{
  "title": "Operations on Real Numbers - Grade 9 CBSE",
  "total_questions": 60,
  "questions": [
    {
      "id": 1,
      "difficulty": "easy",
      "question": "What is √9 × √4?",
      "options": {
        "A": "6",
        "B": "12",
        "C": "36",
        "D": "3.5"
      },
      "correct_answer": "A"
    },
    {
      "id": 2,
      "difficulty": "easy",
      "question": "Simplify: √25 + √16",
      "options": {
        "A": "9",
        "B": "41",
        "C": "20",
        "D": "5"
      },
      "correct_answer": "B"
    },
    {
      "id": 3,
      "difficulty": "easy",
      "question": "What is 3√2 + 5√2?",
      "options": {
        "A": "8√2",
        "B": "15√2",
        "C": "8√4",
        "D": "15√4"
      },
      "correct_answer": "A"
    },
    {
      "id": 4,
      "difficulty": "easy",
      "question": "Simplify: √8 × √2",
      "options": {
        "A": "4",
        "B": "√16",
        "C": "√10",
        "D": "2√2"
      },
      "correct_answer": "A"
    },
    {
      "id": 5,
      "difficulty": "easy",
      "question": "What is 7√3 - 2√3?",
      "options": {
        "A": "5√3",
        "B": "9√3",
        "C": "5√9",
        "D": "9"
      },
      "correct_answer": "C"
    },
    {
      "id": 6,
      "difficulty": "easy",
      "question": "Simplify: (√5)²",
      "options": {
        "A": "5",
        "B": "25",
        "C": "√25",
        "D": "2√5"
      },
      "correct_answer": "B"
    },
    {
      "id": 7,
      "difficulty": "easy",
      "question": "What is √18 ÷ √2?",
      "options": {
        "A": "3",
        "B": "√9",
        "C": "√20",
        "D": "9"
      },
      "correct_answer": "A"
    },
    {
      "id": 8,
      "difficulty": "easy",
      "question": "Simplify: √50",
      "options": {
        "A": "5√2",
        "B": "25√2",
        "C": "10√5",
        "D": "2√25"
      },
      "correct_answer": "D"
    },
    {
      "id": 9,
      "difficulty": "easy",
      "question": "What is 2√6 × 3√6?",
      "options": {
        "A": "36",
        "B": "12√6",
        "C": "6√36",
        "D": "12"
      },
      "correct_answer": "A"
    },
    {
      "id": 10,
      "difficulty": "easy",
      "question": "Simplify: √12 + √27",
      "options": {
        "A": "5√3",
        "B": "√39",
        "C": "13√3",
        "D": "7√3"
      },
      "correct_answer": "C"
    },
    {
      "id": 11,
      "difficulty": "easy",
      "question": "What is 4√7 - √7?",
      "options": {
        "A": "3√7",
        "B": "4",
        "C": "3",
        "D": "√7"
      },
      "correct_answer": "B"
    },
    {
      "id": 12,
      "difficulty": "easy",
      "question": "Simplify: √72",
      "options": {
        "A": "6√2",
        "B": "8√9",
        "C": "12√6",
        "D": "36√2"
      },
      "correct_answer": "A"
    },
    {
      "id": 13,
      "difficulty": "easy",
      "question": "What is √3 × √12?",
      "options": {
        "A": "6",
        "B": "√15",
        "C": "√36",
        "D": "12"
      },
      "correct_answer": "D"
    },
    {
      "id": 14,
      "difficulty": "easy",
      "question": "Simplify: √20 - √5",
      "options": {
        "A": "√5",
        "B": "√15",
        "C": "2√5",
        "D": "0"
      },
      "correct_answer": "C"
    },
    {
      "id": 15,
      "difficulty": "easy",
      "question": "What is (2√3)²?",
      "options": {
        "A": "12",
        "B": "4√3",
        "C": "4√9",
        "D": "6"
      },
      "correct_answer": "A"
    },
    {
      "id": 16,
      "difficulty": "easy",
      "question": "Simplify: √8 + √18",
      "options": {
        "A": "5√2",
        "B": "√26",
