{
  "title": "Euclid's Division Lemma - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Euclid's division lemma states: For positive integers a and b, there exist unique integers q and r such that:", "options": {"A": "a = bq + r, 0 ≤ r < b", "B": "a = b + rq, 0 ≤ r < b", "C": "a = qr + b, 0 ≤ r < b", "D": "b = aq + r, 0 ≤ r < a"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "For a = 17, b = 5, find q and r in a = bq + r.", "options": {"A": "q=3, r=2", "B": "q=2, r=7", "C": "q=4, r=-3", "D": "q=3, r=1"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "For a = 25, b = 4, find quotient and remainder.", "options": {"A": "q=5, r=5", "B": "q=6, r=1", "C": "q=7, r=-3", "D": "q=6, r=2"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "What is remainder when 46 divided by 7?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "For a = 30, b = 8, find q and r.", "options": {"A": "q=3, r=6", "B": "q=4, r=-2", "C": "q=3, r=5", "D": "q=4, r=3"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "What is quotient when 55 divided by 6?", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "For a = 42, b = 9, find remainder.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "Express 37 in form 5q + r.", "options": {"A": "5×7+2", "B": "5×8-3", "C": "5×7+3", "D": "5×8+1"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "For a = 19, b = 3, find q and r.", "options": {"A": "q=6, r=1", "B": "q=5, r=4", "C": "q=7, r=-2", "D": "q=6, r=2"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "What is remainder when 28 divided by 5?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "Express 52 as 6q + r.", "options": {"A": "6×8+4", "B": "6×9-2", "C": "6×8+5", "D": "6×9+1"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "For a = 64, b = 7, find quotient.", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "What is remainder when 73 divided by 8?", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Express 41 as 9q + r.", "options": {"A": "9×4+5", "B": "9×5-4", "C": "9×4+6", "D": "9×5+1"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "For a = 100, b = 15, find remainder.", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "What is quotient when 85 divided by 12?", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Express 67 as 11q + r.", "options": {"A": "11×6+1", "B": "11×5+12", "C": "11×6+2", "D": "11×7-4"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "For a = 38, b = 6, find q and r.", "options": {"A": "q=6, r=2", "B": "q=5, r=8", "C": "q=7, r=-4", "D": "q=6, r=3"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "What is remainder when 49 divided by 10?", "options": {"A": "7", "B": "8", "C": "9", "D": "0"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "Express 93 as 13q + r.", "options": {"A": "13×7+2", "B": "13×8-11", "C": "13×7+3", "D": "13×8+1"}, "correct_answer": "A"},
    
    {"id": 21, "difficulty": "medium", "question": "Use Euclid's lemma to find HCF of 56 and 72.", "options": {"A": "4", "B": "8", "C": "12", "D": "16"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "Find HCF of 135 and 225 using Euclid's algorithm.", "options": {"A": "15", "B": "25", "C": "35", "D": "45"}, "correct_answer": "D"},
    {"id": 23, "difficulty": "medium", "question": "Using Euclid's algorithm, find HCF of 196 and 38220.", "options": {"A": "14", "B": "28", "C": "56", "D": "98"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "Find HCF of 867 and 255 using Euclid's division lemma.", "options": {"A": "17", "B": "51", "C": "85", "D": "102"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "Use Euclid's algorithm to find HCF of 4052 and 12576.", "options": {"A": "2", "B": "4", "C": "8", "D": "16"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "Find HCF of 65 and 117 using Euclid's division algorithm.", "options": {"A": "1", "B": "13", "C": "26", "D": "39"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "Using Euclid's lemma, find HCF of 1620 and 1725.", "options": {"A": "15", "B": "30", "C": "45", "D": "60"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Find HCF of 96 and 404 by Euclid's algorithm.", "options": {"A": "2", "B": "4", "C": "8", "D": "16"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "Use Euclid's division lemma to find HCF of 240 and 228.", "options": {"A": "6", "B": "12", "C": "24", "D": "48"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "Find HCF of 336 and 54 using Euclid's algorithm.", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "Using Euclid's lemma, find HCF of 90 and 144.", "options": {"A": "6", "B": "9", "C": "12", "D": "18"}, "correct_answer": "D"},
