{"title": "nth term of AP (Arithmetic Progression) - Grade 10 ICSE", "total_questions": 60, "questions": [{"id": 1, "difficulty": "easy", "question": "Find 10th term of AP: 2, 5, 8, 11, ... 🔢", "options": {"A": "29", "B": "26", "C": "32", "D": "35"}, "correct_answer": "A"}, {"id": 2, "difficulty": "easy", "question": "The nth term of AP is given by: 📝", "options": {"A": "a + (n-1)d", "B": "a + nd", "C": "a + (n+1)d", "D": "n(a+d)"}, "correct_answer": "A"}, {"id": 3, "difficulty": "easy", "question": "Find 15th term of AP: 10, 7, 4, 1, ... ➖", "options": {"A": "-32", "B": "-29", "C": "-35", "D": "-26"}, "correct_answer": "A"}, {"id": 4, "difficulty": "easy", "question": "First term a=3, common difference d=4, find 8th term. 🎯", "options": {"A": "31", "B": "27", "C": "35", "D": "39"}, "correct_answer": "A"}, {"id": 5, "difficulty": "easy", "question": "Which term of AP: 21, 18, 15, ... is -81? 🔍", "options": {"A": "35th", "B": "34th", "C": "36th", "D": "37th"}, "correct_answer": "A"}, {"id": 6, "difficulty": "easy", "question": "Find 20th term of AP: -5, -1, 3, 7, ... ⚡", "options": {"A": "71", "B": "67", "C": "75", "D": "79"}, "correct_answer": "A"}, {"id": 7, "difficulty": "easy", "question": "The 5th term of AP is 17 and 9th term is 33. Find common difference. 📊", "options": {"A": "4", "B": "3", "C": "5", "D": "6"}, "correct_answer": "A"}, {"id": 8, "difficulty": "easy", "question": "Find nth term of AP: 1/2, 1, 3/2, 2, ... 🧮", "options": {"A": "n/2", "B": "(n+1)/2", "C": "(n-1)/2", "D": "1 + (n-1)/2"}, "correct_answer": "A"}, {"id": 9, "difficulty": "easy", "question": "Which term of AP: 3, 8, 13, ... is 78? 🎪", "options": {"A": "16th", "B": "15th", "C": "17th", "D": "18th"}, "correct_answer": "A"}, {"id": 10, "difficulty": "easy", "question": "First term a=-2, d=3, find 12th term. 🌟", "options": {"A": "31", "B": "28", "C": "34", "D": "37"}, "correct_answer": "A"}, {"id": 11, "difficulty": "easy", "question": "Find 25th term of AP: 100, 96, 92, 88, ... 📉", "options": {"A": "4", "B": "0", "C": "-4", "D": "8"}, "correct_answer": "A"}, {"id": 12, "difficulty": "easy", "question": "The 3rd term of AP is 7 and 7th term is 23. Find first term. 🎭", "options": {"A": "-1", "B": "1", "C": "0", "D": "2"}, "correct_answer": "A"}, {"id": 13, "difficulty": "easy", "question": "Which term of AP: 4, 9, 14, ... is 129? 🔥", "options": {"A": "26th", "B": "25th", "C": "27th", "D": "28th"}, "correct_answer": "A"}, {"id": 14, "difficulty": "easy", "question": "Find 30th term of AP: 1, 4, 7, 10, ... 🚀", "options": {"A": "88", "B": "85", "C": "91", "D": "94"}, "correct_answer": "A"}, {"id": 15, "difficulty": "easy", "question": "The nth term of AP is 4n+3. Find common difference. 🔄", "options": {"A": "4", "B": "3", "C": "7", "D": "1"}, "correct_answer": "A"}, {"id": 16, "difficulty": "easy", "question": "Find 18th term of AP: -10, -6, -2, 2, ... ⚖️", "options": {"A": "58", "B": "54", "C": "62", "D": "66"}, "correct_answer": "A"}, {"id": 17, "difficulty": "easy", "question": "Which term of AP: 5, 2, -1, ... is -22? 