{
  "title": "Review of Rational Numbers - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Which is a rational number?", "options": {"A": "√2", "B": "π", "C": "3/4", "D": "0.101001000..."}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "Rational numbers can be expressed as:", "options": {"A": "p/q where q≠0", "B": "p/q where p,q integers", "C": "Both A and B", "D": "p/q where q=0"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "Which is NOT rational?", "options": {"A": "0.5", "B": "0.333...", "C": "√4", "D": "√3"}, "correct_answer": "D"},
    {"id": 4, "difficulty": "easy", "question": "The decimal expansion of a rational number is:", "options": {"A": "Always terminating", "B": "Always repeating", "C": "Terminating or repeating", "D": "Non-terminating non-repeating"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "Which is rational? 0.121212...", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Can't say"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Every integer is a rational number:", "options": {"A": "True", "B": "False", "C": "Sometimes", "D": "Never"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "Which fraction is rational?", "options": {"A": "1/2", "B": "√2/2", "C": "π/2", "D": "All"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "0.75 as fraction:", "options": {"A": "3/4", "B": "75/100", "C": "7.5/10", "D": "All"}, "correct_answer": "D"},
    {"id": 9, "difficulty": "easy", "question": "Rational numbers include:", "options": {"A": "Natural numbers", "B": "Whole numbers", "C": "Integers", "D": "All of these"}, "correct_answer": "D"},
    {"id": 10, "difficulty": "easy", "question": "Which decimal represents rational? 0.123123123...", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Only if finite"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "√9 is rational because:", "options": {"A": "It's 3", "B": "Can be 3/1", "C": "Both", "D": "It's not rational"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "Which is rational? -5", "options": {"A": "Yes", "B": "No", "C": "Only positive", "D": "Only negative"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "0.6 as fraction:", "options": {"A": "3/5", "B": "6/10", "C": "60/100", "D": "All"}, "correct_answer": "D"},
    {"id": 14, "difficulty": "easy", "question": "Every fraction is rational:", "options": {"A": "True", "B": "False", "C": "Only proper", "D": "Only improper"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Which terminating decimal? 0.25", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Infinite"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "1/3 as decimal:", "options": {"A": "0.333...", "B": "0.3", "C": "0.33", "D": "All represent same"}, "correct_answer": "D"},
    {"id": 17, "difficulty": "easy", "question": "Zero is rational:", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Never"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Which is rational? 2.5", "options": {"A": "Yes", "B": "No", "C": "Only integers", "D": "Only fractions"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Rational numbers are closed under addition:", "options": {"A": "True", "B": "False", "C": "Sometimes", "D": "Never"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Between any two rationals, there are:", "options": {"A": "Finite rationals", "B": "Infinite rationals", "C": "No rationals", "D": "Exactly one rational"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "Which is rational? √(4/9)", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Only if simplified"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Express 0.4777... as fraction", "options": {"A": "43/90", "B": "47/99", "C": "477/999", "D": "All wrong"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "A number is rational if its decimal expansion:", "options": {"A": "Terminates", "B": "Repeats", "C": "Either", "D": "Neither"}, "correct_answer": "C"},
    {"id": 24, "difficulty": "medium", "question": "Which is rational? (√2)²", "options": {"A": "2, yes", "B": "√4, no", "C": "Both same and rational", "D": "Irrational"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "Convert 1.08333... to fraction", "options": {"A": "13/12", "B": "108333/99999", "C": "1.08/1", "D": "65/60"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "The product of two rationals is:", "options": {"A": "Always rational", "B": "Sometimes irrational", "C": "Never irrational", "D": "A and C"}, "correct_answer": "D"},
    {"id": 27, "difficulty": "medium", "question": "Which rational between 1/3 and 1/2?", "options": {"A": "2/5", "B": "3/8", "C": "5/12", "D": "All"}, "correct_answer": "D"},
    {"id": 28, "difficulty": "medium", "question": "Express 2.135135... as fraction", "options": {"A": "711/333", "B": "2133/999", "C": "2 135/999", "D": "All correct"}, "correct_answer": "D"},
