{
  "title": "Prime Factorisation - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Prime factors of 12:", "options": {"A": "2×6", "B": "3×4", "C": "2²×3", "D": "2×2×2×3"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "Prime factors of 18:", "options": {"A": "2×9", "B": "3×6", "C": "2×3²", "D": "2×2×3×3"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "Prime factors of 24:", "options": {"A": "3×8", "B": "4×6", "C": "2³×3", "D": "2×2×2×2×3"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "Prime factors of 30:", "options": {"A": "3×10", "B": "5×6", "C": "2×3×5", "D": "2×2×3×5"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "Prime factors of 36:", "options": {"A": "4×9", "B": "6×6", "C": "2²×3²", "D": "2×2×3×3×3"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "Prime factors of 42:", "options": {"A": "6×7", "B": "3×14", "C": "2×3×7", "D": "2×2×3×7"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "Prime factors of 48:", "options": {"A": "6×8", "B": "4×12", "C": "2⁴×3", "D": "2×2×2×2×2×3"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "Prime factors of 54:", "options": {"A": "6×9", "B": "3×18", "C": "2×3³", "D": "2×2×3×3×3"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "Prime factors of 60:", "options": {"A": "6×10", "B": "4×15", "C": "2²×3×5", "D": "2×2×2×3×5"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "Prime factors of 72:", "options": {"A": "8×9", "B": "6×12", "C": "2³×3²", "D": "2×2×2×3×3×3"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "Prime factors of 84:", "options": {"A": "7×12", "B": "6×14", "C": "2²×3×7", "D": "2×2×3×7×7"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "Prime factors of 90:", "options": {"A": "9×10", "B": "6×15", "C": "2×3²×5", "D": "2×2×3×3×5"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "Prime factors of 100:", "options": {"A": "10×10", "B": "4×25", "C": "2²×5²", "D": "2×2×5×5×5"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "Prime factors of 108:", "options": {"A": "9×12", "B": "6×18", "C": "2²×3³", "D": "2×2×3×3×3×3"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "Prime factors of 120:", "options": {"A": "10×12", "B": "8×15", "C": "2³×3×5", "D": "2×2×2×3×5×5"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "Prime factors of 144:", "options": {"A": "12×12", "B": "9×16", "C": "2⁴×3²", "D": "2×2×2×2×3×3×3"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "Prime factors of 150:", "options": {"A": "10×15", "B": "6×25", "C": "2×3×5²", "D": "2×2×3×5×5"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "Prime factors of 180:", "options": {"A": "12×15", "B": "9×20", "C": "2²×3²×5", "D": "2×2×3×3×5×5"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "Prime factors of 210:", "options": {"A": "10×21", "B": "14×15", "C": "2×3×5×7", "D": "2×2×3×5×7"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "Prime factors of 240:", "options": {"A": "12×20", "B": "15×16", "C": "2⁴×3×5", "D": "2×2×2×2×3×5×5"}, "correct_answer": "C"},
    
    {"id": 21, "difficulty": "medium", "question": "Find prime factors of 360.", "options": {"A": "2³×3²×5", "B": "2²×3³×5", "C": "2⁴×3²×5", "D": "2³×3×5²"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Find prime factors of 420.", "options": {"A": "2²×3×5×7", "B": "2×3²×5×7", "C": "2²×3×7²", "D": "2³×3×5×7"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Find prime factors of 504.", "options": {"A": "2³×3²×7", "B": "2²×3³×7", "C": "2³×3×7²", "D": "2⁴×3²×7"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Find prime factors of 540.", "options": {"A": "2²×3³×5", "B": "2³×3³×5", "C": "2²×3²×5²", "D": "2³×3²×5"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Find prime factors of 600.", "options": {"A": "2³×3×5²", "B": "2²×3×5³", "C": "2³×3²×5²", "D": "2⁴×3×5²"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Find prime factors of 