{
  "title": "Properties of Cubes (Cubes and Cube Roots) - Grade 8 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Which of these is a perfect cube?", "options": {"A": "16", "B": "27", "C": "36", "D": "50"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "The cube of an even number is always ___", "options": {"A": "even", "B": "odd", "C": "prime", "D": "zero"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "The cube of an odd number is always ___", "options": {"A": "even", "B": "odd", "C": "a fraction", "D": "zero"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "What is the cube of 0?", "options": {"A": "0", "B": "1", "C": "10", "D": "100"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "What is the cube of 1?", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "If a number ends with digit 2, its cube ends with digit ___", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "D"},
    {"id": 7, "difficulty": "easy", "question": "If a number ends with digit 5, its cube ends with digit ___", "options": {"A": "5", "B": "0", "C": "2", "D": "1"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Which of these is NOT a perfect cube?", "options": {"A": "8", "B": "64", "C": "100", "D": "125"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "The cube of a negative number is always ___", "options": {"A": "positive", "B": "negative", "C": "zero", "D": "fraction"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "What is the cube of 10?", "options": {"A": "10", "B": "100", "C": "1000", "D": "10000"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "What is the cube of -2?", "options": {"A": "8", "B": "-8", "C": "4", "D": "-4"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "If a number ends with digit 3, its cube ends with digit ___", "options": {"A": "3", "B": "7", "C": "9", "D": "1"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "Which pattern do the cubes of numbers ending with 4 follow?", "options": {"A": "End with 4", "B": "End with 6", "C": "End with 8", "D": "End with 0"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Is the cube of 7 equal to 343?", "options": {"A": "Yes", "B": "No", "C": "Cannot say", "D": "Only if divided by 7"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Which of these numbers will have 1 as the unit digit of its cube?", "options": {"A": "12", "B": "13", "C": "14", "D": "15"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "The cube of a number 'n' is represented as ___", "options": {"A": "n²", "B": "n³", "C": "2n", "D": "3n"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Which of these is the cube of a single-digit number?", "options": {"A": "100", "B": "144", "C": "216", "D": "300"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "If a number is multiplied by itself twice, we get its ___", "options": {"A": "square", "B": "cube", "C": "double", "D": "triple"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "A perfect cube can end with two zeros. (True/False?)", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "What is the sum of cubes of first two natural numbers (1³ + 2³)?", "options": {"A": "8", "B": "9", "C": "10", "D": "12"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "Which of the following will have 6 as the unit digit of its cube?", "options": {"A": "12", "B": "14", "C": "16", "D": "18"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "If the cube of a number ends with 3, the number itself ends with ___", "options": {"A": "3", "B": "7", "C": "9", "D": "1"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "What is the smallest number by which 675 must be multiplied so that the product is a perfect cube?", "options": {"A": "3", "B": "5", "C": "9", "D": "15"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "The cube of a number is 4913. What is the number?", "options": {"A": "13", "B": "15", "C": "17", "D": "19"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "How many perfect cubes are there between 1 and 1000?", "options": {"A": "9", "B": "10", "C": "11", "D": "12"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "If x³ = 729, then x = ?", "options": {"A": "7", "B": "8", "C": "9", "D": "10"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "The cube of a two-digit number can be a ___ digit number.", "options": {"A": "4 or 5", "B": "5 or 6", "C": "6 or 7", "D": "3 or 4"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "Which of these numbers is a perfect cube? 128, 256, 512, 1024", "options": {"A": "128", "B": "256", "C": "512", "D": "1024"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "If n³ = 2744, what is n?", "options": {"A": "12", "B": "14", "C": "16", "D": "18"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "The cube of 1.2 is:", "options": {"A": "1.44", "B": "1.728", "C": "14.4", "D": "17.28"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Which of these is the cube of an even number? 