{
  "title": "Pythagoras Theorem Applications - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Pythagoras theorem applies to which triangle? 📐", "options": {"A": "Any triangle", "B": "Right triangle", "C": "Equilateral", "D": "Isosceles"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "In right ΔABC, right angled at B, AC² = ? 🔺", "options": {"A": "AB² + BC²", "B": "AB² - BC²", "C": "BC² - AB²", "D": "AB × BC"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "If legs are 3cm and 4cm, hypotenuse = ? 📏", "options": {"A": "5cm", "B": "6cm", "C": "7cm", "D": "8cm"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "A triangle with sides 6,8,10 is? ✅", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Not a triangle"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "Hypotenuse is the side opposite to? 📍", "options": {"A": "Acute angle", "B": "Right angle", "C": "Obtuse angle", "D": "Largest angle"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "If hypotenuse is 13cm, one leg 5cm, other leg = ? 🔢", "options": {"A": "12cm", "B": "10cm", "C": "8cm", "D": "6cm"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "Pythagorean triplet: 5, ?, 13", "options": {"A": "10", "B": "11", "C": "12", "D": "14"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "In right triangle, square of hypotenuse equals sum of squares of? ➕", "options": {"A": "All sides", "B": "Other two sides", "C": "Base and height", "D": "Angles"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "Which is NOT a Pythagorean triplet? ❌", "options": {"A": "3,4,5", "B": "6,8,10", "C": "5,12,13", "D": "4,5,6"}, "correct_answer": "D"},
    {"id": 10, "difficulty": "easy", "question": "If a ladder 🪜 10m long reaches 8m high on wall, foot distance from wall? 🏠", "options": {"A": "6m", "B": "7m", "C": "8m", "D": "9m"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Diagonal of rectangle 3cm by 4cm is? 📐", "options": {"A": "5cm", "B": "6cm", "C": "7cm", "D": "8cm"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "In coordinate geometry, distance between (0,0) and (3,4) is? 📍", "options": {"A": "3", "B": "4", "C": "5", "D": "7"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "A triangle with sides 7,24,25 is? 🔺", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Not possible"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "If sides are 9,12,15, area = ? (1/2 × base × height) 📏", "options": {"A": "54", "B": "60", "C": "72", "D": "90"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Pythagoras theorem is used to find? 🎯", "options": {"A": "Heights", "B": "Distances", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "In 30-60-90 triangle, sides ratio is 1:√3:2. If shortest=5, hypotenuse=? 🔢", "options": {"A": "5√3", "B": "10", "C": "15", "D": "20"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "If diagonal of square is 10√2 cm, side = ? ⬛", "options": {"A": "5cm", "B": "10cm", "C": "15cm", "D": "20cm"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "A pole 🚩 broken at height 8m, top touches 6m from foot. Broken height? 🌳", "options": {"A": "10m", "B": "12m", "C": "14m", "D": "16m"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "Which set forms right triangle? 📐", "options": {"A": "2,3,4", "B": "5,6,7", "C": "8,15,17", "D": "9,10,11"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "Converse of Pythagoras theorem checks if triangle is? 🔄", "options": {"A": "Equilateral", "B": "Right", "C": "Isosceles", "D": "Acute"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "A man walks 14m west, then 48m north. How far from start? 🚶", "options": {"A": "50m", "B": "52m", "C": "54m", "D": "56m"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Ladder 🪜 17m long reaches window 15m high. Foot distance from wall?", "options": {"A": "6m", "B": "7m", "C": "8m", "D": "9m"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "Diagonal of cube with edge 3cm is? 🔲", "options": {"A": "3√2 cm", "B": "3√3 cm", "C": "6 cm", "D": "9 cm"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "In ΔABC, AB=6cm, BC=8cm, AC=10cm. Which angle is 90°? 📐", "options": {"A": "∠A", "B": "∠B", "C": "∠C", "D": "None"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "Two poles heights 12m & 20m, 16m apart. Top connecting rope length? 🚩", "options": {"A": "18m", "B": "20m", "C": "22m", "D": "24m"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "A rectangle's length is 24cm, diagonal 25cm. Breadth? 📏", "options": {"A": "5cm", "B": "6cm", "C": "7cm", "D": "8cm"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "Equilateral triangle side 6cm. Height? 🔺", "options": {"A": "3√3 cm", "B": "4√3 cm", "C": "5√3 cm", "D": "6√3 cm"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Distance between points (1,2) and (4,6) is? 📍", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "A kite 🪁 flying at height 60m with string 100m. Horizontal distance?", "options": {"A": "80m", "B": "90m", "C": "100m", "D": "120m"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "In rhombus with diagonals 10cm & 24cm, side length? ⬢", "options": {"A": "12cm", "B": "13cm", "C": "14cm", "D": "15cm"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "From top of 15m high building, ladder reaches ground 8m away. Ladder length? 🏢🪜", "options": {"A": "17m", "B": "18m", "C": "19m", "D": "20m"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Is triangle with sides 10cm, 24cm, 26cm right-angled? If yes, which angle?", "options": {"A": "Yes, at 10&24", "B": "Yes, at 24&26", "C": "Yes, at 10&26", "D": "No"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "A wire stretched from top of 12m pole to ground 5m away. Wire length? 