{
  "title": "Sum of n terms of GP - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Formula for sum of n terms of GP when r≠1 is ______. 📝", "options": {"A": "a(1-rⁿ)/(1-r)", "B": "n/2[2a+(n-1)d]", "C": "a/(1-r)", "D": "arⁿ⁻¹"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "Find sum of first 4 terms: 3, 6, 12, ... 🧮", "options": {"A": "30", "B": "45", "C": "48", "D": "56"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "If a=2, r=3, n=4, Sₙ = ? 🔢", "options": {"A": "80", "B": "81", "C": "82", "D": "83"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Sum of first 5 terms of 1, 1/2, 1/4, ... = ? 📉", "options": {"A": "1.9375", "B": "1.96875", "C": "1.75", "D": "1.875"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "For GP with r=1, Sₙ = ______. 🔄", "options": {"A": "a(1-rⁿ)/(1-r)", "B": "na", "C": "a/(1-r)", "D": "0"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "If a=5, r=2, n=3, sum = ? ⚡", "options": {"A": "30", "B": "35", "C": "40", "D": "45"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "Sum of first 3 terms: 10, 20, 40, ... = ? ✨", "options": {"A": "60", "B": "70", "C": "80", "D": "90"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "a=1, r= -1, n=10, S₁₀ = ? ➖➕", "options": {"A": "0", "B": "1", "C": "10", "D": "-1"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Find S₄ for 4, 8, 16, ... 📊", "options": {"A": "48", "B": "60", "C": "64", "D": "72"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "If S₃=21, a=3, r=2, check if correct? ✅", "options": {"A": "Yes", "B": "No", "C": "Can't say", "D": "Maybe"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Sum of first 2 terms of GP with a=7, r=3 = ? 🧩", "options": {"A": "21", "B": "28", "C": "35", "D": "42"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "For 1, 3, 9, ... sum of first 3 terms? 🔥", "options": {"A": "12", "B": "13", "C": "14", "D": "15"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "a=16, r=0.5, n=5, S₅ = ? 📐", "options": {"A": "30", "B": "31", "C": "31.5", "D": "32"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Sum of first n terms when r=1 is ______. 😶", "options": {"A": "a(1-rⁿ)/(1-r)", "B": "a/(1-r)", "C": "na", "D": "arⁿ⁻¹"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "S₃=38, a=2, r=3? Check: 2+6+18=26? ❌", "options": {"A": "True", "B": "False", "C": "Maybe", "D": "None"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "First term=9, r=1/3, sum of first 3 terms? 📉", "options": {"A": "12", "B": "12.33", "C": "13", "D": "13.33"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "If sum of first 2 terms = 12 and a=4, find r. 🔍", "options": {"A": "0.5", "B": "1", "C": "1.5", "D": "2"}, "correct_answer": "D"},
    {"id": 18, "difficulty": "easy", "question": "GP: 5, 15, 45, ... S₄ = ? ⚡", "options": {"A": "200", "B": "210", "C": "220", "D": "230"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Sum formula when |r|<1 and n→∞ becomes ______. ∞", "options": {"A": "a(1-rⁿ)/(1-r)", "B": "a/(1-r)", "C": "na", "D": "0"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "a=1, r=2, S₅ = ? 🧮", "options": {"A": "30", "B": "31", "C": "32", "D": "33"}, "correct_answer": "B"},
    {"id": 21, "difficulty": "medium", "question": "If S₄=30, a=2, find r if r>1. 🤔", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Sum of first 6 terms of GP: 1, -2, 4, -8, ... = ? ➖", "options": {"A": "-21", "B": "21", "C": "63", "D": "-63"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "S₅=93, a=3, r=2. Is this correct? Check: 3+6+12+24+48=93? ✅", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Can't say"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "If Sₙ=63, a=1, r=2, find n. 🔢", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "Sum of first 10 terms of 0.1, 0.01, 0.001, ... ≈ ? 📊", "options": {"A": "0.111", "B": "0.111111111", "C": "0.1111111111", "D": "0.111111"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "For GP: √3, 3, 3√3, ... S₄ = ? 📐", "options": {"A": "12+6√3", "B": "12√3", "C": "6(√3+1)", "D": "3(√3+3)"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "If S₄=80, r=3, find a. 🔍", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Sum of first n terms of GP where a=5, r=1/5? 📉", "options": {"A": "5(1-(1/5)ⁿ)/(4/5)", "B": "5(1+(1/5)ⁿ)/(6/5)", "C": "5(1-(1/5)ⁿ)/(6/5)", "D": "25(1-(1/5)ⁿ)/4"}, "correct_answer": "D"},