        "C": "13√2",
        "D": "7√2"
      },
      "correct_answer": "D"
    },
    {
      "id": 17,
      "difficulty": "easy",
      "question": "What is √75 ÷ √3?",
      "options": {
        "A": "5",
        "B": "25",
        "C": "√25",
        "D": "√78"
      },
      "correct_answer": "A"
    },
    {
      "id": 18,
      "difficulty": "easy",
      "question": "Simplify: 3√5 × 2√5",
      "options": {
        "A": "30",
        "B": "6√5",
        "C": "6√25",
        "D": "15"
      },
      "correct_answer": "B"
    },
    {
      "id": 19,
      "difficulty": "easy",
      "question": "What is √98 simplified?",
      "options": {
        "A": "7√2",
        "B": "49√2",
        "C": "14√7",
        "D": "2√49"
      },
      "correct_answer": "C"
    },
    {
      "id": 20,
      "difficulty": "easy",
      "question": "Simplify: √45 - √20",
      "options": {
        "A": "√5",
        "B": "√25",
        "C": "5√5",
        "D": "0"
      },
      "correct_answer": "B"
    },
    {
      "id": 21,
      "difficulty": "medium",
      "question": "Simplify: (3 + √2)(3 - √2)",
      "options": {
        "A": "7",
        "B": "9 - 2√2",
        "C": "9 + 2√2",
        "D": "11"
      },
      "correct_answer": "C"
    },
    {
      "id": 22,
      "difficulty": "medium",
      "question": "Rationalize: 1/(√5 - 2)",
      "options": {
        "A": "√5 + 2",
        "B": "√5 - 2",
        "C": "1/(√5 + 2)",
        "D": "2 - √5"
      },
      "correct_answer": "A"
    },
    {
      "id": 23,
      "difficulty": "medium",
      "question": "Simplify: √(32) + √(18) - √(8)",
      "options": {
        "A": "5√2",
        "B": "7√2",
        "C": "3√2",
        "D": "√42"
      },
      "correct_answer": "D"
    },
    {
      "id": 24,
      "difficulty": "medium",
      "question": "What is (√7 + √3)²?",
      "options": {
        "A": "10 + 2√21",
        "B": "10",
        "C": "7 + 3 + 2√21",
        "D": "4 + 2√21"
      },
      "correct_answer": "B"
    },
    {
      "id": 25,
      "difficulty": "medium",
      "question": "Simplify: (2√6)/(√3)",
      "options": {
        "A": "2√2",
        "B": "2√3",
        "C": "√2",
        "D": "4"
      },
      "correct_answer": "A"
    },
    {
      "id": 26,
      "difficulty": "medium",
      "question": "Rationalize: 3/(√5 + √2)",
      "options": {
        "A": "√5 - √2",
        "B": "3(√5 - √2)/3",
        "C": "√5 + √2",
        "D": "3/(√5 - √2)"
      },
      "correct_answer": "C"
    },
    {
      "id": 27,
      "difficulty": "medium",
      "question": "Simplify: √(75) + √(48) - √(27)",
      "options": {
        "A": "6√3",
        "B": "4√3",
        "C": "8√3",
        "D": "10√3"
      },
      "correct_answer": "B"
    },
    {
      "id": 28,
      "difficulty": "medium",
      "question": "What is (√5 - √3)(√5 + √3)?",
      "options": {
        "A": "2",
        "B": "8",
        "C": "5 - 3",
        "D": "√2"
      },
      "correct_answer": "C"
    },
    {
      "id": 29,
      "difficulty": "medium",
      "question": "Simplify: √(1/4) + √(9/16)",
      "options": {
        "A": "5/4",
        "B": "1",
        "C": "3/2",
        "D": "7/4"
      },
      "correct_answer": "D"
    },
    {
      "id": 30,
      "difficulty": "medium",
      "question": "Rationalize: √2/(√6 - √2)",
      "options": {
        "A": "(√3 + 1)/2",
        "B": "(√3 - 1)/2",
        "C": "√3 + 1",
        "D": "√3 - 1"
      },
      "correct_answer": "A"
    },
    {
      "id": 31,
      "difficulty": "medium",
      "question": "Simplify: (√8 × √18)/√2",
      "options": {
        "A": "6",
        "B": "12",
        "C": "√6",
        "D": "6√2"
