{
  "title": "Representation of Real Numbers on Number Line - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "On a number line, √4 is located at:", "options": {"A": "2", "B": "1.414", "C": "Between 1 and 2", "D": "Between 2 and 3"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "√9 is represented on number line at:", "options": {"A": "3", "B": "2.236", "C": "Between 2 and 3", "D": "Between 3 and 4"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "The point representing 0 on number line is called:", "options": {"A": "Origin", "B": "Center", "C": "Midpoint", "D": "Zero point"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Which number lies between 2 and 3 on number line?", "options": {"A": "√2", "B": "√3", "C": "√5", "D": "√9"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "On number line, positive numbers are to the:", "options": {"A": "Left of 0", "B": "Right of 0", "C": "Above 0", "D": "Below 0"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Which is between 0 and 1 on number line?", "options": {"A": "√0.5", "B": "√4", "C": "√9", "D": "√16"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "The number √1 is at:", "options": {"A": "0", "B": "1", "C": "Between 0 and 1", "D": "Between -1 and 0"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "On number line, negative numbers are to the:", "options": {"A": "Right", "B": "Left", "C": "Above", "D": "Below"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "Which lies between 1 and 2?", "options": {"A": "√1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "The distance from 0 to 5 on number line is:", "options": {"A": "5 units", "B": "4 units", "C": "6 units", "D": "10 units"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "√0 is located at:", "options": {"A": "0", "B": "1", "C": "Between -1 and 1", "D": "Not on number line"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Between which integers does √10 lie?", "options": {"A": "1 and 2", "B": "2 and 3", "C": "3 and 4", "D": "4 and 5"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "The number -3 is on which side of 0?", "options": {"A": "Right", "B": "Left", "C": "Above", "D": "Below"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "√25 is exactly at:", "options": {"A": "5", "B": "Between 4 and 5", "C": "Between 5 and 6", "D": "25"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Which is NOT on number line?", "options": {"A": "2.5", "B": "-3", "C": "√2", "D": "All are on number line"}, "correct_answer": "D"},
    {"id": 16, "difficulty": "easy", "question": "Between 0 and -1, we can locate:", "options": {"A": "-0.5", "B": "-√2", "C": "-2", "D": "-3"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "√16/4 equals:", "options": {"A": "1", "B": "2", "C": "4", "D": "16"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "The number line extends:", "options": {"A": "Only to right", "B": "Only to left", "C": "Infinitely both sides", "D": "Up to 100"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "√100 is at:", "options": {"A": "10", "B": "Between 9 and 10", "C": "Between 10 and 11", "D": "100"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Every point on number line represents:", "options": {"A": "A natural number", "B": "An integer", "C": "A real number", "D": "A rational number"}, "correct_answer": "C"},

    {"id": 21, "difficulty": "medium", "question": "To represent √5 on number line, we first locate:", "options": {"A": "√4 and √9", "B": "2 and 3", "C": "Point 2", "D": "All of these"}, "correct_answer": "D"},
    {"id": 22, "difficulty": "medium", "question": "The geometric method to represent √n uses:", "options": {"A": "Right triangle", "B": "Circle", "C": "Square", "D": "Rectangle"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "To represent √3, we construct a right triangle with sides:", "options": {"A": "1 and √2", "B": "1 and 2", "C": "√2 and 1", "D": "2 and √2"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "√2 is represented using right triangle with sides:", "options": {"A": "1 and 1", "B": "1 and 2", "C": "2 and 2", "D": "1 and 3"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "For √6, we can use triangle with sides √2 and:", "options": {"A": "2", "B": "√3", "C": "√4", "D": "√5"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "The spiral of Theodorus is used to represent:", "options": {"A": "Rational numbers", "B": "Square roots", "C": "Integers", "D": "Fractions"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "To locate √7 on number line, we need hypotenuse of triangle with legs:", "options": {"A": "√6 and 1", "B": "√5 and √2", "C": "2 and √3", "D": "Any of these"}, "correct_answer": "D"},
    {"id": 28, "difficulty": "medium", "question": "The point representing √10 is between:", "options": {"A": "3 and 3.1", "B": "3.1 and 3.2", "C": "3.16 and 3.17", "D": "3 and 4"}, "correct_answer": "D"},
    {"id": 29, "difficulty": "medium", "question": "For √13, we can use triangle with sides 3 and:", "options": {"A": "2", "B": "√4", "C": "√3", "D": "√2"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "The method to represent √n is based on:", "options": {"A": "Pythagoras theorem", "B": "Euclid's algorithm", "C": "Prime factorization", "D": "Decimal expansion"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "√8 can be located using triangle with sides:", "options": {"A": "2 and 2", "B": "√7 and 1", "C": "√4 and 2", "D": "All of these"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Between which two integers does √17 lie?", "options": {"A": "3 and 4", "B": "4 and 5", "C": "5 and 6", "D": "6 and 7"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "To represent √11, we can use legs:", "options": {"A": "√10 and 1", "B": "3 and √2", "C": "√9 and √2", "D": "Any of these"}, "correct_answer": "D"},