    {"id": 32, "difficulty": "medium", "question": "Find HCF of 155 and 1385 using Euclid's division algorithm.", "options": {"A": "5", "B": "15", "C": "25", "D": "35"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Use Euclid's algorithm to find HCF of 504 and 980.", "options": {"A": "14", "B": "28", "C": "42", "D": "56"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "Find HCF of 300 and 550 using Euclid's lemma.", "options": {"A": "25", "B": "50", "C": "75", "D": "100"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "Using Euclid's division algorithm, find HCF of 180 and 252.", "options": {"A": "12", "B": "18", "C": "24", "D": "36"}, "correct_answer": "D"},
    {"id": 36, "difficulty": "medium", "question": "Find HCF of 1651 and 2032 using Euclid's algorithm.", "options": {"A": "13", "B": "17", "C": "19", "D": "23"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Use Euclid's lemma to find HCF of 420 and 130.", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "Find HCF of 75 and 243 using Euclid's division algorithm.", "options": {"A": "1", "B": "3", "C": "5", "D": "9"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "Using Euclid's algorithm, find HCF of 616 and 32.", "options": {"A": "4", "B": "8", "C": "12", "D": "16"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "Find HCF of 455 and 42 using Euclid's lemma.", "options": {"A": "7", "B": "14", "C": "21", "D": "28"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Use Euclid's division algorithm to find HCF of 210 and 55.", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Find HCF of 1260 and 7344 using Euclid's algorithm.", "options": {"A": "12", "B": "24", "C": "36", "D": "48"}, "correct_answer": "C"},
    {"id": 43, "difficulty": "medium", "question": "Using Euclid's lemma, find HCF of 1190 and 1445.", "options": {"A": "85", "B": "95", "C": "105", "D": "115"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Find HCF of 72 and 120 using Euclid's division algorithm.", "options": {"A": "8", "B": "12", "C": "18", "D": "24"}, "correct_answer": "D"},
    {"id": 45, "difficulty": "medium", "question": "Use Euclid's algorithm to find HCF of 100 and 190.", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "medium", "question": "Find HCF of 96 and 72 using Euclid's lemma.", "options": {"A": "12", "B": "18", "C": "24", "D": "36"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "medium", "question": "Using Euclid's division algorithm, find HCF of 280 and 124.", "options": {"A": "2", "B": "4", "C": "8", "D": "12"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "medium", "question": "Find HCF of 156 and 208 using Euclid's algorithm.", "options": {"A": "13", "B": "26", "C": "39", "D": "52"}, "correct_answer": "D"},
    {"id": 49, "difficulty": "medium", "question": "Use Euclid's lemma to find HCF of 180 and 324.", "options": {"A": "18", "B": "27", "C": "36", "D": "54"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "Find HCF of 225 and 450 using Euclid's division algorithm.", "options": {"A": "25", "B": "50", "C": "75", "D": "225"}, "correct_answer": "D"},
    {"id": 51, "difficulty": "medium", "question": "Using Euclid's algorithm, find HCF of 520 and 468.", "options": {"A": "4", "B": "8", "C": "12", "D": "16"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Find HCF of 84 and 105 using Euclid's lemma.", "options": {"A": "7", "B": "14", "C": "21", "D": "28"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "medium", "question": "Use Euclid's division algorithm to find HCF of 145 and 232.", "options": {"A": "29", "B": "31", "C": "37", "D": "41"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Find HCF of 330 and 198 using Euclid's algorithm.", "options": {"A": "22", "B": "33", "C": "44", "D": "66"}, "correct_answer": "D"},
    {"id": 55, "difficulty": "medium", "question": "Using Euclid's lemma, find HCF of 616 and 1300.", "options": {"A": "4", "B": "8", "C": "12", "D": "16"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Find HCF of 432 and 504 using Euclid's division algorithm.", "options": {"A": "36", "B": "48", "C": "54", "D": "72"}, "correct_answer": "D"},
