{
  "title": "Applications_and_word_problems(Arithmetic_Progressions) - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "A taxi charges ₹15 for the first km and ₹8 for each additional km. What is the fare for 5 km?", "options": {"A": "₹47", "B": "₹45", "C": "₹43", "D": "₹39"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "Saving ₹100 in first month, ₹150 in second month, ₹200 in third month forms an AP. What is the common difference?", "options": {"A": "₹25", "B": "₹50", "C": "₹75", "D": "₹100"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "A ladder has 25 rungs. The bottom rung is 45 cm from ground, each rung is 1.5 cm thicker. What is distance between consecutive rungs?", "options": {"A": "1.5 cm", "B": "2.0 cm", "C": "2.5 cm", "D": "3.0 cm"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Temperature drops by 2°C every hour from 25°C. What will be temperature after 5 hours?", "options": {"A": "15°C", "B": "17°C", "C": "13°C", "D": "11°C"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "A plant grows 3 cm in first week, 5 cm in second week, 7 cm in third week. What is the growth in 4th week?", "options": {"A": "8 cm", "B": "9 cm", "C": "10 cm", "D": "11 cm"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Salary increases by ₹2000 every year starting from ₹30000. What will be salary in 3rd year?", "options": {"A": "₹32000", "B": "₹34000", "C": "₹36000", "D": "₹38000"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "A car travels 50 km in first hour, 55 km in second hour, 60 km in third hour. How far in 4th hour?", "options": {"A": "62 km", "B": "63 km", "C": "64 km", "D": "65 km"}, "correct_answer": "D"},
    {"id": 8, "difficulty": "easy", "question": "A pile of logs has 15 logs in bottom layer, 14 in next, 13 in next. How many layers if top has 1 log?", "options": {"A": "12", "B": "13", "C": "14", "D": "15"}, "correct_answer": "D"},
    {"id": 9, "difficulty": "easy", "question": "Production increases by 50 units monthly from 200 units. What is production in 6th month?", "options": {"A": "350", "B": "400", "C": "450", "D": "500"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "Water level drops 5 cm daily from 100 cm. What is level after 7 days?", "options": {"A": "65 cm", "B": "60 cm", "C": "55 cm", "D": "50 cm"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Students in row: 5 in first, 8 in second, 11 in third. How many in 5th row?", "options": {"A": "14", "B": "15", "C": "16", "D": "17"}, "correct_answer": "D"},
    {"id": 12, "difficulty": "easy", "question": "A tree gains 2 cm monthly height starting at 50 cm. Height after 10 months?", "options": {"A": "68 cm", "B": "70 cm", "C": "72 cm", "D": "74 cm"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Saving pattern: ₹20, ₹40, ₹60... How much saved in 8th week?", "options": {"A": "₹140", "B": "₹150", "C": "₹160", "D": "₹170"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "Bus fare increases by ₹5 yearly from ₹20. Fare after 4 years?", "options": {"A": "₹30", "B": "₹35", "C": "₹40", "D": "₹45"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "Bacteria doubles every hour from 100. Count after 3 hours?", "options": {"A": "300", "B": "400", "C": "600", "D": "800"}, "correct_answer": "D"},
    {"id": 16, "difficulty": "easy", "question": "Interest earned: ₹1000, ₹1050, ₹1100... What is interest in 5th year?", "options": {"A": "₹1150", "B": "₹1200", "C": "₹1250", "D": "₹1300"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Pages read daily: 10, 15, 20... How many pages on 6th day?", "options": {"A": "30", "B": "35", "C": "40", "D": "45"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "Train stops: 1st stop 10 people board, 2nd stop 15, 3rd stop 20. How many at 4th stop?", "options": {"A": "22", "B": "24", "C": "25", "D": "26"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "Water consumption reduces by 2L daily from 20L. Consumption on 5th day?", "options": {"A": "10L", "B": "12L", "C": "14L", "D": "16L"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "Building floors: 1st floor 12 ft, 2nd floor 24 ft, 3rd floor 36 ft. Height of 4th floor?", "options": {"A": "44 ft", "B": "46 ft", "C": "48 ft", "D": "50 ft"}, "correct_answer": "C"},
    {"id": 21, "difficulty": "medium", "question": "A contract states penalty of ₹200 for first day, ₹250 for second, ₹300 for third etc. What is penalty for 10th day of delay?", "options": {"A": "₹600", "B": "₹650", "C": "₹700", "D": "₹750"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "A man saved ₹16500 in 5 years. Each year he saved ₹100 more than previous year. How much did he save in first year?", "options": {"A": "₹2800", "B": "₹2900", "C": "₹3000", "D": "₹3100"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "The sum of 5th and 9th terms of an AP is 30. If 10th term is 25, what is the first term?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "D"},
