{
  "title": "Properties of square numbers - Grade 8 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Which of these numbers is a perfect square?", "options": {"A": "18", "B": "25", "C": "30", "D": "42"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "What is the unit digit of 7²?", "options": {"A": "1", "B": "4", "C": "9", "D": "6"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "Which of these cannot be a perfect square?", "options": {"A": "36", "B": "49", "C": "50", "D": "64"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "What is the unit digit of 5²?", "options": {"A": "5", "B": "0", "C": "2", "D": "3"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "Which number squared gives 144?", "options": {"A": "11", "B": "12", "C": "13", "D": "14"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "What is the unit digit of 8²?", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "Which of these is a perfect square between 50 and 65?", "options": {"A": "55", "B": "60", "C": "64", "D": "62"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "What is the square of 0?", "options": {"A": "0", "B": "1", "C": "2", "D": "undefined"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Which number squared gives 81?", "options": {"A": "8", "B": "9", "C": "10", "D": "7"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "What is the unit digit of 4²?", "options": {"A": "4", "B": "6", "C": "8", "D": "2"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "Which of these numbers ends with 1 when squared?", "options": {"A": "4", "B": "6", "C": "9", "D": "2"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "What is 11²?", "options": {"A": "121", "B": "111", "C": "131", "D": "141"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Which of these numbers ends with 6 when squared?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "What is 15²?", "options": {"A": "225", "B": "215", "C": "235", "D": "205"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Which of these is NOT a perfect square?", "options": {"A": "100", "B": "121", "C": "125", "D": "144"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "What is the unit digit of 9²?", "options": {"A": "1", "B": "9", "C": "6", "D": "3"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Which number squared gives 169?", "options": {"A": "12", "B": "13", "C": "14", "D": "15"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "What is the square of 1?", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "Which of these numbers ends with 4 when squared?", "options": {"A": "2", "B": "3", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "What is 20²?", "options": {"A": "400", "B": "200", "C": "300", "D": "100"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "How many numbers between 1 and 100 are perfect squares?", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "Which of these numbers can never be a perfect square?", "options": {"A": "ending with 2", "B": "ending with 5", "C": "ending with 6", "D": "ending with 9"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "If n is an odd number, what can you say about n²?", "options": {"A": "always even", "B": "always odd", "C": "can be even or odd", "D": "always prime"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "What is the sum of first 5 square numbers (1²+2²+3²+4²+5²)?", "options": {"A": "50", "B": "55", "C": "60", "D": "65"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "Which of these will have 1 as unit digit when squared?", "options": {"A": "19", "B": "24", "C": "37", "D": "43"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "How many perfect squares are there between 100 and 200?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "If a number ends with 5 zeros, its square ends with how many zeros?", "options": {"A": "5", "B": "10", "C": "8", "D": "6"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "Which of these is NOT a property of square numbers?", "options": {"A": "end with 0,1,4,5,6,9", "B": "sum of odd numbers", "C": "always even", "D": "product of two consecutive triangular numbers"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "The difference between squares of two consecutive numbers is 23. What are the numbers?", "options": {"A": "11,12", "B": "12,13", "C": "13,14", "D": "14,15"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Which of these numbers will have 6 as unit digit when squared?", "options": {"A": "14", "B": "16", "C": "24", "D": "26"}, "correct_answer": "D"},
    {"id": 31, "difficulty": "medium", "question": "The square of an even number is always:", "options": {"A": "even", "B": "odd", "C": "prime", "D": "multiple of 3"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "How many non-square numbers lie between 12² and 13²?", "options": {"A": "22", "B": "23", "C": "24", "D": "25"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "Which of these is a perfect square of an odd number?", "options": {"A": "256", "B": "289", "C": "324", "D": "400"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "The square of a number ending with 4 ends with:", "options": {"A": "4", "B": "6", "C": "8", "D": "2"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "What is the sum of first 10 square numbers?", "options": {"A": "285", "B": "385", "C": "485", "D": "585"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Which of these can be a perfect square?", "options": {"A": "3333", "B": "4444", "C": "5555", "D": "7777"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "The difference between 25² and 24² is:", "options": {"A": "47", "B": "48", "C": "49", "D": "50"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "A perfect square never ends with:", "options": {"A": "1", "B": "4", "C": "8", "D": "9"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "If n² = 2025, what is n?", "options": {"A": "35", "B": "40", "C": "45", "D": "50"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "The square of a number ending with 6 ends with:", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "How many perfect squares are between 50 and 150?", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "medium", "question": "Which of these numbers when squared gives a number ending with 25?", "options": {"A": "15", "B": "25", "C": "35", "D": "all of these"}, "correct_answer": "D"},