125, 216, 343, 729", "options": {"A": "125", "B": "216", "C": "343", "D": "729"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "What is the unit digit of the cube of 37?", "options": {"A": "1", "B": "3", "C": "7", "D": "9"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "The smallest perfect cube greater than 200 is:", "options": {"A": "216", "B": "225", "C": "256", "D": "289"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "If a number is tripled, its cube becomes ___ times.", "options": {"A": "3", "B": "9", "C": "27", "D": "81"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "Which of these numbers when cubed gives a number between 500 and 600?", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "C"},
    {"id": 36, "difficulty": "medium", "question": "The cube of (-11) is:", "options": {"A": "121", "B": "-121", "C": "1331", "D": "-1331"}, "correct_answer": "D"},
    {"id": 37, "difficulty": "medium", "question": "A perfect cube does not end with two zeros. (True/False?)", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Cannot say"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "What is the cube root of the cube of 21?", "options": {"A": "7", "B": "21", "C": "441", "D": "9261"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "Which of these is NOT a property of cubes of numbers?", "options": {"A": "Cube of an even number is even.", "B": "Cube of an odd number is odd.", "C": "A perfect cube may end with any digit.", "D": "Cube of a number ending in 1 ends in 1."}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "If the cube of a number ends with 8, the number could end with ___", "options": {"A": "2 only", "B": "8 only", "C": "2 or 8", "D": "4 or 6"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Find the smallest natural number by which 392 must be multiplied to get a perfect cube.", "options": {"A": "2", "B": "3", "C": "7", "D": "14"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "medium", "question": "The cube of 0.5 is:", "options": {"A": "0.125", "B": "0.25", "C": "1.25", "D": "12.5"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "How many perfect cubes are there between 500 and 1500?", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "medium", "question": "If a³ = 512, and b³ = 729, what is a + b?", "options": {"A": "17", "B": "19", "C": "21", "D": "23"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Which of these numbers is the cube of a rational number? 0.008, 0.04, 0.16, 0.32", "options": {"A": "0.008", "B": "0.04", "C": "0.16", "D": "0.32"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "A number is doubled. Its new cube will be how many times the original cube?", "options": {"A": "2 times", "B": "4 times", "C": "6 times", "D": "8 times"}, "correct_answer": "D"},
    {"id": 47, "difficulty": "medium", "question": "What is the cube of (-12)?", "options": {"A": "144", "B": "-144", "C": "1728", "D": "-1728"}, "correct_answer": "D"},
    {"id": 48, "difficulty": "medium", "question": "If the unit digit of a number is 9, the unit digit of its cube is:", "options": {"A": "1", "B": "3", "C": "7", "D": "9"}, "correct_answer": "D"},
    {"id": 49, "difficulty": "medium", "question": "The cube of a number x is 8 times the cube of number y. If y=5, what is x?", "options": {"A": "10", "B": "15", "C": "20", "D": "40"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Which of these statements is FALSE about cubes?", "options": {"A": "There are only 10 perfect cubes from 1 to 1000.", "B": "Cube of a negative number is negative.", "C": "A perfect cube can end with exactly two zeros.", "D": "1, 8, 27 are the cubes of 1, 2, 3."}, "correct_answer": "C"},