    {"id": 34, "difficulty": "medium", "question": "The exact position of √2 is found by drawing:", "options": {"A": "A square of side 1", "B": "A right triangle with sides 1,1", "C": "An arc from origin", "D": "All of these"}, "correct_answer": "D"},
    {"id": 35, "difficulty": "medium", "question": "√18 is between:", "options": {"A": "3 and 4", "B": "4 and 5", "C": "5 and 6", "D": "6 and 7"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "For √15, suitable triangle has legs:", "options": {"A": "√14 and 1", "B": "3 and √6", "C": "√9 and √6", "D": "All work"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "√20 is located between:", "options": {"A": "4 and 5", "B": "5 and 6", "C": "6 and 7", "D": "7 and 8"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "The construction for √n always gives:", "options": {"A": "Exact point", "B": "Approximation", "C": "Irrational point", "D": "A and C"}, "correct_answer": "D"},
    {"id": 39, "difficulty": "medium", "question": "√24 lies between:", "options": {"A": "4 and 5", "B": "5 and 6", "C": "6 and 7", "D": "7 and 8"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "For √26, we can use right triangle with sides 5 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "√28 is between:", "options": {"A": "4 and 5", "B": "5 and 6", "C": "6 and 7", "D": "7 and 8"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "The point for √30 is closer to:", "options": {"A": "5", "B": "5.5", "C": "6", "D": "6.5"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "For √32, triangle could have sides √31 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "√35 lies between:", "options": {"A": "5 and 6", "B": "6 and 7", "C": "7 and 8", "D": "8 and 9"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "To locate √40, we might use sides √36 and:", "options": {"A": "2", "B": "√3", "C": "√4", "D": "√5"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "√45 is between:", "options": {"A": "5 and 6", "B": "6 and 7", "C": "7 and 8", "D": "8 and 9"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "For √48, triangle could have sides √47 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "√50 is closest to:", "options": {"A": "7", "B": "7.07", "C": "7.5", "D": "8"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "For √52, we can use sides 7 and:", "options": {"A": "√3", "B": "√4", "C": "√5", "D": "√6"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "√54 is between:", "options": {"A": "6 and 7", "B": "7 and 8", "C": "8 and 9", "D": "9 and 10"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "For √56, suitable legs are √55 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "√60 is closer to:", "options": {"A": "7.5", "B": "7.75", "C": "7.85", "D": "8"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "For √63, triangle could have sides √62 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "√65 lies between:", "options": {"A": "7 and 8", "B": "8 and 9", "C": "9 and 10", "D": "10 and 11"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "To represent √68, we might use sides 8 and:", "options": {"A": "2", "B": "√3", "C": "√4", "D": "√5"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "√70 is between:", "options": {"A": "8 and 9", "B": "9 and 10", "C": "10 and 11", "D": "11 and 12"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "For √72, triangle could have sides √71 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "√75 is closest to:", "options": {"A": "8.5", "B": "8.66", "C": "8.75", "D": "9"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "medium", "question": "For √78, we can use sides √77 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "√80 lies between:", "options": {"A": "8 and 9", "B": "9 and 10", "C": "10 and 11", "D": "11 and 12"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "For √84, suitable legs are √83 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "√85 is closer to:", "options": {"A": "9.1", "B": "9.2", "C": "9.22", "D": "9.3"}, "correct_answer": "C"},
    {"id": 63, "difficulty": "medium", "question": "For √88, triangle could have sides √87 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "√90 is between:", "options": {"A": "9 and 10", "B": "10 and 11", "C": "11 and 12", "D": "12 and 13"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "To represent √92, we might use sides √91 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "√95 lies between:", "options": {"A": "9 and 10", "B": "10 and 11", "C": "11 and 12", "D": "12 and 13"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "For √96, triangle could have sides √95 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "√98 is closest to:", "options": {"A": "9.8", "B": "9.9", "C": "9.95", "D": "10"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "For √99, we can use sides √98 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "√101 is between:", "options": {"A": "10 and 11", "B": "11 and 12", "C": "12 and 13", "D": "13 and 14"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "For √104, suitable legs are √103 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "√105 is closer