{
  "title": "Irrational Numbers - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Which of these is an irrational number?", "options": {"A": "√4", "B": "√9", "C": "√2", "D": "√16"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "π (pi) is:", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Natural number"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "Which number is irrational?", "options": {"A": "0.333...", "B": "0.5", "C": "√3", "D": "7/8"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "The decimal expansion of an irrational number is:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Terminating or repeating"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "Which is NOT an irrational number?", "options": {"A": "√5", "B": "√7", "C": "√25", "D": "√11"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "Irrational numbers can be expressed as:", "options": {"A": "p/q where q ≠ 0", "B": "p/q where p,q are integers", "C": "Cannot be expressed as p/q", "D": "Always as decimals"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "Which of these is rational?", "options": {"A": "π", "B": "√2", "C": "0.101001000...", "D": "3.14"}, "correct_answer": "D"},
    {"id": 8, "difficulty": "easy", "question": "√17 is:", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Natural"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "The number 0.101101110... is:", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Whole number"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "Which is an irrational number between 2 and 3?", "options": {"A": "2.5", "B": "√5", "C": "√4", "D": "2.333..."}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "Every irrational number is a:", "options": {"A": "Real number", "B": "Complex number", "C": "Integer", "D": "Whole number"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "√(9/16) is:", "options": {"A": "Irrational", "B": "Rational", "C": "Neither", "D": "Both"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "The sum of a rational and irrational number is:", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Natural"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Which is irrational?", "options": {"A": "0.75", "B": "√100", "C": "√8", "D": "4/5"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "The product of a non-zero rational and irrational number is:", "options": {"A": "Rational", "B": "Irrational", "C": "Zero", "D": "One"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "√50 is:", "options": {"A": "5√2, irrational", "B": "25, rational", "C": "5, rational", "D": "10, rational"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Which decimal represents an irrational number?", "options": {"A": "0.123123123...", "B": "0.1010010001...", "C": "0.5", "D": "0.625"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "The square root of a prime number is:", "options": {"A": "Always rational", "B": "Always irrational", "C": "Sometimes rational", "D": "Never irrational"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "√0.04 is:", "options": {"A": "0.2, rational", "B": "0.02, irrational", "C": "0.2, irrational", "D": "0.02, rational"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Which is NOT true about irrational numbers?", "options": {"A": "They are real numbers", "B": "They have non-terminating decimals", "C": "They can be negative", "D": "They can be expressed as p/q"}, "correct_answer": "D"},

    {"id": 21, "difficulty": "medium", "question": "Which of these is irrational? √(12/27)", "options": {"A": "2/3", "B": "√(4/9)", "C": "2/√3", "D": "0.666..."}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "The sum of √2 and √3 is:", "options": {"A": "√5", "B": "√6", "C": "Irrational", "D": "Rational"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "Prove that √5 is irrational. Which step is crucial?", "options": {"A": "Assume √5 = p/q", "B": "Assume √5 is rational", "C": "Square both sides", "D": "All of these"}, "correct_answer": "D"},