    {"id": 57, "difficulty": "medium", "question": "Use Euclid's algorithm to find HCF of 850 and 680.", "options": {"A": "85", "B": "170", "C": "255", "D": "340"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "medium", "question": "Find HCF of 144 and 180 using Euclid's lemma.", "options": {"A": "12", "B": "18", "C": "24", "D": "36"}, "correct_answer": "D"},
    {"id": 59, "difficulty": "medium", "question": "Using Euclid's division algorithm, find HCF of 312 and 260.", "options": {"A": "13", "B": "26", "C": "39", "D": "52"}, "correct_answer": "D"},
    {"id": 60, "difficulty": "medium", "question": "Find HCF of 168 and 126 using Euclid's algorithm.", "options": {"A": "14", "B": "21", "C": "28", "D": "42"}, "correct_answer": "D"},
    {"id": 61, "difficulty": "medium", "question": "Use Euclid's lemma to find HCF of 315 and 525.", "options": {"A": "35", "B": "70", "C": "105", "D": "175"}, "correct_answer": "C"},
    {"id": 62, "difficulty": "medium", "question": "Find HCF of 170 and 238 using Euclid's division algorithm.", "options": {"A": "17", "B": "34", "C": "51", "D": "68"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "Using Euclid's algorithm, find HCF of 324 and 144.", "options": {"A": "12", "B": "18", "C": "24", "D": "36"}, "correct_answer": "D"},
    {"id": 64, "difficulty": "medium", "question": "Find HCF of 132 and 220 using Euclid's lemma.", "options": {"A": "11", "B": "22", "C": "33", "D": "44"}, "correct_answer": "D"},
    {"id": 65, "difficulty": "medium", "question": "Use Euclid's division algorithm to find HCF of 150 and 225.", "options": {"A": "25", "B": "50", "C": "75", "D": "100"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "Find HCF of 420 and 378 using Euclid's algorithm.", "options": {"A": "14", "B": "21", "C": "28", "D": "42"}, "correct_answer": "D"},
    {"id": 67, "difficulty": "medium", "question": "Using Euclid's lemma, find HCF of 728 and 900.", "options": {"A": "4", "B": "8", "C": "12", "D": "16"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "Find HCF of 175 and 245 using Euclid's division algorithm.", "options": {"A": "5", "B": "7", "C": "35", "D": "49"}, "correct_answer": "C"},
    {"id": 69, "difficulty": "medium", "question": "Use Euclid's algorithm to find HCF of 288 and 120.", "options": {"A": "12", "B": "18", "C": "24", "D": "36"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "Find HCF of 161 and 345 using Euclid's lemma.", "options": {"A": "1", "B": "7", "C": "23", "D": "46"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "Using Euclid's division algorithm, find HCF of 546 and 312.", "options": {"A": "6", "B": "12", "C": "18", "D": "24"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Find HCF of 270 and 450 using Euclid's algorithm.", "options": {"A": "30", "B": "45", "C": "60", "D": "90"}, "correct_answer": "D"},
    {"id": 73, "difficulty": "medium", "question": "Use Euclid's lemma to find HCF of 385 and 525.", "options": {"A": "5", "B": "7", "C": "35", "D": "70"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "Find HCF of 240 and 330 using Euclid's division algorithm.", "options": {"A": "10", "B": "20", "C": "30", "D": "40"}, "correct_answer": "C"},
    {"id": 75, "difficulty": "medium", "question": "Using Euclid's algorithm, find HCF of 588 and 980.", "options": {"A": "28", "B": "56", "C": "84", "D": "112"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Find HCF of 360 and 504 using Euclid's lemma.", "options": {"A": "36", "B": "48", "C": "60", "D": "72"}, "correct_answer": "D"},
    {"id": 77, "difficulty": "medium", "question": "Use Euclid's division algorithm to find HCF of 156 and 504.", "options": {"A": "12", "B": "24", "C": "36", "D": "48"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Find HCF of 210 and 350 using Euclid's algorithm.", "options": {"A": "10", "B": "20", "C": "30", "D": "70"}, "correct_answer": "D"},
    {"id": 79, "difficulty": "medium", "question": "Using Euclid's lemma, find HCF of 693 and 1071.", "options": {"A": "21", "B": "42", "C": "63", "D": "84"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "Find HCF of 272 and 425 using Euclid's division algorithm.", "options": {"A": "17", "B": "34", "C": "51", "D": "68"}, "correct_answer": "A"},
    