    {"id": 43, "difficulty": "medium", "question": "If x is even, then x² is divisible by:", "options": {"A": "2", "B": "4", "C": "8", "D": "16"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "medium", "question": "The square of a prime number (greater than 3) always leaves remainder ___ when divided by 12.", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "medium", "question": "Which of these is NOT a perfect square?", "options": {"A": "1225", "B": "1296", "C": "1331", "D": "1369"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "The sum of squares of first n natural numbers is given by n(n+1)(2n+1)/6. What is 1²+2²+3²+4²?", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "medium", "question": "A perfect square number can never end with how many zeros?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "If a number ends with 1, its square ends with:", "options": {"A": "1", "B": "3", "C": "7", "D": "9"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "The square of a number is 324. What is the number?", "options": {"A": "16", "B": "17", "C": "18", "D": "19"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "How many numbers between 200 and 300 are perfect squares?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "medium", "question": "Which of these statements is false about square numbers?", "options": {"A": "They end with 0,1,4,5,6,9", "B": "They are sum of consecutive odd numbers", "C": "Square of even number is even", "D": "Square of odd number is even"}, "correct_answer": "D"},
    {"id": 52, "difficulty": "medium", "question": "The product of two consecutive even numbers plus 1 is always:", "options": {"A": "a perfect square", "B": "a prime number", "C": "an even number", "D": "divisible by 3"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "If n² = 5776, what is n?", "options": {"A": "74", "B": "75", "C": "76", "D": "77"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "medium", "question": "A number when squared gives 7921. What is the number?", "options": {"A": "87", "B": "88", "C": "89", "D": "90"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "The difference between squares of two consecutive odd numbers is always divisible by:", "options": {"A": "3", "B": "4", "C": "8", "D": "16"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "Which of these numbers is both a perfect square and perfect cube?", "options": {"A": "64", "B": "81", "C": "100", "D": "125"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "The square of a number ending with 9 ends with:", "options": {"A": "1", "B": "3", "C": "7", "D": "9"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "How many non-square numbers lie between 50² and 51²?", "options": {"A": "100", "B": "101", "C": "102", "D": "103"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Which of these numbers when squared gives an even number?", "options": {"A": "13", "B": "15", "C": "17", "D": "18"}, "correct_answer": "D"},
    {"id": 60, "difficulty": "medium", "question": "If a perfect square ends with 6, its square root ends with:", "options": {"A": "4 or 6", "B": "2 or 8", "C": "3 or 7", "D": "1 or 9"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "The sum of squares of first 3 odd numbers is:", "options": {"A": "14", "B": "21", "C": "28", "D": "35"}, "correct_answer": "D"},
    {"id": 62, "difficulty": "medium", "question": "Which of these numbers is a perfect square of an even number?", "options": {"A": "169", "B": "225", "C": "256", "D": "289"}, "correct_answer": "C"},
    {"id": 63, "difficulty": "medium", "question": "If n is a natural number, then n² + n + 1 is always:", "options": {"A": "even", "B": "odd", "C": "perfect square", "D": "divisible by 3"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "A perfect square leaves remainder 0 or 1 when divided by:", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "The square of a number ending with 0 ends with:", "options": {"A": "0", "B": "00", "C": "000", "D": "0000"}, "correct_answer": "B"},
    {"id": 66, "difficulty": "medium", "question": "Which of these numbers is NOT a perfect square?", "options": {"A": "1521", "B": "1681", "C": "1849", "D": "1936"}, "correct_answer": "D"},
    {"id": 67, "difficulty": "medium", "question": "The difference between squares of two consecutive even numbers is always divisible by:", "options": {"A": "2", "B": "4", "C": "8", "D": "16"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "How many perfect squares are there from 1 to 500?", "options": {"A": "20", "B": "21", "C": "22", "D": "23"}, "correct_answer": "C"},
