{
  "title": "nth Term of GP - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "The nth term of GP is given by ______. 📝", "options": {"A": "a + (n-1)d", "B": "ar^(n-1)", "C": "a(rⁿ - 1)/(r-1)", "D": "a/(1-r)"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "In GP, a=3, r=2, 4th term = ? 🔢", "options": {"A": "12", "B": "18", "C": "24", "D": "48"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "Find the 5th term: 5, 10, 20, ... ⚡", "options": {"A": "40", "B": "60", "C": "80", "D": "100"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "If a=1, r=3, 6th term = ? 🧮", "options": {"A": "81", "B": "243", "C": "729", "D": "27"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "GP: 100, 50, 25,... 5th term? 📉", "options": {"A": "12.5", "B": "6.25", "C": "3.125", "D": "25"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Which term of 2, 6, 18, ... is 4374? 🤔", "options": {"A": "7th", "B": "8th", "C": "9th", "D": "10th"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "If 4th term = 32, r=2, find a. 🔍", "options": {"A": "2", "B": "4", "C": "8", "D": "16"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "a=27, r=1/3, 3rd term = ? 📊", "options": {"A": "3", "B": "1", "C": "9", "D": "1/3"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "5th term of GP is 48, r=2, find a. 🧩", "options": {"A": "3", "B": "6", "C": "12", "D": "24"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Find nth term if a=7, r=3. ✨", "options": {"A": "7×3ⁿ", "B": "7×3^(n-1)", "C": "3×7^(n-1)", "D": "7+3(n-1)"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "GP: -3, 6, -12, ... 6th term? ➖", "options": {"A": "48", "B": "-48", "C": "96", "D": "-96"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "If 2nd term=6, 3rd term=12, find a. 🔧", "options": {"A": "2", "B": "3", "C": "4", "D": "6"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "8th term of 1, 1/2, 1/4, ... = ? 📐", "options": {"A": "1/64", "B": "1/128", "C": "1/256", "D": "1/512"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "If nth term = 5×2^(n-1), 4th term = ? ⚡", "options": {"A": "20", "B": "40", "C": "80", "D": "160"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "GP with a=5, r=1, 10th term = ? 🔄", "options": {"A": "5", "B": "10", "C": "50", "D": "1"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Which term of 4, 12, 36,... is 2916? 🧐", "options": {"A": "6th", "B": "7th", "C": "8th", "D": "9th"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "If a=64, 3rd term=16, find r. 📏", "options": {"A": "1/4", "B": "1/2", "C": "2", "D": "4"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "GP: 0.2, 0.6, 1.8,... 5th term? 📈", "options": {"A": "4.8", "B": "16.2", "C": "5.4", "D": "14.4"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "Find a if 6th term=486, r=3. 🔥", "options": {"A": "2", "B": "3", "C": "6", "D": "9"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "a=1, r=-1, 100th term = ? ➖➕", "options": {"A": "1", "B": "-1", "C": "0", "D": "100"}, "correct_answer": "B"},
    {"id": 21, "difficulty": "medium", "question": "If 5th term of GP is 81 and 2nd term is 24, find r. 🤔", "options": {"A": "1.5", "B": "2", "C": "2.5", "D": "3"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "3rd term = 18, 6th term = 486, find a. 📊", "options": {"A": "2", "B": "3", "C": "6", "D": "9"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "The product of 3rd and 8th term of a GP is 576. If 5th term = 12, find r. ⚖️", "options": {"A": "2", "B": "1/2", "C": "√2", "D": "1/√2"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "If nth term = 160, a=5, r=2, find n. 🔍", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "GP has a=8, r=√2. Which term is 64? 📐", "options": {"A": "7th", "B": "8th", "C": "9th", "D": "10th"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "If 7th term is 1/64 and r=1/2, find a. 🧮", "options": {"A": "1", "B": "2", "C": "4", "D": "8"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Three numbers in GP: middle is 6, product is 216. Find others. 🧩", "options": {"A": "3,12", "B": "2,18", "C": "4,9", "D": "1,36"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "If pth term = q, qth term = p (p≠q), find (p+q)th term. 🔥", "options": {"A": "0", "B": "1", "C": "p+q", "D": "pq"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "a=3, r=4, find term number that equals 3072. 🚀", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "If 4th term = 54, 7th term = 1458, find 10th term. 📈", "options": {"A": "39366", "B": "4374", "C": "13122", "D": "2916"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "GP's nth term is 0.0016, a=25, r=0.2. Find n. 🔢", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "If 3rd term is 4 times 1st term, find r. ⚡", "options": {"A": "2", "B": "±2", "C": "4", "D": "±4"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "a=√5, r=√5, 5th term = ? 📐", "options": {"A": "25", "B": "5√5", "C": "125", "D": "25√5"}, "correct_answer": "D"},
