{"title": "Sum of n terms (Arithmetic Progression) - Grade 10 ICSE", "total_questions": 60, "questions": [{"id": 1, "difficulty": "easy", "question": "Sum of first n terms of AP is given by: 📝", "options": {"A": "n/2[2a+(n-1)d]", "B": "n/2[2a+nd]", "C": "n[2a+(n-1)d]", "D": "n/2[a+(n-1)d]"}, "correct_answer": "A"}, {"id": 2, "difficulty": "easy", "question": "Find sum of first 10 natural numbers. 🔢", "options": {"A": "55", "B": "50", "C": "60", "D": "45"}, "correct_answer": "A"}, {"id": 3, "difficulty": "easy", "question": "Find sum of first 20 terms of AP: 1, 4, 7, 10, ... ➕", "options": {"A": "590", "B": "600", "C": "580", "D": "610"}, "correct_answer": "A"}, {"id": 4, "difficulty": "easy", "question": "Sum of first n natural numbers is: 🌟", "options": {"A": "n(n+1)/2", "B": "n(n-1)/2", "C": "n²", "D": "2n(n+1)"}, "correct_answer": "A"}, {"id": 5, "difficulty": "easy", "question": "Find sum of first 15 multiples of 8. 🎯", "options": {"A": "960", "B": "920", "C": "1000", "D": "880"}, "correct_answer": "A"}, {"id": 6, "difficulty": "easy", "question": "Find sum: 2 + 4 + 6 + ... + 100 📊", "options": {"A": "2550", "B": "2500", "C": "2600", "D": "2450"}, "correct_answer": "A"}, {"id": 7, "difficulty": "easy", "question": "Sum of first 25 odd numbers is: ⚡", "options": {"A": "625", "B": "600", "C": "650", "D": "575"}, "correct_answer": "A"}, {"id": 8, "difficulty": "easy", "question": "Find sum of first 12 terms of AP: 5, 9, 13, 17, ... 🚀", "options": {"A": "324", "B": "300", "C": "348", "D": "372"}, "correct_answer": "A"}, {"id": 9, "difficulty": "easy", "question": "Sum of first 30 even numbers is: 🔢", "options": {"A": "930", "B": "900", "C": "960", "D": "870"}, "correct_answer": "A"}, {"id": 10, "difficulty": "easy", "question": "Find sum of first 40 positive integers divisible by 6. ➗", "options": {"A": "4920", "B": "4800", "C": "5040", "D": "4680"}, "correct_answer": "A"}, {"id": 11, "difficulty": "easy", "question": "Sum of first 8 terms of AP: 10, 6, 2, -2, ... 📉", "options": {"A": "-32", "B": "-24", "C": "-40", "D": "-16"}, "correct_answer": "A"}, {"id": 12, "difficulty": "easy", "question": "Sum of first n odd numbers is: 🎭", "options": {"A": "n²", "B": "n(n+1)", "C": "n(n-1)", "D": "2n"}, "correct_answer": "A"}, {"id": 13, "difficulty": "easy", "question": "Find sum: (-5) + (-8) + (-11) + ... to 15 terms ➖", "options": {"A": "-390", "B": "-360", "C": "-420", "D": "-330"}, "correct_answer": "A"}, {"id": 14, "difficulty": "easy", "question": "Sum of first 18 terms of AP: 100, 95, 90, 85, ... 📉", "options": {"A": "495", "B": "450", "C": "540", "D": "585"}, "correct_answer": "A"}, {"id": 15, "difficulty": "easy", "question": "Find sum of all 2-digit multiples of 3. 🔍", "options": {"A": "1665", "B": "1635", "C": "1695", "D": "1605"}, "correct_answer": "A"}, {"id": 16, "difficulty": "easy", "question": "Sum of first 16 terms of AP: 1/2, 1, 3/2, 2, ... 