    {"id": 29, "difficulty": "medium", "question": "√0.04 is rational because:", "options": {"A": "0.2 = 1/5", "B": "Terminating decimal", "C": "Both", "D": "It's irrational"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "The sum of rational and irrational is:", "options": {"A": "Rational", "B": "Irrational", "C": "Either", "D": "Always irrational"}, "correct_answer": "D"},
    {"id": 31, "difficulty": "medium", "question": "Which is rational? 0.101101110...", "options": {"A": "Yes", "B": "No", "C": "If pattern emerges", "D": "Only terminating"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "Convert 0.428571428571... to fraction", "options": {"A": "3/7", "B": "428571/999999", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "The quotient of non-zero rationals is:", "options": {"A": "Rational", "B": "Irrational", "C": "Either", "D": "Never defined"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Find rational between √2 and √3", "options": {"A": "1.5", "B": "1.6", "C": "1.7", "D": "All"}, "correct_answer": "D"},
    {"id": 35, "difficulty": "medium", "question": "Express 0.579 as fraction", "options": {"A": "579/1000", "B": "193/333", "C": "Can't exact", "D": "A only"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Which operation on rationals may give irrational?", "options": {"A": "Addition", "B": "Subtraction", "C": "Multiplication", "D": "Division by zero", "E": "None of these with non-zero"}, "correct_answer": "E"},
    {"id": 37, "difficulty": "medium", "question": "Convert 0.41666... to fraction", "options": {"A": "5/12", "B": "41666/99999", "C": "0.41/0.99", "D": "25/60"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "The difference of two rationals is:", "options": {"A": "Always rational", "B": "Sometimes irrational", "C": "Never rational", "D": "Undefined"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Which is rational? 22/7", "options": {"A": "Yes", "B": "No, it's π", "C": "Approximation of π but rational", "D": "A and C"}, "correct_answer": "D"},
    {"id": 40, "difficulty": "medium", "question": "Express 3.142857142857... as fraction", "options": {"A": "22/7", "B": "3142857/999999", "C": "3 142857/999999", "D": "All"}, "correct_answer": "D"},
    {"id": 41, "difficulty": "medium", "question": "The additive inverse of a rational is:", "options": {"A": "Rational", "B": "Irrational", "C": "Same", "D": "Zero"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Find 3 rationals between 0.1 and 0.2", "options": {"A": "0.11,0.12,0.13", "B": "0.15,0.16,0.17", "C": "0.101,0.102,0.103", "D": "All correct"}, "correct_answer": "D"},
    {"id": 43, "difficulty": "medium", "question": "Convert 0.2666... to fraction", "options": {"A": "4/15", "B": "2666/9999", "C": "0.26/0.99", "D": "8/30"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Multiplicative inverse of 2/3 is:", "options": {"A": "3/2", "B": "-2/3", "C": "-3/2", "D": "0.666..."}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Which decimal is rational? 0.123456789", "options": {"A": "Yes, terminating", "B": "No, pattern", "C": "Maybe", "D": "Only if repeating"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Express 1.0625 as fraction", "options": {"A": "17/16", "B": "10625/10000", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "medium", "question": "Between 1/5 and 1/4, there are:", "options": {"A": "No rationals", "B": "Finite rationals", "C": "Infinite rationals", "D": "Exactly one"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "Convert 0.571428 to fraction (approximation)", "options": {"A": "4/7 ≈0.57142857", "B": "571428/1000000", "C": "Both", "D": "Neither exact"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "medium", "question": "The rational number 0 can be written as:", "options": {"A": "0/1", "B": "0/2", "C": "0/-5", "D": "All"}, "correct_answer": "D"},
    {"id": 50, "difficulty": "medium", "question": "Which is NOT always rational? √(p/q) where p,q integers", "options": {"A": "True", "B": "False", "C": "Sometimes", "D": "Only if p,q perfect squares"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Express 2.1333... as fraction", "options": {"A": "32/15", "B": "21333/9999", "C": "2.13/1", "D": "64/30"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Every integer n can be written as:", "options": {"A": "n/1", "B": "2n/2", "C": "-n/-1", "D": "All"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "medium", "question": "Which is rational? (√3)/(√12)", "options": {"A": "1/2, yes", "B": "√(1/4), yes", "C": "0.5, yes", "D": "All correct"}, "correct_answer": "D"},
