{
  "title": "GP Definition (Geometric Progression) - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Which of the following is a GP? 📈", "options": {"A": "2, 4, 6, 8", "B": "3, 6, 12, 24", "C": "5, 10, 15, 20", "D": "1, 3, 6, 10"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "In GP, each term is obtained by multiplying the previous term by a fixed number called _____. 🔢", "options": {"A": "common difference", "B": "common ratio", "C": "common factor", "D": "common multiple"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "Find the common ratio of the GP: 5, 15, 45. ⚡", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "Which sequence has a constant ratio? 🤔", "options": {"A": "1, 4, 9, 16", "B": "2, 4, 8, 16", "C": "1, 3, 6, 9", "D": "10, 20, 30, 40"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "First term = 7, common ratio = 2. What's the 2nd term? 🧮", "options": {"A": "14", "B": "21", "C": "28", "D": "7"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Is 100, 50, 25, 12.5 a GP? 🧐", "options": {"A": "Yes", "B": "No", "C": "Can't say", "D": "Maybe"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "If first term = 3, common ratio = 1, what is the GP? 🔄", "options": {"A": "3, 6, 9", "B": "3, 3, 3", "C": "3, 4, 5", "D": "3, 0, 0"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "What is the common ratio of GP: 81, 27, 9? 📉", "options": {"A": "1/2", "B": "1/3", "C": "3", "D": "1/4"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "Which is NOT a property of GP? ❌", "options": {"A": "Constant ratio", "B": "Exponential growth", "C": "Linear increase", "D": "Can have fractional ratio"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "If ratio is negative, terms alternate in ______. ➖➕", "options": {"A": "value", "B": "size", "C": "sign", "D": "position"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "Find missing term in GP: 4, __, 36. (ratio > 0) 🔍", "options": {"A": "12", "B": "16", "C": "20", "D": "24"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "GP with ratio 0 after first term becomes: 😐", "options": {"A": "all same", "B": "all zero after first", "C": "increasing", "D": "undefined"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "Which term comes next in GP: 2, 6, 18, ___? ⏭️", "options": {"A": "36", "B": "54", "C": "72", "D": "24"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Is 0, 0, 0, ... a GP? 🤨", "options": {"A": "Yes", "B": "No", "C": "Only if ratio 0", "D": "No common ratio"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "GP's nth term formula uses ______. 📐", "options": {"A": "a + (n-1)d", "B": "ar^(n-1)", "C": "n/2[2a+(n-1)d]", "D": "a/(1-r)"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "If first term = 1, ratio = -1, first 4 terms are? 🔄", "options": {"A": "1, 1, 1, 1", "B": "1, -1, 1, -1", "C": "1, 0, -1, -2", "D": "1, 2, 3, 4"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Common ratio = 0.5, first term = 64. 3rd term? 📊", "options": {"A": "32", "B": "16", "C": "8", "D": "24"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "In GP, if ratio > 1, sequence ______. 📈", "options": {"A": "decreases", "B": "increases", "C": "constant", "D": "alternates"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "Identify GP: 🕵️", "options": {"A": "1, 1/2, 1/3, 1/4", "B": "1, 1/2, 1/4, 1/8", "C": "2, 4, 6, 8", "D": "3, 9, 18, 36"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "First term 9, ratio 1/3. 2nd term? 🧐", "options": {"A": "3", "B": "6", "C": "12", "D": "27"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "If 3, x, 27 are in GP, find x. 🤔", "options": {"A": "6", "B": "9", "C": "12", "D": "15"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "For GP: √2, 2, 2√2, ... ratio is? 📐", "options": {"A": "√2", "B": "2", "C": "1/√2", "D": "2√2"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Three numbers in GP have product 216 and sum 21. Middle term? 🧮", "options": {"A": "3", "B": "6", "C": "9", "D": "12"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "If a, b, c in GP, which is true? ✅", "options": {"A": "b = (a+c)/2", "B": "b² = ac", "C": "2b = a + c", "D": "b = √(a+c)"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "Find common ratio if 4th term = 32, 1st term = 4. 📏", "options": {"A": "2", "B": "3", "C": "√2", "D": "4"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "In a GP, a₅/a₂ = 27. What is r³? 🧠", "options": {"A": "3", "B": "9", "C": "27", "D": "81"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "If 2ᵏ, 4ᵏ⁻², 8ᵏ are in GP, find k. 🔢", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "After how many terms does GP 0.01, 0.1, 1, ... exceed 100? 🚀", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "Which term of GP 1/16, 1/8, 1/4, ... is 64? 🔎", "options": {"A": "8th", "B": "9th", "C": "10th", "D": "11th"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "If first term = -3, ratio = -2, find 5th term. ❄️", "options": {"A": "-48", "B": "48", "C": "-24", "D": "24"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Sum of first 2 terms = 12, product = 32. Find GP if terms positive. 🌟", "options": {"A": "4, 8, ...", "B": "8, 4, ...", "C": "2, 10, ...", "D": "6, 6, ..."}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "If x+2, 2x, 2x+3 are in GP, find x. 