    {"id": 24, "difficulty": "medium", "question": "A company produced 5000 units in 3rd year and 7000 units in 7th year. Assuming production increases uniformly, what was production in first year?", "options": {"A": "4000", "B": "4100", "C": "4200", "D": "4300"}, "correct_answer": "D"},
    {"id": 25, "difficulty": "medium", "question": "The angles of a quadrilateral are in AP with common difference 10°. What is the smallest angle?", "options": {"A": "60°", "B": "65°", "C": "70°", "D": "75°"}, "correct_answer": "D"},
    {"id": 26, "difficulty": "medium", "question": "A sum of ₹2800 is to be used to give 7 cash prizes. If each prize is ₹100 less than preceding prize, what is value of first prize?", "options": {"A": "₹600", "B": "₹650", "C": "₹700", "D": "₹750"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "In a school, students stand in rows to form AP. If there are 25 rows and number of students in successive rows are 5, 7, 9,... how many students in last row?", "options": {"A": "51", "B": "52", "C": "53", "D": "54"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "A man arranges to pay off debt of ₹3600 by 40 monthly installments which form an AP. When 30 installments are paid, he dies leaving 1/3 of debt unpaid. What is first installment?", "options": {"A": "₹40", "B": "₹45", "C": "₹50", "D": "₹55"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "A spiral is made from 100 semicircles with radii 0.5cm, 1cm, 1.5cm,... What is total length of spiral?", "options": {"A": "50π cm", "B": "100π cm", "C": "150π cm", "D": "200π cm"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "A manufacturer produced 600 units in 3rd year and 700 units in 7th year. Assuming uniform increase, what is total production in first 10 years?", "options": {"A": "6525", "B": "6625", "C": "6725", "D": "6825"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "A man starts job at ₹8000 monthly with annual increment of ₹500. What will be his monthly salary in 15th year?", "options": {"A": "₹14500", "B": "₹14700", "C": "₹14900", "D": "₹15000"}, "correct_answer": "D"},
    {"id": 32, "difficulty": "medium", "question": "Between 1 and 31, m numbers are inserted so that resulting sequence is AP. If ratio of 7th and (m-1)th numbers is 5:9, find m.", "options": {"A": "12", "B": "13", "C": "14", "D": "15"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "A carpenter makes chairs. First chair takes 20 hours, second takes 18 hours, third takes 16 hours etc. How long to make 10 chairs?", "options": {"A": "110 hours", "B": "115 hours", "C": "120 hours", "D": "125 hours"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Subba Rao started work in 1995 at ₹5000 monthly with annual increment of ₹200. In which year did his income reach ₹7000?", "options": {"A": "1999", "B": "2000", "C": "2001", "D": "2002"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "Ramkali saved ₹5 in first week, then increased weekly saving by ₹1.75. After n weeks, her total saving was ₹72.75. Find n.", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "C"},
    {"id": 36, "difficulty": "medium", "question": "A ladder has rungs 25 cm apart. The rungs decrease uniformly from 45 cm at bottom to 25 cm at top. If top and bottom rungs are 2.5 m apart, how many rungs?", "options": {"A": "9", "B": "10", "C": "11", "D": "12"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "The house tax on first ₹2500 is ₹50, on next ₹2500 is ₹75, on next ₹2500 is ₹100 etc. What is tax on property worth ₹25000?", "options": {"A": "₹1000", "B": "₹1100", "C": "₹1200", "D": "₹1300"}, "correct_answer": "D"},
    {"id": 38, "difficulty": "medium", "question": "A small terrace at football ground has 15 steps each 50 m long built of solid concrete. First step requires 2 m³ concrete, second requires 2¼ m³ etc. Total concrete required?", "options": {"A": "25.5 m³", "B": "26.25 m³", "C": "27 m³", "D": "27.75 m³"}, "correct_answer": "D"},