📉", "options": {"A": "10th", "B": "11th", "C": "9th", "D": "12th"}, "correct_answer": "A"}, {"id": 18, "difficulty": "easy", "question": "The nth term of AP is 7-3n. Find first term. 🎨", "options": {"A": "4", "B": "7", "C": "-3", "D": "10"}, "correct_answer": "A"}, {"id": 19, "difficulty": "easy", "question": "Find 40th term of AP: 0.5, 1.0, 1.5, 2.0, ... 📈", "options": {"A": "20", "B": "20.5", "C": "19.5", "D": "21"}, "correct_answer": "A"}, {"id": 20, "difficulty": "easy", "question": "The 4th term of AP is 14 and 10th term is 32. Find d. 🔢", "options": {"A": "3", "B": "2", "C": "4", "D": "5"}, "correct_answer": "A"}, {"id": 21, "difficulty": "medium", "question": "If 7 times the 7th term equals 11 times 11th term of AP, find 18th term. 🤔", "options": {"A": "0", "B": "1", "C": "-1", "D": "2"}, "correct_answer": "A"}, {"id": 22, "difficulty": "medium", "question": "The sum of 4th and 8th term of AP is 24 and sum of 6th and 10th is 44. Find first term and d. 🔍", "options": {"A": "a=-13, d=5", "B": "a=-5, d=13", "C": "a=13, d=5", "D": "a=5, d=13"}, "correct_answer": "A"}, {"id": 23, "difficulty": "medium", "question": "Which term of AP: 20, 19¼, 18½, ... is first negative term? 📉", "options": {"A": "28th", "B": "27th", "C": "29th", "D": "30th"}, "correct_answer": "A"}, {"id": 24, "difficulty": "medium", "question": "The 5th term of AP is 0. Prove that its 9th term is double the 2nd term. 🧠", "options": {"A": "True", "B": "False", "C": "Cannot determine", "D": "Only if d=0"}, "correct_answer": "A"}, {"id": 25, "difficulty": "medium", "question": "Find three numbers in AP whose sum is 15 and product is 80. 🔢", "options": {"A": "2,5,8", "B": "3,5,7", "C": "4,5,6", "D": "1,5,9"}, "correct_answer": "A"}, {"id": 26, "difficulty": "medium", "question": "The nth term of AP is 2n+5. Which term equals 55? 🎯", "options": {"A": "25th", "B": "24th", "C": "26th", "D": "27th"}, "correct_answer": "A"}, {"id": 27, "difficulty": "medium", "question": "If pth term is q and qth term is p of an AP, find (p+q)th term. 🔄", "options": {"A": "0", "B": "p+q", "C": "p-q", "D": "1"}, "correct_answer": "A"}, {"id": 28, "difficulty": "medium", "question": "Find four numbers in AP whose sum is 20 and sum of squares is 120. 📊", "options": {"A": "2,4,6,8", "B": "1,3,5,7", "C": "3,5,7,9", "D": "0,4,8,12"}, "correct_answer": "A"}, {"id": 29, "difficulty": "medium", "question": "The nth term of AP is 4n-3. Find sum of first 20 terms. ➕", "options": {"A": "780", "B": "820", "C": "740", "D": "860"}, "correct_answer": "A"}, {"id": 30, "difficulty": "medium", "question": "If m times mth term equals n times nth term of AP, show that (m+n)th term is 0. MCQ: If 5×5th = 8×8th, then 13th term = ? 🎲", "options": {"A": "0", "B": "1", "C": "5", "D": "8"}, "correct_answer": "A"}, {"id": 31, "difficulty": "medium", "question": "Find 31st term of AP whose 11th term is 38 and 16th term is 73. 🚀", "options": {"A": "178", "B": "183", "C": "188", "D": "193"}, "correct_answer": "A"}, {"id": 32, "difficulty": "medium", "question": "The sum of three numbers in AP is 27 and product is 648. Find numbers. 