    {"id": 51, "difficulty": "medium", "question": "What is the unit digit of (13³ + 17³)?", "options": {"A": "0", "B": "2", "C": "4", "D": "6"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "If a perfect cube ends with 4, its cube root ends with ___", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "Find the smallest number by which 1600 must be divided to make it a perfect cube.", "options": {"A": "10", "B": "20", "C": "25", "D": "50"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "medium", "question": "The cube of the sum 5+6 is NOT equal to the sum of their cubes. (True/False?)", "options": {"A": "True", "B": "False", "C": "Equal only for 0", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "How many perfect cubes are there from 1 to 500?", "options": {"A": "7", "B": "8", "C": "9", "D": "10"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "If n is a perfect cube, then which of these must be true about its prime factorisation?", "options": {"A": "Every prime factor has an even exponent.", "B": "Every prime factor has an exponent multiple of 3.", "C": "It has only one prime factor.", "D": "It has an odd number of prime factors."}, "correct_answer": "B"},
    {"id": 57, "difficulty": "medium", "question": "What is the cube of 25?", "options": {"A": "625", "B": "12500", "C": "15625", "D": "62500"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "The cube of 1.5 is:", "options": {"A": "2.25", "B": "3.375", "C": "22.5", "D": "33.75"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "medium", "question": "Which of these is the cube of a number between 3 and 4?", "options": {"A": "30", "B": "40", "C": "50", "D": "64"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "If the cube of a number is subtracted from the cube of its successor, the difference is 331. Find the number.", "options": {"A": "9", "B": "10", "C": "11", "D": "12"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "What is the unit digit of the cube of 58?", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "A perfect cube can have exactly ___ zeros at the end.", "options": {"A": "any number", "B": "only 3 or multiples of 3", "C": "only 2", "D": "only 1"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "If x³ = 0.027, then x = ?", "options": {"A": "0.3", "B": "0.03", "C": "0.003", "D": "0.9"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "The cube of which number is equal to the sum of the cubes of 6 and 8?", "options": {"A": "10", "B": "12", "C": "14", "D": "16"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Which of these numbers is both a perfect square and a perfect cube?", "options": {"A": "64", "B": "81", "C": "100", "D": "121"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "If (2n)³ = 512, what is n?", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "B"},
    {"id": 67, "difficulty": "medium", "question": "The cube of a fraction less than 1 is ___ the original fraction.", "options": {"A": "greater than", "B": "less than", "C": "equal to", "D": "double of"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "What is the smallest perfect cube that is divisible by 4 and 9?", "options": {"A": "36", "B": "144", "C": "216", "D": "576"}, "correct_answer": "C"},
    {"id": 69, "difficulty": "medium", "question": "The difference of cubes of two consecutive numbers 10 and 11 is:", "options": {"A": "111", "B": "221", "C": "331", "D": "441"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "If a number ends with three zeros, its cube ends with at least ___ zeros.", "options": {"A": "3", "B": "6", "C": "9", "D": "12"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "Which of these is the cube of a two-digit odd number?", "options": {"A": "1331", "B": "1728", "C": "2197", "D": "2744"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "medium", "question": "What is the cube of (-0.1)?", "options": {"A": "-0.001", "B": "-0.01", "C": "-0.1", "D": "-1"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "How many perfect cubes are there between 1000 and 2000?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 74, "difficulty": "medium", "question": "If the cube of a number is 10,648, the number is between ___", "options": {"A": "10 and 15", "B": "15 and 20", "C": "20 and 25", "D": "25 and 30"}, "correct_answer": "C"},
    {"id": 75, "difficulty": "medium", "question": "The cube of a number is 8 times the number itself. The number could be:", "options": {"A": "0", "B": "2", "C": "4", "D": "All of these"}, "correct_answer": "D"},
    {"id": 76, "difficulty": "medium", "question": "Which of these is NOT a cube of an integer? 1000, 1331, 1444, 1728", "options": {"A": "1000", "B": "1331", "C": "1444", "D": "1728"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "What is the sum of the cubes of the first three natural numbers?", "options": {"A": "9", "B": "18", "C": "27", "D": "36"}, "correct_answer": "D"},
    {"id": 78, "difficulty": "medium", "question": "If the cube root of a number is 12, what is the cube of that number?", "options": {"A": "144", "B": "1728", "C": "20736", "D": "248832"}, "correct_answer": "D"},
