{
  "title": "Pythagoras Theorem - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "📐 Pythagoras theorem applies to which type of triangle?", "options": {"A": "Any triangle", "B": "Right-angled triangle", "C": "Isosceles triangle", "D": "Equilateral triangle"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "🔺 In a right triangle, the side opposite the right angle is called the...", "options": {"A": "Base", "B": "Perpendicular", "C": "Hypotenuse", "D": "Leg"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "✅ In the formula a² + b² = c², 'c' represents the length of the...", "options": {"A": "Shorter side", "B": "Hypotenuse", "C": "Perpendicular", "D": "Base"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "📏 If a triangle has sides 3 cm, 4 cm, and 5 cm, it is a right triangle. Which side is the hypotenuse?", "options": {"A": "3 cm", "B": "4 cm", "C": "5 cm", "D": "Cannot say"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "🔺 The Pythagorean triplet (3, 4, 5) satisfies 3² + 4² = ?", "options": {"A": "5", "B": "25", "C": "7", "D": "9"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "✅ If the legs of a right triangle are 6 and 8, the hypotenuse is...", "options": {"A": "10", "B": "14", "C": "100", "D": "48"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "📐 A triangle with sides 6, 8, 10 is a right triangle because 6² + 8² = ?", "options": {"A": "10", "B": "100", "C": "36", "D": "64"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "🔺 Which of the following is a Pythagorean triplet?", "options": {"A": "2, 3, 4", "B": "5, 12, 13", "C": "7, 9, 11", "D": "8, 15, 16"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "✅ In a right triangle, if one leg is 9 and hypotenuse is 15, the other leg is...", "options": {"A": "6", "B": "12", "C": "18", "D": "24"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "📏 The hypotenuse is always the... side in a right triangle.", "options": {"A": "shortest", "B": "longest", "C": "same as legs", "D": "middle"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "🔺 If the base is 5 and perpendicular is 12, the hypotenuse is...", "options": {"A": "13", "B": "17", "C": "25", "D": "60"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "✅ The converse of Pythagoras theorem helps determine if a triangle is...", "options": {"A": "equilateral", "B": "isosceles", "C": "right-angled", "D": "acute"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "📐 A triangle with sides 5, 12, 13 is right-angled because 5² + 12² = ?", "options": {"A": "13", "B": "169", "C": "25", "D": "144"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "🔺 If a right triangle has legs of equal length, it is...", "options": {"A": "scalene", "B": "isosceles right triangle", "C": "equilateral", "D": "obtuse"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "✅ In an isosceles right triangle, if each leg is 1, the hypotenuse is √2. (True/False)", "options": {"A": "True", "B": "False", "C": "Sometimes", "D": "Only if base is 1"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "📏 Which set could be sides of a right triangle?", "options": {"A": "1, 2, 3", "B": "2, 3, 4", "C": "3, 4, 5", "D": "4, 5, 6"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "🔺 If hypotenuse is 10 and one leg is 6, the other leg is...", "options": {"A": "4", "B": "8", "C": "12", "D": "16"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "✅ The Pythagorean theorem is named after a mathematician from...", "options": {"A": "India", "B": "Greece", "C": "China", "D": "Egypt"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "📐 In a right triangle, the square on the hypotenuse equals the sum of squares on the other two sides. This is...", "options": {"A": "always true", "B": "sometimes true", "C": "never true", "D": "only for isosceles"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "🔺 If a triangle has sides 9, 40, 41, it is right-angled. The hypotenuse is...", "options": {"A": "9", "B": "40", "C": "41", "D": "None"}, "correct_answer": "C"},
    {"id": 21, "difficulty": "medium", "question": "📐 A ladder 10 m long reaches a window 8 m above the ground. How far is the foot of the ladder from the wall?", "options": {"A": "2 m", "B": "6 m", "C": "10 m", "D": "12 m"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "🔺 In a right triangle, if one acute angle is 45°, then the sides are in ratio...", "options": {"A": "1:1:√2", "B": "1:√3:2", "C": "3:4:5", "D": "5:12:13"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "✅ The diagonal of a rectangle of sides 6 and 8 is...", "options": {"A": "10", "B": "14", "C": "28", "D": "100"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "📏 Which triangle with given sides is not right-angled?", "options": {"A": "7, 24, 25", "B": "8, 15, 17", "C": "9, 40, 41", "D": "10, 24, 25"}, "correct_answer": "D"},
    {"id": 25, "difficulty": "medium", "question": "🔺 In an isosceles right triangle, the hypotenuse is 10√2. Each leg is...", "options": {"A": "5", "B": "10", "C": "5√2", "D": "20"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "✅ A triangle with sides 8, 15, 17 is right-angled. The right angle is opposite side...", "options": {"A": "8", "B": "15", "C": "17", "D": "Cannot say"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "📐 If the sides of a triangle are 5, k, 13 and it is right-angled, k could be...", "options": {"A": "12", "B": "8", "C": "18", "D": "Both A and B"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "🔺 The hypotenuse of a right triangle is 25. One leg is 7. The other leg is...", "options": {"A": "24", "B": "18", "C": "√674", "D": "32"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "✅ In a right triangle, if the legs are x and x+1, and hypotenuse is x+2, find x.", "options": {"A": "1", "B": "3", "C": "5", "D": "7"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "📏 A man walks 15 m east and 8 m north. How far is he from the starting point?", "options": {"A": "17 m", "B": "23 m", "C": "7 m", "D": "20 