    {"id": 29, "difficulty": "medium", "question": "S₃=21, S₆=189, find r. ⚖️", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "If sum of first 3 terms = 13/9, a=1, r=1/3, verify. ✅", "options": {"A": "True", "B": "False", "C": "Maybe", "D": "None"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "GP: 2, 6, 18,... sum till 5 terms = ? 🚀", "options": {"A": "242", "B": "243", "C": "244", "D": "245"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "a= -3, r= -2, S₅ = ? ➖❄️", "options": {"A": "-33", "B": "33", "C": "-99", "D": "99"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Sum of first 8 terms of 1, 1/2, 1/4, ... ≈ ? 📈", "options": {"A": "1.996", "B": "1.998", "C": "1.992", "D": "1.984"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "If S₂=12, S₄=60, find a and r (r>1). 🔧", "options": {"A": "a=3, r=2", "B": "a=4, r=2", "C": "a=6, r=2", "D": "a=3, r=3"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "GP with r= -1, n=9, a=10, S₉ = ? 🔄", "options": {"A": "10", "B": "0", "C": "90", "D": "-10"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Sum of first 7 terms: 5, 10, 20, ... = ? ✨", "options": {"A": "630", "B": "635", "C": "640", "D": "645"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "S₃=38, a=2, find r if r>0. 📏", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "If a=1, r=0.5, S₆ = ? 🧮", "options": {"A": "1.96875", "B": "1.984375", "C": "1.9921875", "D": "1.99609375"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "S₁₀ of GP: 3, 6, 12,... = ? 🔥", "options": {"A": "3069", "B": "3072", "C": "3075", "D": "3078"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "For what n does Sₙ of 2, 4, 8, ... exceed 1000? 📊", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "hard", "question": "If Sₙ, S₂ₙ, S₃ₙ are sums of n, 2n, 3n terms of GP, then (S₂ₙ - Sₙ)² = ? 🧠", "options": {"A": "Sₙ(S₃ₙ - S₂ₙ)", "B": "Sₙ(S₂ₙ - Sₙ)", "C": "S₃ₙ - Sₙ", "D": "Sₙ×S₂ₙ"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "Sum of first n terms of GP is 255. If a=1, r=2, find n. 🔍", "options": {"A": "7", "B": "8", "C": "9", "D": "10"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "hard", "question": "If Sₘ = n and Sₙ = m for a GP (m≠n), find Sₘ₊ₙ. 🔥", "options": {"A": "0", "B": "1", "C": "-(m+n)", "D": "m+n"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "hard", "question": "GP: a=7, r=3. How many terms to exceed sum 10000? 🚀", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "hard", "question": "Sum of first 10 terms = 1023, first term=1. Find r. 📐", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "If S₆/S₃ = 9, find r². ⚡", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "hard", "question": "GP with r=2, S₅=93. Find a. 🧩", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "hard", "question": "Three numbers in GP with sum 14 and product 64. Find sum of their squares. 📊", "options": {"A": "84", "B": "96", "C": "108", "D": "120"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "If S₁+S₂+S₃+...+Sₙ = (Sₙ)(k), find k in terms of r. 🔢", "options": {"A": "r/(r-1)", "B": "(rⁿ-1)/(r-1)", "C": "1/(1-r)", "D": "n"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "Sum of infinite GP is 6, sum of first 2 terms is 9/2. Find a. ∞", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "If Sₙ = 3(2ⁿ - 1), find Tₙ. 📝", "options": {"A": "3×2ⁿ⁻¹", "B": "3×2ⁿ", "C": "6ⁿ⁻¹", "D": "2ⁿ⁺¹"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "For GP, Sₘ = Sₙ (m≠n). Then Sₘ₊ₙ = ? 🤯", "options": {"A": "0", "B": "a", "C": "1", "D": "r^(m+n)"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "Sum of first n terms: Sₙ = 4ⁿ - 1. Is it GP? 🔍", "options": {"A": "Yes", "B": "No", "C": "Only if n even", "D": "Can't say"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "If S₅ = 2111, a=1, r= -2? Check. ❌", "options": {"A": "True", "B": "False", "C": "Maybe", "D": "None"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "hard", "question": "GP: 5, 10, 20,... find n if Sₙ = 635. 🧮", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "hard", "question": "S₁₀ of GP where a=2, r=√2? 📐", "options": {"A": "2(√2¹⁰ - 1)/(√2 - 1)", "B": "2(1 - √2¹⁰)/(1-√2)", "C": "2(√2¹⁰ - 1)/(√2 + 1)", "D": "2(√2⁹ - 1)/(√2 - 1)"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "If Sₙ = rSₙ₋₁ + a, find r in terms of a, Sₙ. 🔥", "options": {"A": "(Sₙ - a)/Sₙ₋₁", "B": "Sₙ/Sₙ₋₁", "C": "a/(Sₙ - Sₙ₋₁)", "D": "(Sₙ - Sₙ₋₁)/a"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "Sum of first 3 terms = 13, product = 27. Find GP if terms positive. 🌟", "options": {"A": "1, 3, 9", "B": "3, 3, 3", "C": "9, 3, 1", "D": "1, 9, 81"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "If sum of first p terms = sum of first q terms (p≠q), then Sₚ₊q = ? ⚖️", "options": {"A": "0", "B": "a", "C": "p+q", "D": "apq"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "GP with r=1/2, Sₙ=31.9375, a=16. Find n. 🔟", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "C"}
  ]
}