630.", "options": {"A": "2×3²×5×7", "B": "2²×3²×5×7", "C": "2×3×5²×7", "D": "2×3×5×7²"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Find prime factors of 720.", "options": {"A": "2⁴×3²×5", "B": "2³×3³×5", "C": "2⁴×3×5²", "D": "2³×3²×5²"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Find prime factors of 840.", "options": {"A": "2³×3×5×7", "B": "2²×3×5×7²", "C": "2³×3²×5×7", "D": "2²×3×5²×7"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Find prime factors of 900.", "options": {"A": "2²×3²×5²", "B": "2³×3²×5²", "C": "2²×3³×5²", "D": "2²×3²×5³"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Find prime factors of 960.", "options": {"A": "2⁶×3×5", "B": "2⁵×3²×5", "C": "2⁶×3²×5", "D": "2⁵×3×5²"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Find prime factors of 1008.", "options": {"A": "2⁴×3²×7", "B": "2³×3²×7²", "C": "2⁴×3³×7", "D": "2³×3³×7"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Find prime factors of 1080.", "options": {"A": "2³×3³×5", "B": "2⁴×3³×5", "C": "2³×3²×5²", "D": "2⁴×3²×5"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Find prime factors of 1152.", "options": {"A": "2⁷×3²", "B": "2⁶×3³", "C": "2⁷×3³", "D": "2⁸×3²"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Find prime factors of 1260.", "options": {"A": "2²×3²×5×7", "B": "2³×3²×5×7", "C": "2²×3³×5×7", "D": "2²×3²×5²×7"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Find prime factors of 1320.", "options": {"A": "2³×3×5×11", "B": "2²×3×5×11²", "C": "2³×3²×5×11", "D": "2²×3×5²×11"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Find prime factors of 1440.", "options": {"A": "2⁵×3²×5", "B": "2⁶×3²×5", "C": "2⁵×3³×5", "D": "2⁵×3²×5²"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Find prime factors of 1512.", "options": {"A": "2³×3³×7", "B": "2⁴×3³×7", "C": "2³×3²×7²", "D": "2³×3³×7²"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Find prime factors of 1680.", "options": {"A": "2⁴×3×5×7", "B": "2³×3×5×7²", "C": "2⁴×3²×5×7", "D": "2³×3×5²×7"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Find prime factors of 1800.", "options": {"A": "2³×3²×5²", "B": "2⁴×3²×5²", "C": "2³×3³×5²", "D": "2³×3²×5³"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Find prime factors of 1980.", "options": {"A": "2²×3²×5×11", "B": "2³×3²×5×11", "C": "2²×3³×5×11", "D": "2²×3²×5²×11"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Find prime factors of 2100.", "options": {"A": "2²×3×5²×7", "B": "2³×3×5²×7", "C": "2²×3²×5²×7", "D": "2²×3×5×7²"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Find prime factors of 2310.", "options": {"A": "2×3×5×7×11", "B": "2²×3×5×7×11", "C": "2×3²×5×7×11", "D": "2×3×5²×7×11"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Find prime factors of 2520.", "options": {"A": "2³×3²×5×7", "B": "2⁴×3²×5×7", "C": "2³×3³×5×7", "D": "2³×3²×5²×7"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Find prime factors of 2772.", "options": {"A": "2²×3²×7×11", "B": "2³×3²×7×11", "C": "2²×3³×7×11", "D": "2²×3²×7×11²"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Find prime factors of 3000.", "options": {"A": "2³×3×5³", "B": "2⁴×3×5³", "C": "2³×3²×5³", "D": "2³×3×5⁴"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Find prime factors of 3150.", "options": {"A": "2×3²×5²×7", "B": "2²×3²×5²×7", "C": "2×3³×5²×7", "D": "2×3²×5³×7"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Find prime factors of 3360.", "options": {"A": "2⁵×3×5×7", "B": "2⁶×3×5×7", "C": "2⁵×3²×5×7", "D": "2⁵×3×5²×7"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Find prime factors of 3600.", "options": {"A": "2⁴×3²×5²", "B": "2⁵×3²×5²", "C": "2⁴×3³×5²", "D": "2⁴×3²×5³"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Find prime factors of 3780.", "options": {"A": "2²×3³×5×7", "B": "2³×3³×5×7", "C": "2²×3⁴×5×7", "D": "2²×3³×5²×7"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Find prime factors of 