🧩", "options": {"A": "6,9,12", "B": "4,9,14", "C": "8,9,10", "D": "3,9,15"}, "correct_answer": "A"}, {"id": 33, "difficulty": "medium", "question": "Which term of AP: 3, 15, 27, ... is 120 more than its 21st term? ⚡", "options": {"A": "31st", "B": "32nd", "C": "33rd", "D": "34th"}, "correct_answer": "A"}, {"id": 34, "difficulty": "medium", "question": "If 9th term of AP is 0, prove that 29th term is double 19th term. MCQ: If 9th=0, then 29th/19th = ? 🏆", "options": {"A": "2", "B": "1", "C": "3", "D": "4"}, "correct_answer": "A"}, {"id": 35, "difficulty": "medium", "question": "Find 15th term from end of AP: 2, 5, 8, ..., 95. 🔚", "options": {"A": "53", "B": "50", "C": "47", "D": "44"}, "correct_answer": "A"}, {"id": 36, "difficulty": "medium", "question": "The nth term of AP is 3n+2. Is 100 a term? If yes, which? 🔢", "options": {"A": "Yes, 32nd", "B": "Yes, 33rd", "C": "No", "D": "Yes, 34th"}, "correct_answer": "A"}, {"id": 37, "difficulty": "medium", "question": "If a,b,c are in AP, then (a+2b-c)(2b+c-a)(c+a-b) equals? 🌈", "options": {"A": "8abc", "B": "4abc", "C": "2abc", "D": "abc"}, "correct_answer": "A"}, {"id": 38, "difficulty": "medium", "question": "Find 10th term of AP whose 4th term is 5 and 8th term is 13. ⚙️", "options": {"A": "19", "B": "17", "C": "21", "D": "23"}, "correct_answer": "A"}, {"id": 39, "difficulty": "medium", "question": "The 24th term of AP is twice its 10th term. Show that 36th term is twice 16th term. MCQ: If 24th=2×10th, then 36th/16th = ? 🎪", "options": {"A": "2", "B": "3", "C": "1", "D": "4"}, "correct_answer": "A"}, {"id": 40, "difficulty": "medium", "question": "Find 20th term of AP: √2, 3√2, 5√2, ... 📐", "options": {"A": "39√2", "B": "41√2", "C": "37√2", "D": "43√2"}, "correct_answer": "A"}, {"id": 41, "difficulty": "hard", "question": "If pth, qth, rth terms of AP are a,b,c respectively, prove that a(q-r)+b(r-p)+c(p-q)=0. MCQ: Given relation, if p,q,r are distinct, then? 🧬", "options": {"A": "The relation holds", "B": "a=b=c", "C": "p+q=r", "D": "No relation"}, "correct_answer": "A"}, {"id": 42, "difficulty": "hard", "question": "If the sum of first n terms of AP is 3n²+5n, find its nth term. 🔥", "options": {"A": "6n+2", "B": "6n+5", "C": "3n+5", "D": "3n+2"}, "correct_answer": "A"}, {"id": 43, "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": "148:111", "B": "111:148", "C": "7:4", "D": "4:7"}, "correct_answer": "A"}, {"id": 44, "difficulty": "hard", "question": "If a,b,c are in AP, prove that a²(b+c), b²(c+a), c²(a+b) are in AP. MCQ: Given a,b,c in AP, then these are? 🎯", "options": {"A": "In AP", "B": "In GP", "C": "In HP", "D": "Not in progression"}, "correct_answer": "A"}, {"id": 45, "difficulty": "hard", "question": "The interior angles of a polygon are in AP. Smallest angle=120°, common difference=5°. Find number of sides if largest angle is 165°. 📐", "options": {"A": "9", "B": "8", "C": "10", "D": "7"}, "correct_answer": "A"}, {"id": 46, "difficulty": "hard", "question": "If 1/(b+c), 1/(c+a), 1/(a+b) are in AP, prove that a²,b²,c² are in AP. MCQ: Given condition implies? 🚀", "options": {"A": "a²,b²,c² in AP", "B": "a,b,c in AP", "C": "a,b,c in GP", "D": "a,b,c in HP"}, "correct_answer": "A"}, {"id": 47, "difficulty": "hard", "question": "The pth term of AP is 1/q and qth term is 1/p. Find sum of first pq terms. 