{
"title": "Properties_of_square_numbers(Squares_and_Square_Roots) - Grade 8 ICSE",
"total_questions": 60,
"questions": [
{"id": 1, "difficulty": "easy", "question": "Which of these is a square number? 🟥", "options": {"A": "10", "B": "16", "C": "18", "D": "22"}, "correct_answer": "B"},
{"id": 2, "difficulty": "easy", "question": "A perfect square ends with which digit? ✨", "options": {"A": "2", "B": "3", "C": "7", "D": "9"}, "correct_answer": "D"},
{"id": 3, "difficulty": "easy", "question": "How many non-square numbers lie between 6² and 7²? 🧩", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "C"},
{"id": 4, "difficulty": "easy", "question": "Is 144 a perfect square? ✅", "options": {"A": "No", "B": "Maybe", "C": "Yes", "D": "Not sure"}, "correct_answer": "C"},
{"id": 5, "difficulty": "easy", "question": "The square of an even number is always _______. 🔲", "options": {"A": "Odd", "B": "Even", "C": "Prime", "D": "Zero"}, "correct_answer": "B"},
{"id": 6, "difficulty": "easy", "question": "The square of an odd number is always _______. 🌙", "options": {"A": "Even", "B": "Odd", "C": "A decimal", "D": "Zero"}, "correct_answer": "B"},
{"id": 7, "difficulty": "easy", "question": "Which number squared gives 64? 🤔", "options": {"A": "7", "B": "9", "C": "8", "D": "6"}, "correct_answer": "C"},
{"id": 8, "difficulty": "easy", "question": "The unit digit of square of 45 will be? 🔢", "options": {"A": "4", "B": "0", "C": "5", "D": "2"}, "correct_answer": "C"},
{"id": 9, "difficulty": "easy", "question": "How many natural numbers lie between 9² and 10²? 📊", "options": {"A": "17", "B": "18", "C": "19", "D": "20"}, "correct_answer": "B"},
{"id": 10, "difficulty": "easy", "question": "Which is NOT a perfect square? 🚫", "options": {"A": "121", "B": "169", "C": "200", "D": "225"}, "correct_answer": "C"},
{"id": 11, "difficulty": "easy", "question": "The unit digit of (27)² is? 🎯", "options": {"A": "7", "B": "4", "C": "9", "D": "3"}, "correct_answer": "C"},
{"id": 12, "difficulty": "easy", "question": "If a number ends with 5, its square ends with? 🔟", "options": {"A": "0", "B": "5", "C": "2", "D": "1"}, "correct_answer": "B"},
{"id": 13, "difficulty": "easy", "question": "How many non-square numbers lie between 10² and 11²? 🌟", "options": {"A": "18", "B": "19", "C": "20", "D": "21"}, "correct_answer": "C"},
{"id": 14, "difficulty": "easy", "question": "The sum of first 5 odd numbers is a perfect square. What is it? 🔶", "options": {"A": "16", "B": "25", "C": "36", "D": "49"}, "correct_answer": "B"},
{"id": 15, "difficulty": "easy", "question": "Square of 0 is? 0️⃣", "options": {"A": "1", "B": "0", "C": "10", "D": "100"}, "correct_answer": "B"},
{"id": 16, "difficulty": "easy", "question": "Square of 1 is? 1️⃣", "options": {"A": "0", "B": "2", "C": "1", "D": "3"}, "correct_answer": "C"},
{"id": 17, "difficulty": "easy", "question": "Which of these is the square of 12? 📐", "options": {"A": "132", "B": "144", "C": "154", "D": "164"}, "correct_answer": "B"},
{"id": 18, "difficulty": "easy", "question": "Is 400 a perfect square? 🧠", "options": {"A": "No", "B": "Yes", "C": "Only sometimes", "D": "Cannot say"}, "correct_answer": "B"},
{"id": 19, "difficulty": "easy", "question": "The square of 25 ends with digit? 🎲", "options": {"A": "0", "B": "2", "C": "4", "D": "5"}, "correct_answer": "D"},
{"id": 20, "difficulty": "easy", "question": "Which of these numbers squared gives 900? ⚡", "options": {"A": "28", "B": "29", "C": "30", "D": "31"}, "correct_answer": "C"},
{"id": 21, "difficulty": "medium", "question": "The sum of first n odd numbers is 81. What is n? 🧮", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "B"},