    {"id": 24, "difficulty": "medium", "question": "The product of √8 and √2 is:", "options": {"A": "4, rational", "B": "√16, irrational", "C": "4√2, irrational", "D": "√10, irrational"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Which is irrational? (√3 + 1)²", "options": {"A": "4 + 2√3", "B": "4", "C": "2√3", "D": "None, it's rational"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "The number 0.123456789101112... is:", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Natural"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "If x is irrational and y is rational, then x+y is:", "options": {"A": "Always rational", "B": "Always irrational", "C": "Sometimes rational", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "√(0.09) is:", "options": {"A": "0.3, rational", "B": "0.03, irrational", "C": "0.3, irrational", "D": "0.03, rational"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Which pair are both irrational? √2, √8", "options": {"A": "Yes", "B": "No, √8 = 2√2", "C": "No, both rational", "D": "No, √8 is rational"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "The decimal 0.12122122212222... is:", "options": {"A": "Terminating", "B": "Repeating", "C": "Non-repeating", "D": "Rational"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "(√3 - √2)(√3 + √2) =", "options": {"A": "1, rational", "B": "√6, irrational", "C": "5, rational", "D": "√5, irrational"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Which is an irrational number between 0 and 1?", "options": {"A": "0.5", "B": "√0.5", "C": "0.333...", "D": "1/3"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "If a is rational and b is irrational, then ab is:", "options": {"A": "Always irrational", "B": "Always rational", "C": "Rational if a=0", "D": "B and C"}, "correct_answer": "D"},
    {"id": 34, "difficulty": "medium", "question": "√(81/25) is:", "options": {"A": "9/5, rational", "B": "√81/√25, irrational", "C": "3.24, irrational", "D": "4.05, rational"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "The sum of 0.333... and √2 is:", "options": {"A": "Rational", "B": "Irrational", "C": "0.333...+√2", "D": "B and C"}, "correct_answer": "D"},
    {"id": 36, "difficulty": "medium", "question": "Which is false? Every irrational number is:", "options": {"A": "Real", "B": "Non-terminating decimal", "C": "Non-repeating decimal", "D": "Can be written as p/q"}, "correct_answer": "D"},
    {"id": 37, "difficulty": "medium", "question": "(√5 + 1)(√5 - 1) =", "options": {"A": "4, rational", "B": "√24, irrational", "C": "6, rational", "D": "5, rational"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "The number 1.010010001... is:", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Whole"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "If √n is irrational, then n must be:", "options": {"A": "Prime", "B": "Non-perfect square", "C": "Even", "D": "Odd"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "√(144/169) is:", "options": {"A": "12/13, rational", "B": "Irrational", "C": "12.3/13, irrational", "D": "1.2/1.3, rational"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Which expression is irrational? 2√3 × 3√3", "options": {"A": "18", "B": "6√3", "C": "6√9", "D": "18, rational"}, "correct_answer": "D"},
    {"id": 42, "difficulty": "medium", "question": "The difference of two irrational numbers is:", "options": {"A": "Always irrational", "B": "Always rational", "C": "Can be rational", "D": "Never zero"}, "correct_answer": "C"},
    {"id": 43, "difficulty": "medium", "question": "0.123123123... + √2 is:", "options": {"A": "Rational", "B": "Irrational", "C": "0.123...+√2", "D": "B and C"}, "correct_answer": "D"},
    {"id": 44, "difficulty": "medium", "question": "√50 + √18 =", "options": {"A": "8√2, irrational", "B": "√68, irrational", "C": "68, rational", "D": "8, rational"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "If x² = 7, then x is:", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Natural"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "medium", "question": "Which is rational? √(0.0081)", "options": {"A": "0.09", "B": "0.9", "C": "0.009", "D": "0.0009"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "The quotient of two irrational numbers can be:", "options": {"A": "Always irrational", "B": "Always rational", "C": "Rational or irrational", "D": "Never rational"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "√(1/4) is:", "options": {"A": "0.5, rational", "B": "1/2, irrational", "C": "√1/√4, irrational", "D": "0.25, rational"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "If √p is irrational, p can be:", "options": {"A": "4", "B": "9", "C": "12", "D": "16"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "Which is irrational? (√2 + √3)²", "options": {"A": "5 + 2√6", "B": "5", "C": "2√6", "D": "All are irrational"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "The number 0.10110111011110... is:", "options": {"A": "Rational", "B": "Irrational", "C": "Terminating", "D": "Repeating"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "√27/√3 =", "options": {"A": "3, rational", "B": "√9, irrational", "C": "√24, irrational", "D": "9, rational"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "If a and b are irrational, a+b can be:", "options": {"A": "Rational", "B": "Irrational", "C": "Either", "D": "Neither"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "medium", "question": "Which is an irrational number between √2 and √3?", "options": {"A": "1.5", "B": "√2.5", "C": "1.6", "D": "√1.6"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "(√8 × √18) is:", "options": {"A": "12, rational", "B": "√144, irrational", "C": "12√2, irrational", "D": "144, rational"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "The decimal expansion of √2 is:", "options": {"A": "1.41421356... non-repeating", "B": "1.41421356... repeating", "C": "1.414, terminating", "D": "1.41, terminating"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "√0.0009 is:", "options": {"A": "0.03, rational", "B": "0.003, irrational", "C": "0.03, irrational", "D": "0.003, rational"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "If √x is irrational, x cannot be:", "options": {"A": "2", "B": "3", "C": "5", "D": "9"}, "correct_answer": "D"},
    {"id": 59, "difficulty": "medium", "question": "Which sum is irrational? √2 + √2", "options": {"A": "2√2, irrational", "B": "√4, rational", "C": "2, rational", "D": "4, rational"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "The number 0.123456789 is:", "options": {"A": "Rational", "B": "Irrational", "C": "Terminating", "D": "A and C"}, "correct_answer": "D"},
    {"id": 61, "difficulty": "medium", "question": "√(32/2) =", "options": {"A": "4, rational", "B": "√16, irrational", "C": "4√2, irrational", "D": "16, rational"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "If a is irrational, 1/a is:", "options": {"A": "Always irrational", "B": "Always rational", "C": "Sometimes rational", "D": "Never defined"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Which is irrational? √(0.04)", "options": {"A": "0.2", "B": "1/5", "C": "20%", "D": "All are rational"}, "correct_answer": "D"},
    {"id": 64, "difficulty": "medium", "question": "The product of √12 and √3 is:", "options": {"A": "6, rational", "B": "√36, irrational", "C": "6√3, irrational", "D": "36, rational"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "0.121212... × √3 is:", "options": {"A": "Rational", "B": "Irrational", "C": "0.121212√3", "D": "B and C"}, "correct_answer": "D"},
    {"id": 66, "difficulty": "medium", "question": "√(1/9) is:", "options": {"A": "1/3, rational", "B": "0.333..., irrational", "C": "√1/√9, irrational", "D": "0.3, irrational"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "If n is not a perfect square, √n is:", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Natural"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "(√5 + 2)(√5 - 2) =", "options": {"A": "1, rational", "B": "9, rational", "C": "√21, irrational", "D": "3, rational"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "The decimal 0.101001000100001... is:", "options": {"A": "Terminating", "B": "Repeating", "C": "Non-repeating", "D": "Rational"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "√75 simplified is:", "options": {"A": "5√3, irrational", "B": "25√3, irrational", "C": "√25×3, rational", "D": "8.66, rational"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "Which is rational? √0.49", "options": {"A": "0.7", "B": "0.07", "C": "√49/√100", "D": "A and C"}, "correct_answer": "D"},
    {"id": 72, "difficulty": "medium", "question": "If x is irrational, x² can be:", "options": {"A": "Irrational only", "B": "Rational only", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "√(9/4) + √(16/25) =", "options": {"A": "3/2 + 4/5, rational", "B": "√(9/4 + 16/25), irrational", "C": "√(289/100), rational", "D": "A and C"}, "correct_answer": "D"},
    {"id": 74, "difficulty": "medium", "question": "The number 1.234567891011... is:", "options": {"A": "Rational", "B": "Irrational", "C": "Terminating", "D": "Repeating"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "√20 × √5 =", "options": {"A": "10, rational", "B": "√100, irrational", "C": "10√5, irrational", "D": "100, rational"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "If √a is irrational, a cannot be:", "options": {"A": "Prime", "B": "Composite", "C": "Perfect square", "D": "Odd"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "(√7 - √5)(√7 + √5) =", "options": {"A": "2, rational", "B": "√2, irrational", "C": "12, rational", "D": "√12, irrational"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "0.777... × √2 is:", "options": {"A": "Rational", "B": "Irrational", "C": "0.777...√2", "D": "B and C"}, "correct_answer": "D"},