🧮", "options": {"A": "68", "B": "64", "C": "72", "D": "60"}, "correct_answer": "A"}, {"id": 17, "difficulty": "easy", "question": "Sum of first 50 natural numbers is: 🌈", "options": {"A": "1275", "B": "1250", "C": "1300", "D": "1225"}, "correct_answer": "A"}, {"id": 18, "difficulty": "easy", "question": "Find sum: 7 + 10 + 13 + ... + 100 📈", "options": {"A": "1717", "B": "1700", "C": "1734", "D": "1683"}, "correct_answer": "A"}, {"id": 19, "difficulty": "easy", "question": "Sum of first 14 multiples of 7 is: ⚓", "options": {"A": "735", "B": "700", "C": "770", "D": "805"}, "correct_answer": "A"}, {"id": 20, "difficulty": "easy", "question": "Sum of first 100 integers is: 🎪", "options": {"A": "5050", "B": "5000", "C": "5100", "D": "4950"}, "correct_answer": "A"}, {"id": 21, "difficulty": "medium", "question": "Find sum of first 24 terms of AP whose nth term is 3+2n. 🤔", "options": {"A": "672", "B": "648", "C": "696", "D": "624"}, "correct_answer": "A"}, {"id": 22, "difficulty": "medium", "question": "How many terms of AP: 9, 17, 25, ... must be taken to give sum 636? 🔢", "options": {"A": "12", "B": "11", "C": "13", "D": "10"}, "correct_answer": "A"}, {"id": 23, "difficulty": "medium", "question": "If sum of first 7 terms of AP is 49 and sum of first 17 terms is 289, find sum of first n terms. 🧠", "options": {"A": "n²", "B": "2n²", "C": "n²/2", "D": "3n²"}, "correct_answer": "A"}, {"id": 24, "difficulty": "medium", "question": "Find sum of all 3-digit natural numbers divisible by 7. 🔍", "options": {"A": "70336", "B": "71064", "C": "69608", "D": "68901"}, "correct_answer": "A"}, {"id": 25, "difficulty": "medium", "question": "How many terms of AP: -6, -11/2, -5, ... are needed for sum -25? ➖", "options": {"A": "20", "B": "15", "C": "25", "D": "10"}, "correct_answer": "A"}, {"id": 26, "difficulty": "medium", "question": "The sum of first n terms of AP is 3n²+2n. Find the AP. 📊", "options": {"A": "5, 11, 17, ...", "B": "5, 8, 11, ...", "C": "2, 5, 8, ...", "D": "3, 8, 13, ..."}, "correct_answer": "A"}, {"id": 27, "difficulty": "medium", "question": "Find sum of all natural numbers between 100 and 200 divisible by 4. 🎯", "options": {"A": "3900", "B": "3800", "C": "4000", "D": "4100"}, "correct_answer": "A"}, {"id": 28, "difficulty": "medium", "question": "If sum of first m terms = sum of first n terms of AP (m≠n), find sum of first (m+n) terms. 🔄", "options": {"A": "0", "B": "m+n", "C": "mn", "D": "1"}, "correct_answer": "A"}, {"id": 29, "difficulty": "medium", "question": "Find sum of all odd numbers between 0 and 100. 🎲", "options": {"A": "2500", "B": "2400", "C": "2600", "D": "2550"}, "correct_answer": "A"}, {"id": 30, "difficulty": "medium", "question": "The sum of first 15 terms of AP is 750 and first term is 10. Find common difference. ⚙️", "options": {"A": "6", "B": "5", "C": "4", "D": "7"}, "correct_answer": "A"}, {"id": 31, "difficulty": "medium", "question": "Find sum of integers from 1 to 100 divisible by 2 or 5. 🔢", "options": {"A": "3050", "B": "3000", "C": "3100", "D": "3150"}, "correct_answer": "A"}, {"id": 32, "difficulty": "medium", "question": "How many terms of AP: 25, 22, 19, ... are needed for sum 116? 