m"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "🔺 If the diagonal of a square is 10√2 cm, its side is...", "options": {"A": "5 cm", "B": "10 cm", "C": "10√2 cm", "D": "20 cm"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "✅ In triangle ABC, right-angled at B, if AB=6 cm, BC=8 cm, then AC=?", "options": {"A": "10 cm", "B": "14 cm", "C": "20 cm", "D": "24 cm"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "📐 A 26 m long ladder reaches a window 24 m high. Distance of foot from wall is...", "options": {"A": "10 m", "B": "12 m", "C": "14 m", "D": "20 m"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "🔺 Which of the following is NOT a Pythagorean triplet?", "options": {"A": "20, 21, 29", "B": "11, 60, 61", "C": "13, 84, 85", "D": "16, 63, 65"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "✅ In a right triangle, the hypotenuse is 10 and one leg is 8. The area is...", "options": {"A": "24", "B": "40", "C": "30", "D": "48"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "medium", "question": "📏 If a triangle has sides 2.5, 6, 6.5, is it right-angled?", "options": {"A": "Yes", "B": "No", "C": "Only if scaled", "D": "Cannot say"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "🔺 The sides of a triangle are 10, 24, 26. The triangle is...", "options": {"A": "acute", "B": "obtuse", "C": "right", "D": "isosceles"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "✅ In an equilateral triangle of side 'a', the altitude is...", "options": {"A": "a√3/2", "B": "a/2", "C": "a√2", "D": "a"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "📐 A rectangle has length 15 and width 8. The length of its diagonal is...", "options": {"A": "17", "B": "23", "C": "20", "D": "30"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "🔺 In a right triangle, if one acute angle is 30°, the sides are in ratio 1:√3:2. If the side opposite 30° is 5, hypotenuse is...", "options": {"A": "5√3", "B": "10", "C": "15", "D": "5"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "hard", "question": "📐 In triangle ABC, ∠B=90°, AB=9, AC=15. Find BC.", "options": {"A": "12", "B": "10", "C": "8", "D": "6"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "🔺 A wire stretched from top of a 12 m pole to a point on ground 5 m away from foot of pole. Length of wire?", "options": {"A": "13 m", "B": "15 m", "C": "17 m", "D": "20 m"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "✅ In an isosceles triangle, base=16 cm, equal sides=17 cm. Find height.", "options": {"A": "8 cm", "B": "15 cm", "C": "20 cm", "D": "30 cm"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "hard", "question": "📏 Find the perimeter of a rhombus with diagonals 10 and 24.", "options": {"A": "52", "B": "48", "C": "68", "D": "100"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "🔺 In triangle PQR, right-angled at Q, PR=25, PQ=24. The length of QR is?", "options": {"A": "1", "B": "7", "C": "49", "D": "√49"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "hard", "question": "✅ A triangle has sides 7, 24, 25. Its area is...", "options": {"A": "84", "B": "168", "C": "100", "D": "50"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "📐 The sides of a triangle are in ratio 3:4:5. If perimeter is 72, the sides are...", "options": {"A": "18, 24, 30", "B": "15, 20, 25", "C": "9, 12, 15", "D": "27, 36, 45"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "🔺 In a right triangle, the median to the hypotenuse is half the hypotenuse. If hypotenuse=26, median=?", "options": {"A": "13", "B": "26", "C": "10", "D": "24"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "✅ A point is 8 cm away from center of circle of radius 6 cm. Find shortest distance from point to circle.", "options": {"A": "2 cm", "B": "4 cm", "C": "10 cm", "D": "14 cm"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "📏 In an equilateral triangle of side 10 cm, the altitude is...", "options": {"A": "5√3 cm", "B": "10√3 cm", "C": "5 cm", "D": "10 cm"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "🔺 A ladder 17 m long reaches a window 15 m high. The distance of foot from wall is...", "options": {"A": "8 m", "B": "10 m", "C": "12 m", "D": "14 m"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "✅ In a right triangle, the altitude to the hypotenuse divides it into segments 4 and 9. The altitude is...", "options": {"A": "6", "B": "13", "C": "√36", "D": "√52"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "📐 The diagonal of a square is 12√2 cm. Its area is...", "options": {"A": "144 cm²", "B": "72 cm²", "C": "48 cm²", "D": "24 cm²"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "🔺 In triangle ABC, AB=AC=25 cm, BC=14 cm. Find the length of altitude from A.", "options": {"A": "24 cm", "B": "20 cm", "C": "15 cm", "D": "10 cm"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "✅ A rectangular field is 30 m long and 16 m wide. Diagonal length?", "options": {"A": "34 m", "B": "46 m", "C": "50 m", "D": "60 m"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "📏 In an isosceles right triangle, area=32 cm². Length of hypotenuse?", "options": {"A": "8√2 cm", "B": "16 cm", "C": "8 cm", "D": "12 cm"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "🔺 A triangle with sides 11, 60, 61 is right-angled. The right angle is opposite side...", "options": {"A": "11", "B": "60", "C": "61", "D": "None"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "hard", "question": "✅ The distance between opposite corners of a rectangular box 3×4×12 is...", "options": {"A": "13", "B": "15", "C": "17", "D": "19"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "📐 In a right triangle, the hypotenuse is 13 and one leg is 5. The altitude to the hypotenuse is...", "options": {"A": "60/13", "B": "12", "C": "13/2", "D": "5"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "✅ Which of the following triangles is right-angled? (Sides given)", "options": {"A": "10, 24, 26", "B": "12, 35, 37", "C": "9, 40, 41", "D": "All of these"}, "correct_answer": "D"}
  ]
}