    {"id": 69, "difficulty": "medium", "question": "If a number is multiplied by itself, the product is called:", "options": {"A": "cube", "B": "square", "C": "power", "D": "multiple"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "The square of a two-digit number has how many digits at most?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "Which of these numbers ends with 9 when squared?", "options": {"A": "7", "B": "13", "C": "17", "D": "23"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "A perfect square between 250 and 300 is:", "options": {"A": "256", "B": "289", "C": "324", "D": "361"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "The sum of first n odd numbers is:", "options": {"A": "n", "B": "n²", "C": "2n", "D": "n(n+1)"}, "correct_answer": "B"},
    {"id": 74, "difficulty": "medium", "question": "If n² = 2401, what is n?", "options": {"A": "47", "B": "48", "C": "49", "D": "50"}, "correct_answer": "C"},
    {"id": 75, "difficulty": "medium", "question": "A number ending with 2,3,7 or 8 is never a:", "options": {"A": "prime number", "B": "composite number", "C": "perfect square", "D": "odd number"}, "correct_answer": "C"},
    {"id": 76, "difficulty": "medium", "question": "The square of a number ending with 5 always ends with:", "options": {"A": "5", "B": "25", "C": "125", "D": "625"}, "correct_answer": "B"},
    {"id": 77, "difficulty": "medium", "question": "How many non-square numbers between 15² and 16²?", "options": {"A": "28", "B": "29", "C": "30", "D": "31"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "If a perfect square ends with 1, its square root ends with:", "options": {"A": "1 or 9", "B": "2 or 8", "C": "3 or 7", "D": "4 or 6"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "Which of these numbers is a perfect square?", "options": {"A": "1024", "B": "1025", "C": "1026", "D": "1027"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "The square of an integer is called:", "options": {"A": "perfect square", "B": "perfect cube", "C": "prime number", "D": "composite number"}, "correct_answer": "A"},
    {"id": 81, "difficulty": "hard", "question": "Prove that the square of any integer is of the form 3k or 3k+1. Which form does 47² belong to?", "options": {"A": "3k", "B": "3k+1", "C": "3k+2", "D": "none of these"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "How many perfect squares between 1 and 1000 are divisible by 7?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "If a perfect square has 4 digits and begins with 3, what could be its unit digit?", "options": {"A": "1", "B": "4", "C": "6", "D": "any of these"}, "correct_answer": "D"},
    {"id": 84, "difficulty": "hard", "question": "Find the number of perfect squares between 1000 and 2000.", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "C"},
    {"id": 85, "difficulty": "hard", "question": "The square of a number is 10 more than 9 times the number. Find the number.", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "B"},
    {"id": 86, "difficulty": "hard", "question": "If n is a natural number, then n(n+1)(n+2)(n+3)+1 is always:", "options": {"A": "a perfect square", "B": "a perfect cube", "C": "prime number", "D": "even number"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "How many perfect squares between 1 and 500 are divisible by both 2 and 3?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "The product of four consecutive natural numbers plus 1 is always:", "options": {"A": "a perfect square", "B": "a perfect cube", "C": "prime number", "D": "even number"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "Find the sum of all perfect squares between 50 and 200.", "options": {"A": "355", "B": "385", "C": "415", "D": "445"}, "correct_answer": "B"},
    {"id": 90, "difficulty": "hard", "question": "If the square of a number is subtracted from 68, the result is 4 less than 8 times the number. Find the number.", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "How many perfect squares between 100 and 1000 have the digit 5 in units place?", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "The sum of squares of three consecutive integers is 50. Find the integers.", "options": {"A": "3,4,5", "B": "4,5,6", "C": "5,6,7", "D": "6,7,8"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "A perfect square number has 31 as its tens digit. What could be its units digit?", "options": {"A": "1", "B": "4", "C": "6", "D": "9"}, "correct_answer": "C"},
    {"id": 94, "difficulty": "hard", "question": "Find the number of two-digit perfect squares whose tens digit is odd.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "If a² + b² = 65 and ab = 8, find a² - b² (given a > b > 0).", "options": {"A": "49", "B": "48", "C": "47", "D": "46"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "How many perfect squares between 1 and 1000 have their digits summing to an odd number?", "options": {"A": "15", "B": "16", "C": "17", "D": "18"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "The difference between squares of two numbers is 120. The numbers are consecutive even numbers. Find them.", "options": {"A": "28,30", "B": "30,32", "C": "32,34", "D": "34,36"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "Find the smallest number by which 180 must be multiplied to get a perfect square.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 99, "difficulty": "hard", "question": "A perfect square number has 4 digits. When its digits are reversed, it's still a perfect square. Find such a number.", "options": {"A": "1089", "B": "9801", "C": "1024", "D": "4096"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "Find the sum of all perfect squares between 200 and 800.", "options": {"A": "5115", "B": "5215", "C": "5315", "D": "5415"}, "correct_answer": "A"}
  ]
}