    {"id": 81, "difficulty": "hard", "question": "Use Euclid's algorithm to find HCF of 441, 567 and 693.", "options": {"A": "21", "B": "42", "C": "63", "D": "84"}, "correct_answer": "C"},
    {"id": 82, "difficulty": "hard", "question": "Find HCF of 336, 54 and 112 using Euclid's division lemma.", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "Using Euclid's algorithm, show that square of any positive integer is of form 3m or 3m+1.", "options": {"A": "Let a=3q,3q+1,3q+2", "B": "Let a=4q,4q+1,4q+2", "C": "Let a=5q,5q+1,5q+2", "D": "Let a=2q,2q+1"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Show that cube of any positive integer is of form 9m, 9m+1 or 9m+8.", "options": {"A": "Let a=3q,3q+1,3q+2", "B": "Let a=4q,4q+1,4q+2", "C": "Let a=5q,5q+1,5q+2", "D": "Let a=2q,2q+1"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "Use Euclid's lemma to show that any positive odd integer is of form 6q+1, 6q+3 or 6q+5.", "options": {"A": "a=6q+r, r=0,1,2,3,4,5", "B": "a=4q+r, r=0,1,2,3", "C": "a=3q+r, r=0,1,2", "D": "a=2q+r, r=0,1"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "Show that square of any positive integer cannot be of form 3m+2.", "options": {"A": "a=3q,3q+1,3q+2", "B": "a=4q,4q+1,4q+2", "C": "a=5q,5q+1,5q+2", "D": "Let a=2q,2q+1"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Use Euclid's division lemma to show that cube of any positive integer is of form 7m or 7m±1.", "options": {"A": "a=7q+r, r=0 to 6", "B": "a=6q+r, r=0 to 5", "C": "a=5q+r, r=0 to 4", "D": "a=4q+r, r=0 to 3"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "Find HCF of 180, 252 and 324 using Euclid's algorithm.", "options": {"A": "12", "B": "18", "C": "24", "D": "36"}, "correct_answer": "D"},
    {"id": 89, "difficulty": "hard", "question": "Show that any positive even integer is of form 4q or 4q+2.", "options": {"A": "a=4q+r, r=0,1,2,3", "B": "a=3q+r, r=0,1,2", "C": "a=6q+r, r=0,1,2,3,4,5", "D": "a=2q+r, r=0,1"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "Using Euclid's lemma, show that square of any integer is of form 4q or 4q+1.", "options": {"A": "a=4q,4q+1,4q+2,4q+3", "B": "a=3q,3q+1,3q+2", "C": "a=5q,5q+1,5q+2,5q+3,5q+4", "D": "a=2q,2q+1"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Find HCF of 240, 336 and 96 using Euclid's division algorithm.", "options": {"A": "12", "B": "24", "C": "36", "D": "48"}, "correct_answer": "D"},
    {"id": 92, "difficulty": "hard", "question": "Show that product of three consecutive positive integers is divisible by 6.", "options": {"A": "Use form 6q,6q+1,...,6q+5", "B": "Use form 3q,3q+1,3q+2", "C": "Use form 2q,2q+1", "D": "Use Euclid directly"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Use Euclid's algorithm to find HCF of 210, 315 and 147.", "options": {"A": "7", "B": "14", "C": "21", "D": "28"}, "correct_answer": "C"},
    {"id": 94, "difficulty": "hard", "question": "Show that square of any positive integer is of form 5q, 5q+1 or 5q+4.", "options": {"A": "a=5q,5q+1,5q+2,5q+3,5q+4", "B": "a=4q,4q+1,4q+2,4q+3", "C": "a=3q,3q+1,3q+2", "D": "a=2q,2q+1"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Find HCF of 1260, 1440 and 1620 using Euclid's division lemma.", "options": {"A": "60", "B": "90", "C": "120", "D": "180"}, "correct_answer": "D"},
    {"id": 96, "difficulty": "hard", "question": "Show that cube of any positive integer is of form 4m or 4m+1 or 4m+3.", "options": {"A": "a=4q,4q+1,4q+2,4q+3", "B": "a=3q,3q+1,3q+2", "C": "a=5q,5q+1,5q+2,5q+3,5q+4", "D": "a=2q,2q+1"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "Use Euclid's algorithm to find HCF of 140, 196 and 308.", "options": {"A": "14", "B": "28", "C": "42", "D": "56"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "Show that any positive integer is of form 3q, 3q+1 or 3q+2.", "options": {"A": "By Euclid's lemma with b=3", "B": "By Euclid's lemma with b=4", "C": "By Euclid's lemma with b=5", "D": "By Euclid's lemma with b=2"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "Find HCF of 360, 504 and 672 using Euclid's division algorithm.", "options": {"A": "12", "B": "24", "C": "36", "D": "48"}, "correct_answer": "B"},
    {"id": 100, "difficulty": "hard", "question": "Show that square of any odd integer is of form 8m+1.", "options": {"A": "Let odd = 2q+1, square it", "B": "Let odd = 3q+1, square it", "C": "Let odd = 4q+1, square it", "D": "Let odd = 5q+1, square it"}, "correct_answer": "A"}
  ]
}