    {"id": 39, "difficulty": "medium", "question": "150 workers were engaged to finish job in certain days. 4 workers dropped on second day, 4 more on third day etc. Work finished in 8 more days. Number of days work lasted?", "options": {"A": "23", "B": "24", "C": "25", "D": "26"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "A manufacturer of TV sets produced 600 sets in 3rd year and 700 in 7th year. Assuming production increases uniformly by fixed number yearly, find production in 10th year.", "options": {"A": "750", "B": "775", "C": "800", "D": "825"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "medium", "question": "The sum of 3rd and 7th terms of AP is 6 and product is 8. Find common difference.", "options": {"A": "±1", "B": "±2", "C": "±3", "D": "±4"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "A person buys national savings certificates of value exceeding previous year by ₹100. After 20 years, total value is ₹12000. Value of first certificate?", "options": {"A": "₹100", "B": "₹150", "C": "₹200", "D": "₹250"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "In potato race, bucket is placed 5 m from first potato. Subsequent potatoes placed 3 m apart in straight line. 10 potatoes. Competitor starts from bucket, picks potato and runs back. Total distance run?", "options": {"A": "320 m", "B": "340 m", "C": "360 m", "D": "380 m"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "medium", "question": "If sum of n terms of AP is 3n²+5n and its mth term is 164, find m.", "options": {"A": "25", "B": "26", "C": "27", "D": "28"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "Between 1 and 31, m numbers inserted making AP. Ratio of 7th to (m-1)th numbers is 5:9. Find m.", "options": {"A": "12", "B": "13", "C": "14", "D": "15"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "A sum of ₹700 is to be used for 7 prizes. Each prize is ₹20 less than preceding prize. Value of smallest prize?", "options": {"A": "₹40", "B": "₹50", "C": "₹60", "D": "₹70"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "In flower bed, 23 rose plants in first row, 21 in second, 19 in third etc. 5 rose plants in last row. Number of rows?", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "Temperature recorded at 12 noon was 10°C. Every hour it rose by 2°C. Temperature at 5 PM?", "options": {"A": "18°C", "B": "20°C", "C": "22°C", "D": "24°C"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "A contract on construction job specifies penalty for delay: ₹200 for first day, ₹250 for second, ₹300 for third etc. Penalty for 30 days delay?", "options": {"A": "₹2775", "B": "₹2825", "C": "₹2875", "D": "₹2925"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "Students make human chain. 27 students in first row, 25 in second, 23 in third etc. If there are 10 rows, how many students?", "options": {"A": "160", "B": "170", "C": "180", "D": "190"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "medium", "question": "Savings scheme: ₹1000 first month, ₹1100 second, ₹1200 third etc. Total saved in 2 years?", "options": {"A": "₹37200", "B": "₹37500", "C": "₹37800", "D": "₹38100"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Water tank capacity 2000L. 100L removed first day, 150L second, 200L third etc. Days to empty tank?", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "medium", "question": "Loan repayment: ₹1000 first month, ₹950 second, ₹900 third etc. Last installment ₹50. Number of installments?", "options": {"A": "18", "B": "19", "C": "20", "D": "21"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "medium", "question": "AP formed by production: 600 units in 6th year, 700 in 10th year. Production in 15th year?", "options": {"A": "775", "B": "800", "C": "825", "D": "850"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "Tree planting: 50 trees first year, 55 second, 60 third etc. Trees in 12th year?", "options": {"A": "95", "B": "100", "C": "105", "D": "110"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "Salary starts ₹30000 with ₹2500 annual increment. Total earnings in 10 years?", "options": {"A": "₹412500", "B": "₹425000", "C": "₹437500", "D": "₹450000"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "medium", "question": "Students in rows: 35 first, 33 second, 31 third etc. If 5 students in last row, how many rows?", "options": {"A": "14", "B": "15", "C": "16", "D": "17"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "AP of 25 terms. Sum of last 10 terms is 1065, common difference is 5. Find first term.