+b=6, find ab. 🔥",
      "options": { "A": "8", "B": "12", "C": "6", "D": "9" },
      "correct_answer": "A"
    },
    {
      "id": 55,
      "difficulty": "hard",
      "question": "Cube root of a perfect cube ending in 3 ends in? 🧠",
      "options": { "A": "7", "B": "3", "C": "9", "D": "1" },
      "correct_answer": "A"
    },
    {
      "id": 56,
      "difficulty": "hard",
      "question": "A perfect cube can end with exactly two zeros? 🚫",
      "options": {
        "A": "No",
        "B": "Yes",
        "C": "Sometimes",
        "D": "If divisible by 100"
      },
      "correct_answer": "A"
    },
    {
      "id": 57,
      "difficulty": "hard",
      "question": "If n is integer, n³ - n is divisible by 24 for? 📏",
      "options": {
        "A": "n odd",
        "B": "n even",
        "C": "n not multiple of 3",
        "D": "n>3"
      },
      "correct_answer": "A"
    },
    {
      "id": 58,
      "difficulty": "hard",
      "question": "The cube of which number is equal to its square? 🔄",
      "options": {
        "A": "0 and 1",
        "B": "0 only",
        "C": "1 only",
        "D": "-1, 0, 1"
      },
      "correct_answer": "A"
    },
    {
      "id": 59,
      "difficulty": "hard",
      "question": "If a perfect cube is divisible by 8, its cube root divisible by? ✅",
      "options": { "A": "2", "B": "4", "C": "8", "D": "Depends" },
      "correct_answer": "A"
    },
    {
      "id": 60,
      "difficulty": "hard",
      "question": "For a positive integer n, (n+1)³ - n³ = ? ⚡",
      "options": {
        "A": "3n²+3n+1",
        "B": "n²+n+1",
        "C": "3n³+3n+1",
        "D": "2n²+2n+1"
      },
      "correct_answer": "A"
    }
  ]
}