🧩", "options": {"A": "8", "B": "7", "C": "9", "D": "10"}, "correct_answer": "A"}, {"id": 33, "difficulty": "medium", "question": "The sum of first 20 terms of AP is 400 and first term is 5. Find 10th term. 🎪", "options": {"A": "23", "B": "21", "C": "25", "D": "27"}, "correct_answer": "A"}, {"id": 34, "difficulty": "medium", "question": "Find sum of all 2-digit numbers which leave remainder 3 when divided by 5. ➗", "options": {"A": "990", "B": "945", "C": "1035", "D": "1080"}, "correct_answer": "A"}, {"id": 35, "difficulty": "medium", "question": "If sum of n terms is 2n²+5n, find 20th term. 🔥", "options": {"A": "83", "B": "85", "C": "87", "D": "81"}, "correct_answer": "A"}, {"id": 36, "difficulty": "medium", "question": "Find sum of first 30 terms of AP whose 10th term is 42 and 20th term is 82. 📈", "options": {"A": "2190", "B": "2100", "C": "2280", "D": "2400"}, "correct_answer": "A"}, {"id": 37, "difficulty": "medium", "question": "How many terms of AP: 63, 60, 57, ... must be taken for sum 693? 🎨", "options": {"A": "21", "B": "22", "C": "20", "D": "23"}, "correct_answer": "A"}, {"id": 38, "difficulty": "medium", "question": "The sum of first 16 terms is 112 and next 8 terms is 248. Find AP. 📐", "options": {"A": "a=1, d=2", "B": "a=2, d=3", "C": "a=3, d=4", "D": "a=4, d=1"}, "correct_answer": "A"}, {"id": 39, "difficulty": "medium", "question": "Find sum of all natural numbers between 300 and 600 divisible by 9. 🎯", "options": {"A": "16848", "B": "17010", "C": "16524", "D": "17280"}, "correct_answer": "A"}, {"id": 40, "difficulty": "medium", "question": "If sum of first p terms = sum of first q terms (p≠q), show that sum of first (p+q) terms is 0. MCQ: For AP, if Sp=Sq, then Sp+q = ? 🌀", "options": {"A": "0", "B": "p+q", "C": "1", "D": "pq"}, "correct_answer": "A"}, {"id": 41, "difficulty": "hard", "question": "If sum of first m terms = n and sum of first n terms = m (m≠n) of an AP, find sum of first (m+n) terms. 🚀", "options": {"A": "-(m+n)", "B": "m+n", "C": "0", "D": "mn"}, "correct_answer": "A"}, {"id": 42, "difficulty": "hard", "question": "The sum of first n terms of AP is 5n²+3n. If its mth term is 168, find m. 🔥", "options": {"A": "17", "B": "16", "C": "18", "D": "15"}, "correct_answer": "A"}, {"id": 43, "difficulty": "hard", "question": "Find sum of all numbers between 200 and 400 divisible by 7 but not by 14. 🔢", "options": {"A": "8729", "B": "8610", "C": "8848", "D": "8967"}, "correct_answer": "A"}, {"id": 44, "difficulty": "hard", "question": "If sum of p terms = q and sum of q terms = p of AP, show that sum of (p+q) terms = -(p+q). MCQ: Given, then Sp+q = ? 🎭", "options": {"A": "-(p+q)", "B": "p+q", "C": "0", "D": "p-q"}, "correct_answer": "A"}, {"id": 45, "difficulty": "hard", "question": "The sum of first 10 terms of AP is 150 and sum of next 10 terms is 550. Find first term. 