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Houses numbered from 1 to 100. Plates made with digits 2. How many plates?", "options": {"A": "18", "B": "19", "C": "20", "D": "21"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "Fencing costs: ₹15 for first meter, ₹20 for second, ₹25 for third etc. Cost for 20 meters?", "options": {"A": "₹1200", "B": "₹1250", "C": "₹1300", "D": "₹1350"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "Water flow: 20L first minute, 18L second, 16L third etc. Total in 10 minutes?", "options": {"A": "100L", "B": "110L", "C": "120L", "D": "130L"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "Stack of pipes: 20 at bottom, 19 above, 18 next etc. If top has 3 pipes, how many pipes?", "options": {"A": "200", "B": "207", "C": "214", "D": "221"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "Interest: ₹500 first year, ₹550 second, ₹600 third etc. Total interest in 8 years?", "options": {"A": "₹3800", "B": "₹3900", "C": "₹4000", "D": "₹4100"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "Distance covered: 200m first minute, 250m second, 300m third etc. Distance in 12 minutes?", "options": {"A": "5100m", "B": "5250m", "C": "5400m", "D": "5550m"}, "correct_answer": "B"},
    {"id": 65, "difficulty": "medium", "question": "Temperature pattern: 10°C at 6 AM, 12°C at 7 AM, 14°C at 8 AM etc. Temperature at 3 PM?", "options": {"A": "26°C", "B": "28°C", "C": "30°C", "D": "32°C"}, "correct_answer": "B"},
    {"id": 66, "difficulty": "medium", "question": "Seats in theater: 25 first row, 28 second, 31 third etc. 10 rows total. How many seats?", "options": {"A": "385", "B": "395", "C": "405", "D": "415"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "Pages printed: 100 first hour, 110 second, 120 third etc. Total in 8 hours?", "options": {"A": "1080", "B": "1120", "C": "1160", "D": "1200"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "AP: 5, 8, 11,... Which term is 56?", "options": {"A": "16", "B": "17", "C": "18", "D": "19"}, "correct_answer": "C"},
    {"id": 69, "difficulty": "medium", "question": "Students per class: 40 in class 1, 42 in class 2, 44 in class 3 etc. Total students in 12 classes?", "options": {"A": "612", "B": "624", "C": "636", "D": "648"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "Water consumption reduces by 5L weekly from 100L. When will it be 40L?", "options": {"A": "12th week", "B": "13th week", "C": "14th week", "D": "15th week"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "Production increases by 50 units monthly from 500. Production in 15th month?", "options": {"A": "1150", "B": "1200", "C": "1250", "D": "1300"}, "correct_answer": "B"},
    {"id": 72, "difficulty": "medium", "question": "Savings: ₹200 first month, ₹250 second, ₹300 third etc. When total reaches ₹5000?", "options": {"A": "12 months", "B": "13 months", "C": "14 months", "D": "15 months"}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "Distance: 2km first day, 2.5km second, 3km third etc. Total in 2 weeks?", "options": {"A": "59.5km", "B": "63km", "C": "66.5km", "D": "70km"}, "correct_answer": "B"},
    {"id": 74, "difficulty": "medium", "question": "Bricks in wall: 100 bottom layer, 95 next, 90 next etc. Top layer 15 bricks. Total bricks?", "options": {"A": "885", "B": "920", "C": "955", "D": "990"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Exam marks improve by 5 each test: 60, 65, 70 etc. Marks in 10th test?", "options": {"A": "100", "B": "105", "C": "110", "D": "115"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "Water level rises 2cm hourly from 10cm. Height after 8 hours?", "options": {"A": "24cm", "B": "26cm", "C": "28cm", "D": "30cm"}, "correct_answer": "B"},
    {"id": 77, "difficulty": "medium", "question": "Salary: ₹20000 first year, ₹21000 second, ₹22000 third etc. Total earnings in 20 years?", "options": {"A": "₹590000", "B": "₹595000", "C": "₹600000", "D": "₹605000"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Trees planted annually: 100, 120, 140 etc. Trees in 8th year?", "options": {"A": "220", "B": "230", "C": "240", "D": "250"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "Books read monthly: 2, 4, 6 etc. Total in year?", "options": {"A": "144", "B": "156", "C": "168", "D": "180"}, "correct_answer": "B"},
    {"id": 80, "difficulty": "medium", "question": "Water drained from tank: 20L first hour, 25L second, 30L third etc. Tank empties in 10 hours. Tank capacity?", "options": {"A": "425L", "B": "450L", "C": "475L", "D": "500L"}, "correct_answer": "A"},