    {"id": 54, "difficulty": "medium", "question": "Convert 0.818181... to fraction", "options": {"A": "9/11", "B": "81/99", "C": "8181/9999", "D": "All"}, "correct_answer": "D"},
    {"id": 55, "difficulty": "medium", "question": "The set of rational numbers is denoted by:", "options": {"A": "Q", "B": "R", "C": "Z", "D": "N"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Find rational number: (√16)/(√25)", "options": {"A": "4/5", "B": "0.8", "C": "16/25", "D": "All"}, "correct_answer": "D"},
    {"id": 57, "difficulty": "medium", "question": "Express 0.375 as fraction in lowest terms", "options": {"A": "3/8", "B": "375/1000", "C": "Both equivalent", "D": "Neither"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "Which property? a/b + c/d = (ad+bc)/(bd)", "options": {"A": "Closure", "B": "Commutative", "C": "Addition rule", "D": "Distributive"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "medium", "question": "Convert 1.1666... to fraction", "options": {"A": "7/6", "B": "11666/9999", "C": "1.16/1", "D": "14/12"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "The rational numbers are dense, meaning:", "options": {"A": "Between any two, there's another", "B": "They are continuous", "C": "They fill number line", "D": "All of these"}, "correct_answer": "D"},
    {"id": 61, "difficulty": "medium", "question": "Which is rational? 0.9 (repeating)", "options": {"A": "1", "B": "0.999...", "C": "Both represent same rational", "D": "Neither"}, "correct_answer": "C"},
    {"id": 62, "difficulty": "medium", "question": "Express 0.625 as fraction", "options": {"A": "5/8", "B": "625/1000", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 63, "difficulty": "medium", "question": "Find 5 rationals between -1 and 0", "options": {"A": "-0.1,-0.2,-0.3,-0.4,-0.5", "B": "-0.5,-0.25,-0.75,-0.9,-0.99", "C": "-1/2,-1/3,-1/4,-1/5,-1/6", "D": "All valid"}, "correct_answer": "D"},
    {"id": 64, "difficulty": "medium", "question": "Convert 0.20833... to fraction", "options": {"A": "5/24", "B": "20833/99999", "C": "0.208/1", "D": "10/48"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "a/b is rational if:", "options": {"A": "b≠0", "B": "a,b integers", "C": "Both", "D": "a,b real"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "Which decimal expansion indicates rational? 0.1010010001...", "options": {"A": "Yes", "B": "No", "C": "If pattern emerges", "D": "Only if terminates"}, "correct_answer": "B"},
    {"id": 67, "difficulty": "medium", "question": "Express 0.142857 as approximation of fraction", "options": {"A": "1/7 ≈0.14285714", "B": "142857/1000000", "C": "Both", "D": "Neither exact"}, "correct_answer": "C"},
    {"id": 68, "difficulty": "medium", "question": "The standard form of -12/18 is:", "options": {"A": "-2/3", "B": "-6/9", "C": "-12/18", "D": "All equivalent"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Convert 0.5333... to fraction", "options": {"A": "8/15", "B": "5333/9999", "C": "0.53/0.99", "D": "16/30"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "Every terminating decimal is rational:", "options": {"A": "True", "B": "False", "C": "Sometimes", "D": "Only if <1"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "Find rational: (√9 + √16)/(√25)", "options": {"A": "7/5", "B": "1.4", "C": "14/10", "D": "All"}, "correct_answer": "D"},
    {"id": 72, "difficulty": "medium", "question": "Express 0.2777... as fraction", "options": {"A": "5/18", "B": "2777/9999", "C": "0.27/0.99", "D": "10/36"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "The set Q is closed under:", "options": {"A": "+,-,×", "B": "÷ except by 0", "C": "Both", "D": "None"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "Which is rational? 0.00", "options": {"A": "0", "B": "Yes", "C": "Both A and B", "D": "No, it's undefined"}, "correct_answer": "C"},
    {"id": 75, "difficulty": "medium", "question": "Convert 1.8333... to fraction", "options": {"A": "11/6", "B": "18333/9999", "C": "1.83/1", "D": "22/12"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Between 0.33 and 0.34, rationals exist:", "options": {"A": "0.331,0.332,...", "B": "0.335", "C": "0.3333", "D": "All"}, "correct_answer": "D"},
    {"id": 77, "difficulty": "medium", "question": "Express 0.416 as fraction (not exact)", "options": {"A": "104/250", "B": "52/125", "C": "416/1000", "D": "All equivalent"}, "correct_answer": "D"},
    {"id": 78, "difficulty": "medium", "question": "The reciprocal of 0 is:", "options": {"A": "0", "B": "1", "C": "Undefined", "D": "Infinity"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "Convert 0.4666... to fraction", "options": {"A": "7/15", "B": "4666/9999", "C": "0.46/0.99", "D": "14/30"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "√(36/49) is rational:", "options": {"A": "6/7", "B": "0.857142...", "C": "Both represent same rational", "D": "All correct"}, "correct_answer": "D"},