🎲", "options": {"A": "(pq+1)/2", "B": "pq/2", "C": "(pq-1)/2", "D": "pq"}, "correct_answer": "A"}, {"id": 48, "difficulty": "hard", "question": "If the sum of first m terms of AP = sum of first n terms (m≠n), show that sum of first (m+n) terms is 0. MCQ: If Sm=Sn (m≠n), then Sm+n = ? 🏔️", "options": {"A": "0", "B": "m+n", "C": "1", "D": "mn"}, "correct_answer": "A"}, {"id": 49, "difficulty": "hard", "question": "If a,b,c are in AP and a²,b²,c² are in AP, prove that a=b=c or a,b,c are in GP. MCQ: Given both conditions, then? 🌉", "options": {"A": "a=b=c or in GP", "B": "Always a=b=c", "C": "Always in GP", "D": "No conclusion"}, "correct_answer": "A"}, {"id": 50, "difficulty": "hard", "question": "Find 40th term of AP whose 7th term is 34 and 12th term is 64. 🔢", "options": {"A": "244", "B": "240", "C": "248", "D": "252"}, "correct_answer": "A"}, {"id": 51, "difficulty": "hard", "question": "If the sum of n terms of AP is 2n²+3n, find the 25th term. 📈", "options": {"A": "101", "B": "103", "C": "99", "D": "105"}, "correct_answer": "A"}, {"id": 52, "difficulty": "hard", "question": "The sum of three numbers in AP is 24 and their product is 440. Find numbers. 🧩", "options": {"A": "5,8,11", "B": "4,8,12", "C": "6,8,10", "D": "7,8,9"}, "correct_answer": "A"}, {"id": 53, "difficulty": "hard", "question": "If the nth term of AP is 5n-2, find sum of first 40 terms. ➕", "options": {"A": "3980", "B": "4000", "C": "4020", "D": "3960"}, "correct_answer": "A"}, {"id": 54, "difficulty": "hard", "question": "The ratio of sums of first n terms of two APs is (3n+8):(7n+15). Find ratio of their 12th terms. ⚖️", "options": {"A": "7:16", "B": "16:7", "C": "3:7", "D": "7:3"}, "correct_answer": "A"}, {"id": 55, "difficulty": "hard", "question": "If a,b,c,d are in AP, prove that (a+d)² = (b+c)²+4ad-4bc. MCQ: Given AP, then (a+d)² - (b+c)² = ? 🎭", "options": {"A": "4(ad-bc)", "B": "0", "C": "(a-d)²", "D": "4(bc-ad)"}, "correct_answer": "A"}, {"id": 56, "difficulty": "hard", "question": "Find the 50th term of AP whose 10th term is 4 and 16th term is -14. 📉", "options": {"A": "-134", "B": "-136", "C": "-138", "D": "-140"}, "correct_answer": "A"}, {"id": 57, "difficulty": "hard", "question": "The sum of n terms of two APs are in ratio (5n+4):(9n+6). Find ratio of their 18th terms. 🔄", "options": {"A": "179:321", "B": "321:179", "C": "5:9", "D": "9:5"}, "correct_answer": "A"}, {"id": 58, "difficulty": "hard", "question": "If the sum of first p terms = sum of first q terms of AP (p≠q), prove that sum of first (p+q) terms is 0. MCQ: Given Sp=Sq, then Sp+q = ? 🎖️", "options": {"A": "0", "B": "p+q", "C": "1", "D": "pq"}, "correct_answer": "A"}, {"id": 59, "difficulty": "hard", "question": "The nth term of AP is 4n+1. Which term is 109? 🚀", "options": {"A": "27th", "B": "26th", "C": "28th", "D": "29th"}, "correct_answer": "A"}, {"id": 60, "difficulty": "hard", "question": "If a,b,c are in AP, prove that (a-c)² = 4(b²-ac). MCQ: Given AP, then (a-c)² = ? 🔥", "options": {"A": "4(b²-ac)", "B": "b²-ac", "C": "2(b²-ac)", "D": "b²+ac"}, "correct_answer": "A"}]}