3960.", "options": {"A": "2³×3²×5×11", "B": "2⁴×3²×5×11", "C": "2³×3³×5×11", "D": "2³×3²×5²×11"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Find prime factors of 4200.", "options": {"A": "2³×3×5²×7", "B": "2⁴×3×5²×7", "C": "2³×3²×5²×7", "D": "2³×3×5³×7"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Express 15625 as power of prime.", "options": {"A": "5⁶", "B": "5⁵", "C": "5⁷", "D": "5⁸"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Express 4096 as power of prime.", "options": {"A": "2¹²", "B": "2¹³", "C": "2¹⁴", "D": "2¹⁵"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "Express 6561 as power of prime.", "options": {"A": "3⁸", "B": "3⁹", "C": "3¹⁰", "D": "3¹¹"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Express 7776 as power of prime.", "options": {"A": "2⁵×3⁵", "B": "2⁴×3⁵", "C": "2⁵×3⁶", "D": "2⁶×3⁵"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "Express 10000 as power of prime.", "options": {"A": "2⁴×5⁴", "B": "2³×5⁴", "C": "2⁴×5⁵", "D": "2⁵×5⁴"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Express 32768 as power of prime.", "options": {"A": "2¹⁵", "B": "2¹⁶", "C": "2¹⁷", "D": "2¹⁸"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Express 59049 as power of prime.", "options": {"A": "3¹⁰", "B": "3¹¹", "C": "3¹²", "D": "3¹³"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "Express 1048576 as power of prime.", "options": {"A": "2²⁰", "B": "2¹⁹", "C": "2²¹", "D": "2²²"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Express 4782969 as power of prime.", "options": {"A": "3¹⁴", "B": "3¹³", "C": "3¹⁵", "D": "3¹⁶"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "Express 16777216 as power of prime.", "options": {"A": "2²⁴", "B": "2²³", "C": "2²⁵", "D": "2²⁶"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "Find total number of factors of 36.", "options": {"A": "7", "B": "8", "C": "9", "D": "10"}, "correct_answer": "C"},
    {"id": 62, "difficulty": "medium", "question": "Find total number of factors of 48.", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "C"},
    {"id": 63, "difficulty": "medium", "question": "Find total number of factors of 72.", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "Find total number of factors of 100.", "options": {"A": "7", "B": "8", "C": "9", "D": "10"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "Find total number of factors of 144.", "options": {"A": "13", "B": "14", "C": "15", "D": "16"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "Find total number of factors of 180.", "options": {"A": "16", "B": "17", "C": "18", "D": "19"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "Find total number of factors of 240.", "options": {"A": "18", "B": "19", "C": "20", "D": "21"}, "correct_answer": "C"},
    {"id": 68, "difficulty": "medium", "question": "Find total number of factors of 360.", "options": {"A": "22", "B": "23", "C": "24", "D": "25"}, "correct_answer": "C"},
    {"id": 69, "difficulty": "medium", "question": "Find total number of factors of 420.", "options": {"A": "22", "B": "23", "C": "24", "D": "25"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "Find total number of factors of 504.", "options": {"A": "22", "B": "23", "C": "24", "D": "25"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "Find number of even factors of 72.", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "medium", "question": "Find number of odd factors of 90.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "Find number of perfect square factors of 144.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "Find sum of all factors of 28.", "options": {"A": "50", "B": "54", "C": "56", "D": "60"}, "correct_answer": "C"},
    {"id": 75, "difficulty": "medium", "question": "Find sum of all factors of 36.", "options": {"A": "80", "B": "85", "C": "90", "D": "95"}, "correct_answer": "C"},
    {"id": 76, "difficulty": "medium", "question": "Find sum of all factors of 48.", "options": {"A": "120", "B": "124", "C": "128", "D": "132"}, "correct_answer": "B"},