🔌", "options": {"A": "13m", "B": "14m", "C": "15m", "D": "16m"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Diagonal of rectangular field 100m by 60m is? ⚽", "options": {"A": "116.6m", "B": "120m", "C": "125m", "D": "130m"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "In right isosceles triangle, each leg is 7cm. Hypotenuse? 🔺", "options": {"A": "7√2 cm", "B": "14 cm", "C": "7√3 cm", "D": "10 cm"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "A ship 🚢 sails 30km east, then 40km north. Distance from start?", "options": {"A": "50km", "B": "60km", "C": "70km", "D": "80km"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Height of equilateral triangle with side 10cm is? 📏", "options": {"A": "5√3 cm", "B": "10√3 cm", "C": "5 cm", "D": "10 cm"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "If diagonals of rhombus are 16cm & 30cm, perimeter? ⬢", "options": {"A": "68cm", "B": "72cm", "C": "76cm", "D": "80cm"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "From top of cliff ⛰️ 150m high, depression of boat is 30°. Boat distance?", "options": {"A": "150√3 m", "B": "300 m", "C": "150/√3 m", "D": "75√3 m"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "In ΔPQR, PQ=8cm, QR=15cm, PR=17cm. Area? 📐", "options": {"A": "60 cm²", "B": "68 cm²", "C": "120 cm²", "D": "136 cm²"}, "correct_answer": "A"},

    {"id": 41, "difficulty": "hard", "question": "Two towers heights 30m & 40m, 50m apart. Distance between tops? 🗼", "options": {"A": "50√2 m", "B": "50 m", "C": "60 m", "D": "70 m"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "A ladder 🪜 slides down wall. When foot is 6m from wall, top is 8m high. Original ladder length?", "options": {"A": "10m", "B": "12m", "C": "14m", "D": "16m"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "In ΔABC, AD⟂BC. If AB=10cm, BD=6cm, AD=8cm, find AC. 🔺", "options": {"A": "12cm", "B": "14cm", "C": "16cm", "D": "18cm"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "From point O, OA=3cm north, OB=4cm east. Distance AB? 🧭", "options": {"A": "5cm", "B": "6cm", "C": "7cm", "D": "8cm"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "In trapezium ABCD, AB∥CD, AB=10cm, CD=4cm, AD=5cm, BC=5cm. Height? 📐", "options": {"A": "3cm", "B": "4cm", "C": "5cm", "D": "6cm"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "hard", "question": "A wire from top of tower to ground makes 30° with ground. If wire is 200m, tower height? 🗼", "options": {"A": "100m", "B": "100√3 m", "C": "200/√3 m", "D": "150m"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "Diagonal of cuboid 12cm×9cm×8cm is? 📦", "options": {"A": "15cm", "B": "17cm", "C": "19cm", "D": "21cm"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "hard", "question": "In right Δ, median to hypotenuse is half of hypotenuse. If hypotenuse=26cm, median=? 📏", "options": {"A": "10cm", "B": "12cm", "C": "13cm", "D": "15cm"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "hard", "question": "Two circles radii 9cm & 4cm, centers 13cm apart. Length of direct common tangent? ⭕", "options": {"A": "12cm", "B": "13cm", "C": "14cm", "D": "15cm"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "In quadrilateral ABCD, AB=9cm, BC=12cm, CD=5cm, DA=8cm, AC=15cm. Area? 📐", "options": {"A": "66 cm²", "B": "72 cm²", "C": "78 cm²", "D": "84 cm²"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "A point inside rectangle is 5m from one corner, 12m from opposite corner. Distance from other corners if sides are integers? 📏", "options": {"A": "6 & 13", "B": "7 & 14", "C": "8 & 15", "D": "9 & 16"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "hard", "question": "In ΔABC, AB=AC=25cm, BC=14cm. Height from A? 🔺", "options": {"A": "20cm", "B": "22cm", "C": "24cm", "D": "26cm"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "hard", "question": "From top of lighthouse 🚨 100m high, depression of two ships are 30° & 45°. Distance between ships if on same side? 🚢", "options": {"A": "100(√3-1) m", "B": "100√3 m", "C": "100 m", "D": "200 m"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "In right Δ, incircle radius r=3cm, hypotenuse=15cm. Area? 🔺", "options": {"A": "36 cm²", "B": "42 cm²", "C": "48 cm²", "D": "54 cm²"}, "correct_answer": "D"},
    {"id": 55, "difficulty": "hard", "question": "A flagstaff on building subtends equal angles at two points. If points are 40m apart and angles 30°, flagstaff height? 🚩", "options": {"A": "20√3 m", "B": "40/√3 m", "C": "20 m", "D": "30 m"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "hard", "question": "In 3D, distance from origin to point (2,3,6) is? 📍", "options": {"A": "7", "B": "8", "C": "9", "D": "10"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "Two vertical poles are 20m apart. From midpoint, their tops have elevations 30° & 60°. Height difference? 🚩", "options": {"A": "20/√3 m", "B": "20√3 m", "C": "40/√3 m", "D": "10√3 m"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "A ladder length L rests against wall. If foot slips distance d, top slides distance h. Relation? 🪜", "options": {"A": "L² = (L-h)² + (d)²", "B": "L² = (L-d)² + (h)²", "C": "L² = (L-h)² + (L-d)²", "D": "Complex"}, "correct_answer": "D"},
    {"id": 59, "difficulty": "hard", "question": "In right Δ, altitude to hypotenuse divides it into segments 4cm & 9cm. Altitude length? 📏", "options": {"A": "6cm", "B": "7cm", "C": "8cm", "D": "9cm"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "Maximum distance between two points on cylinder of height 12cm, radius 5cm is? 🎯", "options": {"A": "13cm", "B": "17cm", "C": "√194 cm", "D": "24cm"}, "correct_answer": "C"}
  ]
}