    {"id": 81, "difficulty": "hard", "question": "Prove that between any two rationals a and b, there exists another rational", "options": {"A": "(a+b)/2", "B": "Take average", "C": "Both A and B", "D": "No such always exists"}, "correct_answer": "C"},
    {"id": 82, "difficulty": "hard", "question": "Show that 0.999... = 1 using rational number concept", "options": {"A": "Let x=0.999..., 10x=9.999..., subtract", "B": "1/3=0.333..., multiply by 3", "C": "Both proofs", "D": "It's not equal"}, "correct_answer": "C"},
    {"id": 83, "difficulty": "hard", "question": "Find a rational between √2 and √3 without using decimal", "options": {"A": "1.5", "B": "3/2", "C": "Both same", "D": "Can't find"}, "correct_answer": "C"},
    {"id": 84, "difficulty": "hard", "question": "Prove sum of rational and irrational is irrational", "options": {"A": "Assume sum rational, contradiction", "B": "Direct proof", "C": "Counterexample possible", "D": "Not always true"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "Express 3.142857142857... as fraction and show it's not π", "options": {"A": "22/7", "B": "Rational approximation", "C": "π is irrational", "D": "All correct"}, "correct_answer": "D"},
    {"id": 86, "difficulty": "hard", "question": "Find all rational roots of x²-2=0", "options": {"A": "None", "B": "±√2", "C": "±2", "D": "±1"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Show that the set {p/q: p,q integers, q≠0} is countable", "options": {"A": "Can be listed", "B": "Rationals are countable", "C": "Both", "D": "Uncountable"}, "correct_answer": "C"},
    {"id": 88, "difficulty": "hard", "question": "Prove product of non-zero rational and irrational is irrational", "options": {"A": "Assume product rational, contradiction", "B": "Direct proof", "C": "Sometimes rational", "D": "Always rational"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "Find rational number whose decimal expansion is 0.334334334...", "options": {"A": "334/999", "B": "Can be simplified", "C": "Both", "D": "Irrational"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "Show that between any two irrationals, there is a rational", "options": {"A": "Use decimal expansions", "B": "Archimedean property", "C": "Both methods", "D": "Not always true"}, "correct_answer": "C"},
    {"id": 91, "difficulty": "hard", "question": "Prove that √3 is irrational using rational number concepts", "options": {"A": "Assume √3 = p/q in lowest terms", "B": "Square both sides", "C": "Get contradiction", "D": "All steps"}, "correct_answer": "D"},
    {"id": 92, "difficulty": "hard", "question": "Find rational between 0.123123... and 0.124124...", "options": {"A": "0.1235", "B": "0.12361236...", "C": "Many exist", "D": "All correct"}, "correct_answer": "D"},
    {"id": 93, "difficulty": "hard", "question": "Show that the set of rationals has measure zero on real line", "options": {"A": "Countable sets have measure zero", "B": "Can be covered by intervals", "C": "Both", "D": "False statement"}, "correct_answer": "C"},
    {"id": 94, "difficulty": "hard", "question": "Prove that if x² is rational and x is irrational, then 1/x is irrational", "options": {"A": "Assume 1/x rational, then x rational", "B": "Contradiction", "C": "Both", "D": "Not necessarily true"}, "correct_answer": "C"},
    {"id": 95, "difficulty": "hard", "question": "Find all rational numbers p/q such that (p/q)² = 2", "options": {"A": "None", "B": "±√2", "C": "±2", "D": "±1.414"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "Show that between any two rationals, there's an irrational", "options": {"A": "Add √2/2^n between them", "B": "Use decimal construction", "C": "Both methods", "D": "Not always possible"}, "correct_answer": "C"},
    {"id": 97, "difficulty": "hard", "question": "Prove that the decimal 0.101001000100001... is irrational", "options": {"A": "Pattern but not periodic", "B": "Non-repeating", "C": "Both", "D": "Actually rational"}, "correct_answer": "C"},
    {"id": 98, "difficulty": "hard", "question": "Find rational approximation of √2 with error < 0.001", "options": {"A": "1414/1000", "B": "707/500", "C": "Many exist", "D": "All correct"}, "correct_answer": "D"},
    {"id": 99, "difficulty": "hard", "question": "Show that sum of two irrationals can be rational (give example)", "options": {"A": "√2 and -√2", "B": "π and -π", "C": "Both examples", "D": "Never happens"}, "correct_answer": "C"},
    {"id": 100, "difficulty": "hard", "question": "Prove that rational numbers satisfy field axioms", "options": {"A": "Closure, associativity, etc.", "B": "All except completeness", "C": "Both", "D": "They don't form field"}, "correct_answer": "C"}
  ]
}