    {"id": 77, "difficulty": "medium", "question": "Find product of all factors of 12.", "options": {"A": "144", "B": "1728", "C": "20736", "D": "248832"}, "correct_answer": "B"},
    {"id": 78, "difficulty": "medium", "question": "Find product of all factors of 18.", "options": {"A": "324", "B": "5832", "C": "104976", "D": "1889568"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "Find product of all factors of 24.", "options": {"A": "576", "B": "13824", "C": "331776", "D": "7962624"}, "correct_answer": "B"},
    {"id": 80, "difficulty": "medium", "question": "Find product of all factors of 30.", "options": {"A": "900", "B": "27000", "C": "810000", "D": "24300000"}, "correct_answer": "B"},
    
    {"id": 81, "difficulty": "hard", "question": "Find number of zeros at end of 100! (100 factorial).", "options": {"A": "20", "B": "21", "C": "22", "D": "24"}, "correct_answer": "D"},
    {"id": 82, "difficulty": "hard", "question": "Find number of zeros at end of 50!.", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "C"},
    {"id": 83, "difficulty": "hard", "question": "Find number of zeros at end of 25!.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 84, "difficulty": "hard", "question": "Find exponent of 5 in 100!.", "options": {"A": "20", "B": "21", "C": "22", "D": "24"}, "correct_answer": "D"},
    {"id": 85, "difficulty": "hard", "question": "Find exponent of 2 in 100!.", "options": {"A": "95", "B": "97", "C": "99", "D": "101"}, "correct_answer": "B"},
    {"id": 86, "difficulty": "hard", "question": "Find exponent of 3 in 50!.", "options": {"A": "20", "B": "21", "C": "22", "D": "23"}, "correct_answer": "C"},
    {"id": 87, "difficulty": "hard", "question": "Find exponent of 7 in 100!.", "options": {"A": "14", "B": "15", "C": "16", "D": "17"}, "correct_answer": "C"},
    {"id": 88, "difficulty": "hard", "question": "Find exponent of 11 in 100!.", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "Find exponent of 13 in 100!.", "options": {"A": "7", "B": "8", "C": "9", "D": "10"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "Find exponent of 2 in 75!.", "options": {"A": "68", "B": "70", "C": "72", "D": "74"}, "correct_answer": "B"},
    {"id": 91, "difficulty": "hard", "question": "If N = 2³×3²×5, find total factors of N².", "options": {"A": "35", "B": "42", "C": "49", "D": "56"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "If N = 2⁴×3³×5², find total factors of N².", "options": {"A": "125", "B": "150", "C": "175", "D": "200"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "If N = 2⁵×3⁴×5³, find total factors of N³.", "options": {"A": "440", "B": "460", "C": "480", "D": "500"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "Find smallest number with 15 factors.", "options": {"A": "144", "B": "216", "C": "240", "D": "256"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Find smallest number with 18 factors.", "options": {"A": "180", "B": "240", "C": "252", "D": "288"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "Find smallest number with 20 factors.", "options": {"A": "240", "B": "288", "C": "300", "D": "336"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "Find smallest number with 24 factors.", "options": {"A": "360", "B": "420", "C": "480", "D": "504"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "Find smallest number with 30 factors.", "options": {"A": "720", "B": "840", "C": "960", "D": "1080"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "If 2ᵃ×5ᵇ has 12 factors and a+b=7, find a and b.", "options": {"A": "a=3,b=4", "B": "a=4,b=3", "C": "a=5,b=2", "D": "a=2,b=5"}, "correct_answer": "B"},
    {"id": 100, "difficulty": "hard", "question": "If 2ᵃ×3ᵇ has 20 factors and a+b=9, find a and b.", "options": {"A": "a=4,b=5", "B": "a=5,b=4", "C": "a=6,b=3", "D": "a=3,b=6"}, "correct_answer": "A"}
  ]
}