    {"id": 79, "difficulty": "medium", "question": "A perfect cube ends with the digit 7. Which digit could its cube root end with?", "options": {"A": "3 only", "B": "7 only", "C": "3 or 7", "D": "1 or 9"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "Evaluate: (7³ - 5³)", "options": {"A": "98", "B": "118", "C": "218", "D": "318"}, "correct_answer": "C"},

    {"id": 81, "difficulty": "hard", "question": "If n³ is a 7-digit number, then n is a ___ digit number.", "options": {"A": "2 or 3", "B": "3 or 4", "C": "4 or 5", "D": "5 or 6"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "The cube of a number is 238328. What is the number?", "options": {"A": "58", "B": "62", "C": "68", "D": "72"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "How many perfect cubes are there between 100 and 10000?", "options": {"A": "18", "B": "19", "C": "20", "D": "21"}, "correct_answer": "D"},
    {"id": 84, "difficulty": "hard", "question": "If the cube of a number ends with 24, what could be the last two digits of the number?", "options": {"A": "24", "B": "44", "C": "64", "D": "84"}, "correct_answer": "D"},
    {"id": 85, "difficulty": "hard", "question": "Find the smallest number by which 12348 must be multiplied so that the product is a perfect cube.", "options": {"A": "6", "B": "12", "C": "18", "D": "24"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "The difference between the cubes of two consecutive integers is 127. Find the integers.", "options": {"A": "6 and 7", "B": "7 and 8", "C": "8 and 9", "D": "9 and 10"}, "correct_answer": "B"},
    {"id": 87, "difficulty": "hard", "question": "If a³ + b³ = 407 and a + b = 11, find a and b (a<b).", "options": {"A": "4, 7", "B": "5, 6", "C": "3, 8", "D": "2, 9"}, "correct_answer": "B"},
    {"id": 88, "difficulty": "hard", "question": "Which of these is the cube of a number of the form 3n+1?", "options": {"A": "512", "B": "729", "C": "1000", "D": "1331"}, "correct_answer": "D"},
    {"id": 89, "difficulty": "hard", "question": "What is the unit digit of the cube of 123456789?", "options": {"A": "1", "B": "3", "C": "7", "D": "9"}, "correct_answer": "D"},
    {"id": 90, "difficulty": "hard", "question": "The cube of a number x is 125/64. What is the cube of (1/x)?", "options": {"A": "64/125", "B": "125/64", "C": "4/5", "D": "5/4"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "How many perfect cubes are there which are also perfect squares between 1 and 1000000?", "options": {"A": "10", "B": "12", "C": "15", "D": "20"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "If the cube of a three-digit number is an eight-digit number, the original number is at least ___", "options": {"A": "100", "B": "215", "C": "316", "D": "465"}, "correct_answer": "D"},
    {"id": 93, "difficulty": "hard", "question": "The sum of the cubes of three consecutive numbers is 2772. Find the numbers.", "options": {"A": "8, 9, 10", "B": "9, 10, 11", "C": "10, 11, 12", "D": "11, 12, 13"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "Find the smallest natural number 'n' such that n³ is greater than 5000.", "options": {"A": "15", "B": "16", "C": "17", "D": "18"}, "correct_answer": "C"},
    {"id": 95, "difficulty": "hard", "question": "The cube of the difference of two numbers is 1. The numbers are consecutive integers. Find them.", "options": {"A": "0 and 1", "B": "1 and 2", "C": "2 and 3", "D": "3 and 4"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "Which of these statements is always true? (i) Cube of a prime number is prime. (ii) Cube of an even number is divisible by 8. (iii) Cube of an odd number is odd.", "options": {"A": "(i) only", "B": "(ii) only", "C": "(iii) only", "D": "(ii) and (iii)"}, "correct_answer": "D"},
    {"id": 97, "difficulty": "hard", "question": "If (x - 1/x) = 5, what is the value of (x³ - 1/x³)?", "options": {"A": "110", "B": "140", "C": "155", "D": "170"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "A perfect cube number 'N' has 4 as its unit digit. How many possibilities are there for the unit digit of its cube root?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "The cube of a number is 15.625. The number is:", "options": {"A": "1.5", "B": "2.5", "C": "3.5", "D": "4.5"}, "correct_answer": "B"},
    {"id": 100, "difficulty": "hard", "question": "What is the smallest perfect cube that is a multiple of 7, 14, and 21?", "options": {"A": "343", "B": "2744", "C": "9261", "D": "74088"}, "correct_answer": "D"}
  ]
}