      },
      "correct_answer": "B"
    },
    {
      "id": 32,
      "difficulty": "medium",
      "question": "What is 1/(√7 - √6) rationalized?",
      "options": {
        "A": "√7 + √6",
        "B": "√7 - √6",
        "C": "1/(√7 + √6)",
        "D": "7 - 6"
      },
      "correct_answer": "D"
    },
    {
      "id": 33,
      "difficulty": "medium",
      "question": "Simplify: √(200) - √(72) + √(50)",
      "options": {
        "A": "9√2",
        "B": "11√2",
        "C": "7√2",
        "D": "5√2"
      },
      "correct_answer": "C"
    },
    {
      "id": 34,
      "difficulty": "medium",
      "question": "What is (2 + √3)²?",
      "options": {
        "A": "7 + 4√3",
        "B": "4 + 3 + 4√3",
        "C": "7",
        "D": "4 + 3"
      },
      "correct_answer": "A"
    },
    {
      "id": 35,
      "difficulty": "medium",
      "question": "Simplify: (√12 × √27)/√3",
      "options": {
        "A": "6",
        "B": "9",
        "C": "18",
        "D": "3√3"
      },
      "correct_answer": "D"
    },
    {
      "id": 36,
      "difficulty": "medium",
      "question": "Rationalize: 5/(√11 - √6)",
      "options": {
        "A": "√11 + √6",
        "B": "5(√11 + √6)/5",
        "C": "√11 - √6",
        "D": "5/(√11 + √6)"
      },
      "correct_answer": "B"
    },
    {
      "id": 37,
      "difficulty": "medium",
      "question": "Simplify: √(125) + √(45) - √(80)",
      "options": {
        "A": "4√5",
        "B": "6√5",
        "C": "8√5",
        "D": "2√5"
      },
      "correct_answer": "A"
    },
    {
      "id": 38,
      "difficulty": "medium",
      "question": "What is (√6 - 2)(√6 + 2)?",
      "options": {
        "A": "2",
        "B": "4",
        "C": "6 - 4",
        "D": "10"
      },
      "correct_answer": "B"
    },
    {
      "id": 39,
      "difficulty": "medium",
      "question": "Simplify: √(2/9) + √(8/25)",
      "options": {
        "A": "(5√2 + 6√2)/15",
        "B": "11√2/15",
        "C": "√10/15",
        "D": "2√2/3"
      },
      "correct_answer": "C"
    },
    {
      "id": 40,
      "difficulty": "medium",
      "question": "Rationalize: √3/(√12 - √3)",
      "options": {
        "A": "1",
        "B": "√3",
        "C": "√4 - 1",
        "D": "2 - √3"
      },
      "correct_answer": "D"
    },
    {
      "id": 41,
      "difficulty": "hard",
      "question": "Simplify: (√5 + √3)/(√5 - √3) + (√5 - √3)/(√5 + √3)",
      "options": {
        "A": "8",
        "B": "4",
        "C": "√15",
        "D": "2"
      },
      "correct_answer": "B"
    },
    {
      "id": 42,
      "difficulty": "hard",
      "question": "If x = √7 + √6 and y = √7 - √6, find x² + y²",
      "options": {
        "A": "26",
        "B": "28",
        "C": "30",
        "D": "32"
      },
      "correct_answer": "C"
    },
    {
      "id": 43,
      "difficulty": "hard",
      "question": "Simplify: (√2 + 1)/(√2 - 1) + (√2 - 1)/(√2 + 1)",
      "options": {
        "A": "6",
        "B": "4",
        "C": "2√2",
        "D": "8"
      },
      "correct_answer": "D"
    },
    {
      "id": 44,
      "difficulty": "hard",
      "question": "If a = 3 + 2√2, find 1/a",
      "options": {
        "A": "3 - 2√2",
        "B": "3 + 2√2",
        "C": "1/(3 - 2√2)",
        "D": "2√2 - 3"
      },
      "correct_answer": "A"
    },
    {
      "id": 45,
      "difficulty": "hard",
      "question": "Simplify: √(6 + √(20))",
      "options": {
        "A": "√5 + 1",
        "B": "√5 - 1",
        "C": "√3 + √2",
        "D": "√2 + √3"
      },
      "correct_answer": "B"
    },
    {
      "id": 46,
      "difficulty": "hard",
      "question": "If √x + √(x+3) = 3, find x",