🧩", "options": {"A": "-1/2", "B": "2", "C": "4", "D": "6"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "GP's third term is square of first term, second term is 6. Find ratio. ⚖️", "options": {"A": "2", "B": "3", "C": "1.5", "D": "4"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "A bacteria doubles every hour. Starts with 100. After 5 hours? 🦠", "options": {"A": "1600", "B": "3200", "C": "6400", "D": "12800"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "If ratio of GP is 1, sequence is ______. 😶", "options": {"A": "constant", "B": "increasing", "C": "decreasing", "D": "alternating"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "How many terms of GP 3, 6, 12, ... are less than 200? 📊", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "GP with ratio between 0 and 1 is ______. 📉", "options": {"A": "increasing", "B": "decreasing", "C": "constant", "D": "alternating"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "If a GP's 1st and 4th terms are 5 and 40, find ratio. 🔧", "options": {"A": "2", "B": "√2", "C": "∛8", "D": "1.5"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "a, b, c in GP, log a, log b, log c are in ______. 📝", "options": {"A": "AP", "B": "GP", "C": "HP", "D": "None"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "If sum of first 2 terms = 9 and product = 18, find ratio >1. 📐", "options": {"A": "2", "B": "3", "C": "1.5", "D": "4"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "hard", "question": "If (p+q)ᵗʰ and (p-q)ᵗʰ terms of a GP are m and n, then (p)ᵗʰ term is? 🔥", "options": {"A": "√(mn)", "B": "mn", "C": "(m+n)/2", "D": "m/n"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "If each term of a GP is squared, new sequence is ______. 📚", "options": {"A": "AP", "B": "GP", "C": "HP", "D": "None"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "hard", "question": "Sum of infinite GP is 6, first term 2. Find ratio. ∞", "options": {"A": "1/3", "B": "2/3", "C": "1/2", "D": "3/4"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "hard", "question": "If a, b, c, d in GP then (a²+b²), (b²+c²), (c²+d²) are in? 🤯", "options": {"A": "AP", "B": "GP", "C": "HP", "D": "None"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "hard", "question": "GP's first term a, common ratio r. Sum of products of terms taken two at a time? 🧮", "options": {"A": "a²r/(1-r)²", "B": "a²r/(1-r²)", "C": "a²r(1+rⁿ⁻¹)/(1-r)", "D": "Complex"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "hard", "question": "If x, y, z in GP and aˣ = bʸ = cᶻ, then logₐb, log_b c, log_c a in? 📐", "options": {"A": "AP", "B": "GP", "C": "HP", "D": "None"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "hard", "question": "Three numbers in GP whose sum is 21 and product 216 are? 🧩", "options": {"A": "3,6,12", "B": "4,6,9", "C": "2,6,18", "D": "6,6,9"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "If Sₙ = 2ⁿ - 1, is the sequence a GP? 🧐", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Can’t determine"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "GP with common ratio r, sum to infinity S. Sum of cubes of terms = ? 🔷", "options": {"A": "S³/(1-2r³)", "B": "a³/(1-r³)", "C": "S³/(3-2r)", "D": "a³/(1-r)³"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "hard", "question": "If a, b, c in GP and a^{(1/x)} = b^{(1/y)} = c^{(1/z)}, then x, y, z in? 📏", "options": {"A": "AP", "B": "GP", "C": "HP", "D": "None"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "How many GPs with first term 2 and fourth term 128? ⚡", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "hard", "question": "If sum of first n terms of GP is 3(2ⁿ - 1), find 5th term. 🚀", "options": {"A": "48", "B": "96", "C": "24", "D": "12"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "GP's terms alternately positive and negative. Ratio is? 🔄", "options": {"A": ">0", "B": "<0", "C": "=0", "D": "=1"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "hard", "question": "If 1/(a+b), 1/(2b), 1/(b+c) in GP, then a, b, c in? 🔗", "options": {"A": "AP", "B": "GP", "C": "HP", "D": "None"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "Sum of three numbers in GP is 14, sum of squares 84. Largest number? 🏆", "options": {"A": "8", "B": "6", "C": "12", "D": "10"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "If Sₙ, S₂ₙ, S₃ₙ sums of GP, then Sₙ, S₂ₙ-Sₙ, S₃ₙ-S₂ₙ are in? 🔁", "options": {"A": "AP", "B": "GP", "C": "HP", "D": "None"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "hard", "question": "GP has all terms positive, ratio r. If every term is AM of next two, r = ? ⚖️", "options": {"A": "1", "B": "2", "C": "0.5", "D": "√2 - 1"}, "correct_answer": "D"},
    {"id": 58, "difficulty": "hard", "question": "If a, b, c in GP, log a - log 2b, log 2b - log 3c, log 3c - log a in? 📊", "options": {"A": "AP", "B": "GP", "C": "HP", "D": "None"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "hard", "question": "If x = 1 + a + a² + ... ∞ and y = 1 + b + b² + ... ∞, sum xy terms where |a|<1,|b|<1,|ab|<1? ∞", "options": {"A": "xy/(x+y-1)", "B": "xy/(1-ab)", "C": "(xy-1)/(x+y)", "D": "None"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "hard", "question": "If three distinct numbers a, b, c in GP and a+b+c = bx, then x cannot be? ❌", "options": {"A": "2", "B": "-2", "C": "3", "D": "4"}, "correct_answer": "B"}
  ]
}