to:", "options": {"A": "10.2", "B": "10.25", "C": "10.3", "D": "10.35"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "For √108, triangle could have sides √107 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "√110 lies between:", "options": {"A": "10 and 11", "B": "11 and 12", "C": "12 and 13", "D": "13 and 14"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "To represent √112, we might use sides √111 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "√115 is between:", "options": {"A": "10 and 11", "B": "11 and 12", "C": "12 and 13", "D": "13 and 14"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "For √117, triangle could have sides √116 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "√120 is closest to:", "options": {"A": "10.9", "B": "10.95", "C": "11", "D": "11.05"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "For √122, we can use sides √121 and:", "options": {"A": "1", "B": "√2", "C": "√3", "D": "√4"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "√124 is between:", "options": {"A": "11 and 12", "B": "12 and 13", "C": "13 and 14", "D": "14 and 15"}, "correct_answer": "A"},

    {"id": 81, "difficulty": "hard", "question": "Represent √2 + √3 on number line. Which is true?", "options": {"A": "Construct √2, then from that point construct √3", "B": "Add decimals and plot", "C": "Find hypotenuse of triangle with legs √2 and √3", "D": "All methods work"}, "correct_answer": "D"},
    {"id": 82, "difficulty": "hard", "question": "To represent 2+√5, we first locate √5 from:", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "C"},
    {"id": 83, "difficulty": "hard", "question": "The point representing π can be located:", "options": {"A": "Exactly using compass", "B": "Approximately as 3.14", "C": "Using special construction", "D": "B and C"}, "correct_answer": "B"},
    {"id": 84, "difficulty": "hard", "question": "Represent √(√2) on number line. What's the first step?", "options": {"A": "Locate √2", "B": "Locate 1.414", "C": "Construct right angle", "D": "Draw circle"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "For √(3+√5), we need to first construct:", "options": {"A": "√5", "B": "3+√5", "C": "√(3+√5) directly", "D": "A then B then take square root"}, "correct_answer": "D"},
    {"id": 86, "difficulty": "hard", "question": "To locate √2 × √3 = √6, we can:", "options": {"A": "Multiply decimals", "B": "Construct √6 directly", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 87, "difficulty": "hard", "question": "The golden ratio φ = (1+√5)/2 can be located by:", "options": {"A": "First locating √5", "B": "Using geometric mean", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 88, "difficulty": "hard", "question": "Represent 1/√2 on number line by:", "options": {"A": "Locating √2 then taking reciprocal", "B": "Constructing right isosceles triangle", "C": "Using unit circle", "D": "All of these"}, "correct_answer": "D"},
    {"id": 89, "difficulty": "hard", "question": "For √(10-√84), we simplify to √(√7-√3)² = √7-√3. How to locate?", "options": {"A": "Locate √7 and √3 separately", "B": "Find difference", "C": "Both", "D": "Can't represent difference"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "The number √2 + 1/√2 can be located by:", "options": {"A": "Finding decimal", "B": "Geometric construction", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 91, "difficulty": "hard", "question": "To represent cube root of 2, we need:", "options": {"A": "Different construction", "B": "Approximation", "C": "Both", "D": "Impossible"}, "correct_answer": "B"},
    {"id": 92, "difficulty": "hard", "question": "The point for e (Euler's number) is located:", "options": {"A": "Exactly at 2.71828", "B": "Approximately", "C": "Using special construction", "D": "B and C"}, "correct_answer": "B"},
    {"id": 93, "difficulty": "hard", "question": "Represent √(4+2√3) = 1+√3. Construction involves:", "options": {"A": "Locating √3", "B": "Adding 1", "C": "Both", "D": "Direct from expression"}, "correct_answer": "C"},
    {"id": 94, "difficulty": "hard", "question": "For √(7+4√3) = 2+√3, we can:", "options": {"A": "Simplify then locate", "B": "Direct construction", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 95, "difficulty": "hard", "question": "The number (√5-1)/2 (reciprocal of golden ratio) is between:", "options": {"A": "0 and 0.5", "B": "0.5 and 0.6", "C": "0.6 and 0.7", "D": "0.7 and 0.8"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "To represent √(2+√3), first step is:", "options": {"A": "Locate √3", "B": "Locate 2+√3", "C": "Take square root", "D": "All in sequence"}, "correct_answer": "D"},
    {"id": 97, "difficulty": "hard", "question": "The point for log₁₀2 (≈0.3010) can be:", "options": {"A": "Located exactly", "B": "Approximated", "C": "Constructed geometrically", "D": "B and C"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "Represent √(5-2√6) = √3-√2. How?", "options": {"A": "Locate √3 and √2", "B": "Find difference", "C": "Both", "D": "Difference can't be on number line"}, "correct_answer": "C"},
    {"id": 99, "difficulty": "hard", "question": "For √(9+4√5) = 2+√5, construction requires:", "options": {"A": "√5 then add 2", "B": "Direct from expression", "C": "Both work", "D": "Neither works"}, "correct_answer": "C"},
    {"id": 100, "difficulty": "hard", "question": "The number √(6-2√5) = √5-1 is located by:", "options": {"A": "Finding √5", "B": "Subtracting 1", "C": "Both", "D": "Can't represent negative result"}, "correct_answer": "C"}
  ]
}