📊", "options": {"A": "3", "B": "4", "C": "2", "D": "5"}, "correct_answer": "A"}, {"id": 46, "difficulty": "hard", "question": "Find sum of all 3-digit numbers which leave remainder 1 when divided by 4. ➗", "options": {"A": "123525", "B": "124200", "C": "122850", "D": "123900"}, "correct_answer": "A"}, {"id": 47, "difficulty": "hard", "question": "If sum of n terms is 3n²+5n and sum of m terms is 3m²+5m, and m≠n, find sum of (m+n) terms. 🔄", "options": {"A": "3(m+n)²+5(m+n)", "B": "0", "C": "mn", "D": "3mn+5"}, "correct_answer": "A"}, {"id": 48, "difficulty": "hard", "question": "The sum of first 7 terms is 63 and sum of next 7 terms is 161. Find 28th term. 🎪", "options": {"A": "111", "B": "115", "C": "107", "D": "119"}, "correct_answer": "A"}, {"id": 49, "difficulty": "hard", "question": "Find sum of series: 1²+2²+3²+...+n². Formula? 📝", "options": {"A": "n(n+1)(2n+1)/6", "B": "[n(n+1)/2]²", "C": "n(n+1)(n+2)/3", "D": "n(2n+1)(n+1)/3"}, "correct_answer": "A"}, {"id": 50, "difficulty": "hard", "question": "If sum of first n terms is 2n+3n², find rth term. 🔍", "options": {"A": "6r-1", "B": "6r+1", "C": "3r-1", "D": "3r+1"}, "correct_answer": "A"}, {"id": 51, "difficulty": "hard", "question": "The sum of first 8 terms is 100 and sum of first 16 terms is 400. Find sum of first 24 terms. ⚡", "options": {"A": "900", "B": "850", "C": "950", "D": "1000"}, "correct_answer": "A"}, {"id": 52, "difficulty": "hard", "question": "Find sum of all numbers between 100 and 1000 divisible by 11. 🔢", "options": {"A": "44550", "B": "44000", "C": "45000", "D": "45500"}, "correct_answer": "A"}, {"id": 53, "difficulty": "hard", "question": "If sum of first n terms is 4n²-n, find 10th term. 🎯", "options": {"A": "77", "B": "79", "C": "75", "D": "81"}, "correct_answer": "A"}, {"id": 54, "difficulty": "hard", "question": "The sum of three numbers in AP is 36 and product is 1428. Find numbers. 🧩", "options": {"A": "7, 12, 17", "B": "6, 12, 18", "C": "8, 12, 16", "D": "9, 12, 15"}, "correct_answer": "A"}, {"id": 55, "difficulty": "hard", "question": "Find sum of series: 5+11+17+...+95 📈", "options": {"A": "800", "B": "850", "C": "750", "D": "900"}, "correct_answer": "A"}, {"id": 56, "difficulty": "hard", "question": "If sum of first m terms = sum of first n terms of AP (m≠n), prove that sum of first (m+n) terms is 0. MCQ: For AP, Sm=Sn implies Sm+n=? 🏆", "options": {"A": "0", "B": "m+n", "C": "1", "D": "mn"}, "correct_answer": "A"}, {"id": 57, "difficulty": "hard", "question": "Find sum of all 4-digit numbers divisible by 7. 🔢", "options": {"A": "7108640", "B": "7098496", "C": "7118784", "D": "7086240"}, "correct_answer": "A"}, {"id": 58, "difficulty": "hard", "question": "The sum of first 10 terms is 320 and sum of next 10 terms is 820. Find 30th term. 🚀", "options": {"A": "141", "B": "139", "C": "143", "D": "137"}, "correct_answer": "A"}, {"id": 59, "difficulty": "hard", "question": "If sum of n terms is n(5n-3), find 15th term. 🔥", "options": {"A": "142", "B": "140", "C": "144", "D": "138"}, "correct_answer": "A"}, {"id": 60, "difficulty": "hard", "question": "Find sum of all natural numbers between 1 and 1000 divisible by 3 or 5. 🎲", "options": {"A": "233168", "B": "234168", "C": "232168", "D": "235168"}, "correct_answer": "A"}]}