      "options": {
        "A": "1",
        "B": "4",
        "C": "9",
        "D": "16"
      },
      "correct_answer": "C"
    },
    {
      "id": 47,
      "difficulty": "hard",
      "question": "Simplify: (√(10) + √(15))/(√(2) + √(3))",
      "options": {
        "A": "√5",
        "B": "√6",
        "C": "√2 + √3",
        "D": "√3 + √2"
      },
      "correct_answer": "D"
    },
    {
      "id": 48,
      "difficulty": "hard",
      "question": "If x = √(5 + 2√6), find x + 1/x",
      "options": {
        "A": "2√3",
        "B": "2√2",
        "C": "√3 + √2",
        "D": "√6"
      },
      "correct_answer": "B"
    },
    {
      "id": 49,
      "difficulty": "hard",
      "question": "Simplify: √(11 - 2√30)",
      "options": {
        "A": "√6 - √5",
        "B": "√6 + √5",
        "C": "√5 - √6",
        "D": "√30 - 1"
      },
      "correct_answer": "C"
    },
    {
      "id": 50,
      "difficulty": "hard",
      "question": "If a = 2 + √3, find a² + 1/a²",
      "options": {
        "A": "14",
        "B": "16",
        "C": "18",
        "D": "20"
      },
      "correct_answer": "D"
    },
    {
      "id": 51,
      "difficulty": "hard",
      "question": "Simplify: √(8 + 2√15)",
      "options": {
        "A": "√5 + √3",
        "B": "√5 - √3",
        "C": "√3 + √5",
        "D": "√15 + 1"
      },
      "correct_answer": "A"
    },
    {
      "id": 52,
      "difficulty": "hard",
      "question": "If √(x+9) - √x = 3, find x",
      "options": {
        "A": "0",
        "B": "1",
        "C": "4",
        "D": "9"
      },
      "correct_answer": "B"
    },
    {
      "id": 53,
      "difficulty": "hard",
      "question": "Simplify: (√(7) - √(5))/(√(7) + √(5)) + (√(7) + √(5))/(√(7) - √(5))",
      "options": {
        "A": "12",
        "B": "6",
        "C": "24",
        "D": "2"
      },
      "correct_answer": "A"
    },
    {
      "id": 54,
      "difficulty": "hard",
      "question": "If x = 1/(2 - √3), find x² - 4x + 1",
      "options": {
        "A": "0",
        "B": "1",
        "C": "2",
        "D": "3"
      },
      "correct_answer": "B"
    },
    {
      "id": 55,
      "difficulty": "hard",
      "question": "Simplify: √(14 - 4√6)",
      "options": {
        "A": "2√3 - √2",
        "B": "2√3 + √2",
        "C": "√12 - √2",
        "D": "√2 - 2√3"
      },
      "correct_answer": "D"
    },
    {
      "id": 56,
      "difficulty": "hard",
      "question": "If √(x+1) + √(x-1) = 2, find x",
      "options": {
        "A": "5/4",
        "B": "3/2",
        "C": "7/4",
        "D": "2"
      },
      "correct_answer": "C"
    },
    {
      "id": 57,
      "difficulty": "hard",
      "question": "Simplify: √(20 + 8√6)",
      "options": {
        "A": "2√3 + 2√2",
        "B": "2√3 - 2√2",
        "C": "4√3 + √2",
        "D": "√12 + √8"
      },
      "correct_answer": "B"
    },
    {
      "id": 58,
      "difficulty": "hard",
      "question": "If a = √(6 + √(11)) and b = √(6 - √(11)), find a² + b²",
      "options": {
        "A": "12",
        "B": "14",
        "C": "16",
        "D": "18"
      },
      "correct_answer": "A"
    },
    {
      "id": 59,
      "difficulty": "hard",
      "question": "Simplify: (3√2 - 2√3)/(3√2 + 2√3) + (3√2 + 2√3)/(3√2 - 2√3)",
      "options": {
        "A": "30",
        "B": "24",
        "C": "18",
        "D": "12"
      },
      "correct_answer": "C"
    },
    {
      "id": 60,
      "difficulty": "hard",
      "question": "If x = √(5 + √(21)), find x⁴ + 1/x⁴",
      "options": {
        "A": "322",
        "B": "324",
        "C": "326",
        "D": "328"
      },
      "correct_answer": "D"
    }
  ]
}