    {"id": 34, "difficulty": "medium", "question": "Which term of GP 1/3, 1, 3, ... is 243? 🌟", "options": {"A": "6th", "B": "7th", "C": "8th", "D": "9th"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "If (m+n)th term = 256, a=1, r=2, and m×n=12, possible m,n? 🤯", "options": {"A": "3,4", "B": "2,6", "C": "1,12", "D": "All"}, "correct_answer": "D"},
    {"id": 36, "difficulty": "medium", "question": "GP with negative r: a=16, 3rd term = 4. Find 6th term. ➖", "options": {"A": "-0.5", "B": "0.5", "C": "-0.25", "D": "0.25"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "If 10th term is 1024 times 2nd term, r⁸ = ? 🧠", "options": {"A": "256", "B": "512", "C": "1024", "D": "2048"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "Find a GP where 4th term = 8 and 7th term = 64. 📊", "options": {"A": "1,2,4,...", "B": "2,4,8,...", "C": "0.5,1,2,...", "D": "4,8,16,..."}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "nth term of GP = 3×2^(n-1). What is r? 🔄", "options": {"A": "2", "B": "3", "C": "6", "D": "1.5"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "If a=1, r= -2, find 10th term. ❄️", "options": {"A": "512", "B": "-512", "C": "256", "D": "-256"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "hard", "question": "If pth, qth, rth terms of GP are x, y, z, then x^(q-r)×y^(r-p)×z^(p-q) = ? 🔥", "options": {"A": "0", "B": "1", "C": "xyz", "D": "a"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "In a GP, product of first 3 terms = 1, sum of their logs = 0. Find r. 📝", "options": {"A": "1", "B": "-1", "C": "±1", "D": "0"}, "correct_answer": "C"},
    {"id": 43, "difficulty": "hard", "question": "If Tₙ = 2ⁿ + 3ⁿ, is this a GP? 🤔", "options": {"A": "Yes", "B": "No", "C": "Only if n≥2", "D": "Can't say"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "hard", "question": "Sum of first two terms = 9, sum of 4th and 5th terms = 288. Find 10th term. 🧮", "options": {"A": 1536, "B": 3072, "C": 6144, "D": 12288}, "correct_answer": "C"},
    {"id": 45, "difficulty": "hard", "question": "If (k+2)th term is geometric mean of kth and (k+4)th term, find r². ⚖️", "options": {"A": "r", "B": "r²", "C": "1", "D": "2"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "GP with a and r positive. If T₇ = 8T₄, find r. 📊", "options": {"A": "2", "B": "√2", "C": "∛2", "D": "∜2"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "hard", "question": "If Tₙ = arⁿ⁻¹ and Tₘ = b, Tₖ = c, then r^(m-k) = ? 🔎", "options": {"A": "(b/a)^(1/(m-1))", "B": "(c/b)^(1/(k-m))", "C": "(b/c)^(1/(m-k))", "D": "a/b"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "hard", "question": "GP of even number of terms. Product of all terms = (middle term)^(number of terms). Find rⁿ. 🧩", "options": {"A": "1", "B": "0", "C": "r", "D": "a"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "If T₅ = 48, T₈ = 384, find T₁₂. 🚀", "options": {"A": "1536", "B": "2048", "C": "3072", "D": "4096"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "hard", "question": "Three numbers in GP with sum 14 and squares sum 84. Largest term? 🏆", "options": {"A": "8", "B": "12", "C": "16", "D": "4"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "If T₂ + T₅ = 36 and T₄ + T₇ = 144, find T₁₀. 🔥", "options": {"A": "512", "B": "1024", "C": "1536", "D": "2048"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "hard", "question": "GP where Tₙ₊₂ = Tₙ₊₁ + Tₙ for all n, a=1. Find r. 🔄", "options": {"A": "Golden ratio φ", "B": "1/φ", "C": "√φ", "D": "φ²"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "If log Tₙ = (n-1) log 2 + log 5, find T₆. 📝", "options": {"A": "80", "B": "160", "C": "320", "D": "640"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "hard", "question": "In GP, T₁ + T₂ = 12, T₃ + T₄ = 108. Find T₆. ⚡", "options": {"A": "324", "B": "486", "C": "648", "D": "972"}, "correct_answer": "D"},
    {"id": 55, "difficulty": "hard", "question": "If Tₘ = n, Tₙ = m, find T_(m+n). 🔢", "options": {"A": "0", "B": "1", "C": "a^(m+n-1)", "D": "r^(m+n-1)"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "hard", "question": "GP with r=2, T₁₀ = 1024a. Find a if T₅ = 32. 📐", "options": {"A": "1", "B": "2", "C": "4", "D": "8"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "hard", "question": "If T₃ = 12, T₆ = 96, find T₉/T₁₂. 🔁", "options": {"A": "1/8", "B": "1/4", "C": "1/2", "D": "1/16"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "Sum of n terms Sₙ = 2ⁿ - 1. Find Tₙ. 📚", "options": {"A": "2^(n-1)", "B": "2ⁿ", "C": "2ⁿ - 2^(n-1)", "D": "1"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "If Tₙ = 2Tₙ₋₁ + 1 and T₁=1, is it a GP? ❌", "options": {"A": "Yes", "B": "No", "C": "For n>2", "D": "If T₁=2"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "hard", "question": "In GP, Tₚ = x, T_q = y, T_ᵣ = z. Prove x^(q-r)×y^(r-p)×z^(p-q)=1. Which option confirms? ✅", "options": {"A": "It's always 0", "B": "It's always 1", "C": "It's a^3", "D": "It's r^(pqr)"}, "correct_answer": "B"}
  ]
}