{"id": 22, "difficulty": "medium", "question": "If a number has 1 or 9 in the unit's place, its square ends with? 🔍", "options": {"A": "1", "B": "3", "C": "6", "D": "9"}, "correct_answer": "A"},
{"id": 23, "difficulty": "medium", "question": "Which pair are NOT consecutive perfect squares? 🔄", "options": {"A": "64, 81", "B": "100, 121", "C": "144, 169", "D": "196, 225"}, "correct_answer": "D"},
{"id": 24, "difficulty": "medium", "question": "How many non-square numbers lie between 15² and 16²? 🏁", "options": {"A": "28", "B": "29", "C": "30", "D": "31"}, "correct_answer": "C"},
{"id": 25, "difficulty": "medium", "question": "The square of a number is 1024. The number is? 💡", "options": {"A": "31", "B": "32", "C": "33", "D": "34"}, "correct_answer": "B"},
{"id": 26, "difficulty": "medium", "question": "A perfect square never ends with which digit? ❌", "options": {"A": "1", "B": "4", "C": "6", "D": "8"}, "correct_answer": "D"},
{"id": 27, "difficulty": "medium", "question": "If 2n is a perfect square, what can be said about n? 🤓", "options": {"A": "n is prime", "B": "n is odd", "C": "n is even", "D": "n is square"}, "correct_answer": "C"},
{"id": 28, "difficulty": "medium", "question": "The square of a negative number (-8) is? 🔄", "options": {"A": "-64", "B": "64", "C": "-16", "D": "16"}, "correct_answer": "B"},
{"id": 29, "difficulty": "medium", "question": "Which of these is a square of an even number? 🌈", "options": {"A": "529", "B": "576", "C": "625", "D": "729"}, "correct_answer": "B"},
{"id": 30, "difficulty": "medium", "question": "A number ending with 2 or 8 has a square ending with? 📍", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "B"},
{"id": 31, "difficulty": "medium", "question": "How many numbers between 50 and 100 are perfect squares? 🔎", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
{"id": 32, "difficulty": "medium", "question": "The difference between squares of two consecutive numbers 12 and 13 is? ➖", "options": {"A": "1", "B": "23", "C": "25", "D": "27"}, "correct_answer": "C"},
{"id": 33, "difficulty": "medium", "question": "If a number's square ends in 6, the number could end in? 🔢", "options": {"A": "2 or 8", "B": "4 or 6", "C": "1 or 9", "D": "3 or 7"}, "correct_answer": "B"},
{"id": 34, "difficulty": "medium", "question": "Which of these is NOT a property of square numbers? 🚩", "options": {"A": "Can end with 4", "B": "Can be sum of odd numbers", "C": "Can be negative", "D": "Of even number is even"}, "correct_answer": "C"},
{"id": 35, "difficulty": "medium", "question": "The number of zeroes at the end of a perfect square is always _______. 🌀", "options": {"A": "Odd", "B": "Even", "C": "Prime", "D": "Any number"}, "correct_answer": "B"},
{"id": 36, "difficulty": "medium", "question": "A square number can never end with exactly _______ zeros. 🎯", "options": {"A": "One", "B": "Two", "C": "Three", "D": "Four"}, "correct_answer": "A"},
{"id": 37, "difficulty": "medium", "question": "If n² = 2025, then n = ? 🧩", "options": {"A": "44", "B": "45", "C": "46", "D": "47"}, "correct_answer": "B"},
{"id": 38, "difficulty": "medium", "question": "The sum of squares of first 3 natural numbers is? ➕", "options": {"A": "10", "B": "12", "C": "14", "D": "16"}, "correct_answer": "C"},
{"id": 39, "difficulty": "medium", "question": "Which of these is a triangular number and a square number? 🔺🔲", "options": {"A": "25", "B": "36", "C": "49", "D": "64"}, "correct_answer": "B"},
{"id": 40, "difficulty": "medium", "question": "The square of a proper fraction is _______ the original fraction. 📉", "options": {"A": "greater than", "B": "less than", "C": "equal to", "D": "double of"}, "correct_answer": "B"},
{"id": 41, "difficulty": "hard", "question": "Which of these numbers is a perfect square of a rational number? 0.04? 🧠", "options": {"A": "0.2", "B": "0.02", "C": "0.16", "D": "0.004"}, "correct_answer": "A"},