    {"id": 81, "difficulty": "hard", "question": "A man saved ₹16500 in 5 years. In each succeeding year, he saved ₹100 more than he saved in the preceding year. How much did he save in the first year?", "options": {"A": "₹2800", "B": "₹2900", "C": "₹3000", "D": "₹3100"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "The sum of first 7 terms of an AP is 49 and sum of first 17 terms is 289. Find sum of first n terms.", "options": {"A": "n²", "B": "2n²", "C": "3n²", "D": "4n²"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "If the sum of m terms of an AP is equal to sum of n terms, show that sum of (m+n) terms is zero. For AP with first term 3, common difference 2, find m and n such that S_m = S_n.", "options": {"A": "m=5, n=7", "B": "m=6, n=8", "C": "m=7, n=9", "D": "m=8, n=10"}, "correct_answer": "B"},
    {"id": 84, "difficulty": "hard", "question": "A manufacturer of TV sets produced 600 sets in third year and 700 sets in seventh year. Assuming production increases uniformly by fixed number every year, find total production in first 7 years.", "options": {"A": "4200", "B": "4375", "C": "4550", "D": "4725"}, "correct_answer": "B"},
    {"id": 85, "difficulty": "hard", "question": "200 logs are stacked with 20 logs in bottom row, 19 in next row, 18 in next row and so on. In how many rows are 200 logs placed?", "options": {"A": "14", "B": "15", "C": "16", "D": "17"}, "correct_answer": "C"},
    {"id": 86, "difficulty": "hard", "question": "A spiral is made from 100 semicircles with radii 0.5cm, 1cm, 1.5cm,... What is total length of spiral? (Take π=22/7)", "options": {"A": "550 cm", "B": "1100 cm", "C": "1650 cm", "D": "2200 cm"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "The sum of four consecutive numbers in AP is 32 and ratio of product of first and last to product of two middle terms is 7:15. Find the numbers.", "options": {"A": "2,6,10,14", "B": "4,8,12,16", "C": "5,7,9,11", "D": "3,7,11,15"}, "correct_answer": "C"},
    {"id": 88, "difficulty": "hard", "question": "A ladder has rungs 25 cm apart. The rungs decrease uniformly from 45 cm at bottom to 25 cm at top. If top and bottom rungs are 2.5 m apart, what is length of wood required for rungs?", "options": {"A": "3.25 m", "B": "3.50 m", "C": "3.75 m", "D": "4.00 m"}, "correct_answer": "C"},
    {"id": 89, "difficulty": "hard", "question": "The houses of a row are numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses preceding house numbered x is equal to sum of numbers following x. Find x.", "options": {"A": "30", "B": "32", "C": "34", "D": "35"}, "correct_answer": "D"},
    {"id": 90, "difficulty": "hard", "question": "If sum of first p terms of AP is equal to sum of first q terms where p≠q, then sum of first (p+q) terms is:", "options": {"A": "0", "B": "1", "C": "p+q", "D": "pq"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "In an AP, if S_n = 3n² + 5n, find a_n (nth term).", "options": {"A": "6n+2", "B": "6n+3", "C": "6n+4", "D": "6n+5"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "If ratio of sums of m and n terms of AP is m²:n², show that ratio of mth and nth terms is (2m-1):(2n-1). For a=5, d=2, verify for m=3, n=4.", "options": {"A": "9:13", "B": "11:15", "C": "13:17", "D": "15:19"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Find sum of all two-digit numbers which when divided by 4 yields remainder 1.", "options": {"A": "1012", "B": "1112", "C": "1212", "D": "1312"}, "correct_answer": "C"},
    {"id": 94, "difficulty": "hard", "question": "Find sum of integers between 100 and 200 that are divisible by 9.", "options": {"A": "1584", "B": "1683", "C": "1782", "D": "1881"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "If sum of n terms of AP is given by S_n = 2n² + 3n, find the AP.", "options": {"A": "5,9,13,...", "B": "5,11,17,...", "C": "7,11,15,...", "D": "7,13,19,..."}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "The sum of first n terms of two APs are in ratio (7n+1):(4n+27). Find ratio of their 11th terms.", "options": {"A": "3:4", "B": "4:5", "C": "5:6", "D": "6:7"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "If m times mth term of AP equals n times nth term, with m≠n, show that (m+n)th term is zero. For AP 2,5,8,... find m,n satisfying 3a_m = 5a_n.", "options": {"A": "m=3,n=5", "B": "m=4,n=6", "C": "m=5,n=7", "D": "m=6,n=8"}, "correct_answer": "C"},
    {"id": 98, "difficulty": "hard", "question": "Find sum of all natural numbers between 250 and 1000 which are exactly divisible by 3.", "options": {"A": "156375", "B": "157375", "C": "158375", "D": "159375"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "The sum of three numbers in AP is 24 and their product is 440. Find the numbers.", "options": {"A": "5,8,11", "B": "6,8,10", "C": "7,8,9", "D": "4,8,12"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "The pth term of AP is q and qth term is p. Find (p+q)th term.", "options": {"A": "0", "B": "1", "C": "p+q", "D": "p-q"}, "correct_answer": "A"}
  ]
}