    {"id": 79, "difficulty": "medium", "question": "√(0.64) is:", "options": {"A": "0.8, rational", "B": "0.08, irrational", "C": "0.8, irrational", "D": "0.08, rational"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "If a and b are irrational, a-b can be:", "options": {"A": "0", "B": "Rational", "C": "Irrational", "D": "All of these"}, "correct_answer": "D"},

    {"id": 81, "difficulty": "hard", "question": "Prove that 3 + √5 is irrational. Which assumption leads to contradiction?", "options": {"A": "Assume it's rational", "B": "Assume √5 is rational", "C": "Assume 3 is irrational", "D": "Assume it's integer"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "The sum of two irrational numbers √2 and 2-√2 is:", "options": {"A": "Irrational", "B": "Rational", "C": "2, rational", "D": "0, rational"}, "correct_answer": "C"},
    {"id": 83, "difficulty": "hard", "question": "Which is irrational? (√3 + √2)/(√3 - √2)", "options": {"A": "5 + 2√6", "B": "5", "C": "1", "D": "√6"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "If x = 1 + √2, then x² - 2x is:", "options": {"A": "1, rational", "B": "-1, rational", "C": "2√2, irrational", "D": "√2, irrational"}, "correct_answer": "B"},
    {"id": 85, "difficulty": "hard", "question": "The product of √(2 + √3) and √(2 - √3) is:", "options": {"A": "1, rational", "B": "√(4-3), rational", "C": "√1, rational", "D": "All of these"}, "correct_answer": "D"},
    {"id": 86, "difficulty": "hard", "question": "Which expression is rational? (√5 + 1)/(√5 - 1)", "options": {"A": "(3+√5)/2", "B": "3/2 + √5/2", "C": "Both are same and irrational", "D": "Actually rationalized gives rational"}, "correct_answer": "C"},
    {"id": 87, "difficulty": "hard", "question": "If a = √2 and b = √8, then a/b is:", "options": {"A": "0.5, rational", "B": "1/2, rational", "C": "√(1/4), rational", "D": "All of these"}, "correct_answer": "D"},
   {"id":88,"difficulty":"hard","question":"The number 0.1234567891011121314... is known as:","options":{"A":"Champernowne constant","B":"Liouville constant","C":"Euler's number","D":"Pi"},"correct_answer":"A"},
{"id":89,"difficulty":"hard","question":"If x = √7 - √5 and y = √7 + √5, then xy is:","options":{"A":"2, rational","B":"√2, irrational","C":"√12, irrational","D":"12, rational"},"correct_answer":"A"},
{"id":90,"difficulty":"hard","question":"Which is irrational? log₁₀2","options":{"A":"Always irrational","B":"Rational","C":"0.3010, rational","D":"Can be expressed as p/q"},"correct_answer":"A"},
{"id":91,"difficulty":"hard","question":"The value of (√6 + √3)² - (√6 - √3)² is:","options":{"A":"12, rational","B":"4√18, irrational","C":"√12, irrational","D":"6√2, irrational"},"correct_answer":"D"},
{"id":92,"difficulty":"hard","question":"If p and q are primes, √pq is:","options":{"A":"Always irrational","B":"Rational if p=q","C":"Irrational if p≠q","D":"All of these"},"correct_answer":"D"},
{"id":93,"difficulty":"hard","question":"The expression (√2 + √3)/(√2 - √3) rationalized is:","options":{"A":"-5 - 2√6","B":"5 + 2√6","C":"1","D":"-1"},"correct_answer":"A"},
{"id":94,"difficulty":"hard","question":"Which of these is always irrational? √p where p is:","options":{"A":"Even","B":"Odd","C":"Prime","D":"Non-perfect square"},"correct_answer":"D"},
{"id":95,"difficulty":"hard","question":"If x = 1/(√2 + 1), then x is:","options":{"A":"√2 - 1, irrational","B":"0.414..., irrational","C":"Cannot be simplified","D":"A and B"},"correct_answer":"D"},
{"id":96,"difficulty":"hard","question":"The sum of √45 and √125 is:","options":{"A":"8√5, irrational","B":"√170, irrational","C":"13√5, irrational","D":"√45+125, irrational"},"correct_answer":"A"},
{"id":97,"difficulty":"hard","question":"Which is true? Between any two irrationals, there is:","options":{"A":"A rational","B":"An irrational","C":"Both","D":"Neither"},"correct_answer":"C"},
{"id":98,"difficulty":"hard","question":"If a = √3 + √2 and b = √3 - √2, then a² + b² is:","options":{"A":"10, rational","B":"6 + 2√6, irrational","C":"12, rational","D":"8, rational"},"correct_answer":"A"},
{"id":99,"difficulty":"hard","question":"The number 0.101001000100001... is:","options":{"A":"Algebraic irrational","B":"Transcendental","C":"Rational","D":"Integer"},"correct_answer":"A"},
{"id":100,"difficulty":"hard","question":"Which operation on irrationals always gives irrational? √a × √b where a,b are:","options":{"A":"Primes","B":"Non-perfect squares","C":"Such that ab is non-perfect square","D":"Coprime"},"correct_answer":"C"}
]
}