{"id": 42, "difficulty": "hard", "question": "If (x-1)(x+1) = 624, and x>0, find x. 🔐", "options": {"A": "24", "B": "25", "C": "26", "D": "27"}, "correct_answer": "B"},
{"id": 43, "difficulty": "hard", "question": "How many natural numbers n are there such that n² < 2000? 🌐", "options": {"A": "43", "B": "44", "C": "45", "D": "46"}, "correct_answer": "B"},
{"id": 44, "difficulty": "hard", "question": "The square of a number is 4 more than 3 times the number. The number could be? ⚡", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "D"},
{"id": 45, "difficulty": "hard", "question": "Which of these CANNOT be the unit digit of a perfect square? 🚨", "options": {"A": "2", "B": "5", "C": "6", "D": "9"}, "correct_answer": "A"},
{"id": 46, "difficulty": "hard", "question": "The product of four consecutive natural numbers plus 1 is always a _______. 🔄", "options": {"A": "Prime number", "B": "Even number", "C": "Perfect square", "D": "Multiple of 3"}, "correct_answer": "C"},
{"id": 47, "difficulty": "hard", "question": "Find the smallest number by which 180 must be multiplied to make it a perfect square. 📈", "options": {"A": "3", "B": "5", "C": "6", "D": "7"}, "correct_answer": "B"},
{"id": 48, "difficulty": "hard", "question": "A number has 14 zeros at the end. Can it be a perfect square? ❓", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Only if odd"}, "correct_answer": "B"},
{"id": 49, "difficulty": "hard", "question": "If √(1 + √(1 + √(1 + ...))) = x, then x² - x - 1 = 0. What is x? ∞", "options": {"A": "0.5", "B": "1", "C": "1.618...", "D": "2"}, "correct_answer": "C"},
{"id": 50, "difficulty": "hard", "question": "The sum of squares of first 10 natural numbers is? 🧮", "options": {"A": "285", "B": "365", "C": "385", "D": "405"}, "correct_answer": "C"},
{"id": 51, "difficulty": "hard", "question": "Which of these is a perfect square? 2025, 3025, 4225, 5625 🔢", "options": {"A": "All", "B": "3 of them", "C": "2 of them", "D": "1 of them"}, "correct_answer": "A"},
{"id": 52, "difficulty": "hard", "question": "A perfect square leaves a remainder of 0 or 1 when divided by? ➗", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
{"id": 53, "difficulty": "hard", "question": "If the square of a number is subtracted from 65, the result is the number itself. The number is? ➖", "options": {"A": "7", "B": "8", "C": "9", "D": "10"}, "correct_answer": "B"},
{"id": 54, "difficulty": "hard", "question": "How many perfect squares are divisors of 144? 📦", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
{"id": 55, "difficulty": "hard", "question": "The sum of first n odd numbers is 1225. n is? 🔶", "options": {"A": "35", "B": "45", "C": "55", "D": "65"}, "correct_answer": "A"},
{"id": 56, "difficulty": "hard", "question": "Which of these numbers is both a square and a cube? 🔲🔼", "options": {"A": "64", "B": "81", "C": "125", "D": "144"}, "correct_answer": "A"},
{"id": 57, "difficulty": "hard", "question": "The number of non-square numbers between 100² and 101² is? 🔢", "options": {"A": "200", "B": "201", "C": "202", "D": "203"}, "correct_answer": "A"},
{"id": 58, "difficulty": "hard", "question": "The unit digit of (173)² is? 🔟", "options": {"A": "1", "B": "3", "C": "7", "D": "9"}, "correct_answer": "D"},
{"id": 59, "difficulty": "hard", "question": "If a perfect square ends with 25, its square root ends with? 🎲", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "D"},
{"id": 60, "difficulty": "hard", "question": "A number is such that its square is equal to the number added to 56. Find the number. ➕", "options": {"A": "7", "B": "8", "C": "-7", "D": "Both B and C"}, "correct_answer": "D"}
]
}