{
  "title": "Heights and Distances - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "A ladder 10m long rests against a wall making 60° with ground. Height reached on wall:", "options": {"A": "5 m", "B": "5√3 m", "C": "10√3 m", "D": "20 m"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "A tree breaks and top touches ground 10m from foot making 30°. Original height:", "options": {"A": "10√3 m", "B": "20/√3 m", "C": "15 m", "D": "20 m"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "From point 20m from tower, angle of elevation=30°. Tower height:", "options": {"A": "20/√3 m", "B": "20√3 m", "C": "40 m", "D": "10√3 m"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "A kite string 100m makes 60° with ground. Kite height:", "options": {"A": "50 m", "B": "50√3 m", "C": "100/√3 m", "D": "100 m"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "Two poles 6m and 11m tall. If distance between=10m, distance between tops:", "options": {"A": "5√5 m", "B": "12 m", "C": "13 m", "D": "15 m"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Shadow of 10m pole is 10√3m. Sun's elevation:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "From top of 50m tower, angle of depression to car=45°. Car distance:", "options": {"A": "25 m", "B": "50 m", "C": "75 m", "D": "100 m"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "A man 1.8m tall sees top of pole at 45°. If 10m from pole, pole height:", "options": {"A": "10 m", "B": "11.8 m", "C": "12 m", "D": "13.8 m"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "From ship, lighthouse top at 30° elevation. Lighthouse 60m. Distance:", "options": {"A": "60√3 m", "B": "120 m", "C": "60/√3 m", "D": "30√3 m"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Two buildings 20m apart. From top of 15m building, angle of depression to top of other=30°. Other building height:", "options": {"A": "15-20/√3 m", "B": "15+20/√3 m", "C": "20√3 m", "D": "35 m"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "A ladder makes 60° with ground. If foot 2m from wall, length:", "options": {"A": "2 m", "B": "4 m", "C": "2√3 m", "D": "4/√3 m"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "From point, elevation=45°. Moving 10m closer makes 60°. Initial distance:", "options": {"A": "5(3+√3) m", "B": "10(√3+1) m", "C": "15 m", "D": "20 m"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Height of tower when shadow=height:", "options": {"A": "Any", "B": "Double", "C": "Half", "D": "√3 times"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "From top of 30m tower, depression to object=60°. Object distance:", "options": {"A": "30/√3 m", "B": "30√3 m", "C": "60 m", "D": "15√3 m"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Two vertical poles 15m apart. Heights 10m,20m. Distance between tops:", "options": {"A": "5√10 m", "B": "15√2 m", "C": "25 m", "D": "5√13 m"}, "correct_answer": "D"},
    {"id": 16, "difficulty": "easy", "question": "A 5m ladder reaches window 4m high. Angle with ground:", "options": {"A": "sin⁻¹(4/5)", "B": "cos⁻¹(3/5)", "C": "tan⁻¹(4/3)", "D": "All"}, "correct_answer": "D"},
    {"id": 17, "difficulty": "easy", "question": "From airplane 1000m high, depression to runway=30°. Horizontal distance:", "options": {"A": "1000√3 m", "B": "2000 m", "C": "500√3 m", "D": "1500 m"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Flagpole height when shadow=2×height:", "options": {"A": "30° elevation", "B": "45°", "C": "60°", "D": "26.565°"}, "correct_answer": "D"},
    {"id": 19, "difficulty": "easy", "question": "From cliff 80m high, depression to boat=60°. Boat distance:", "options": {"A": "80/√3 m", "B": "80√3 m", "C": "160 m", "D": "40√3 m"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Two towers equal height. Distance between=50m. From midpoint, elevation=30°. Height:", "options": {"A": "25/√3 m", "B": "25√3 m", "C": "50/√3 m", "D": "50√3 m"}, "correct_answer": "A"},

    {"id": 21, "difficulty": "medium", "question": "From top of 75m tower, angles of depression of two cars on same side are 30° and 45°. Distance between cars:", "options": {"A": "75(√3-1) m", "B": "75 m", "C": "150 m", "D": "75√3 m"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "A man on cliff sees boat at 30° depression. After boat moves 100m toward cliff, depression=45°. Cliff height:", "options": {"A": "50(√3+1) m", "B": "100(√3-1) m", "C": "50√3 m", "D": "100/(√3-1) m"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Two poles 18m and 12m. From top of taller, depression to top of shorter=45°. Distance:", "options": {"A": "6 m", "B": "12 m", "C": "18 m", "D": "24 m"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "From point on ground, elevation to tower top=60°. From point 40m away, depression to same point=30°. Tower height:", "options": {"A": "20√3 m", "B": "40√3 m", "C": "60 m", "D": "80 m"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "A man 1.5m tall observes cloud at 30° elevation. Reflection shows 60° depression. Cloud height:", "options": {"A": "3 m", "B": "4.5 m", "C": "6 m", "D": "7.5 m"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "From hill top, depressions to two milestones 1km apart are 30° and 45°. Hill height:", "options": {"A": "500(√3-1) m", "B": "500(√3+1) m", "C": "1000/(√3+1) m", "D": "500√3 m"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "From 60m tower, depression to car=45°. After car moves, depression=30°. Distance moved:", "options": {"A": "60(√3-1) m", "B": "60√3 m", "C": "120 m", "D": "60(3-√3) m"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Two ships from 100m lighthouse have depressions 30° and 45°. Distance between ships:", "options": {"A": "100(√3-1) m", "B": "100 m", "C": "200 m", "D": "100√3 m"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "From tower top, depression to foot of building=60° and to top=30°. If tower=60m, building height:", "options": {"A": "20 m", "B": "30 m", "C": "40 m", "D": "50 m"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "Plane at 3000√3m sees ships at depressions 60° and 30°. Distance between ships:", "options": {"A": "2000 m", "B": "3000 m", "C": "4000 m", "D": "6000 m"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "From 50m tower, depression to A=45°. From A, depression to B=30°. If AB=50m, height difference B to ground:", "options": {"A": "25(√3-1) m", "B": "50(2-√3) m", "C": "25√3 m", "D": "50/√3 m"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "Two towers 30m and 40m. From top of shorter, depression to foot of taller=45°. Distance:", "options": {"A": "10 m", "B": "20 m", "C": "30 m", "D": "40 m"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "From top of 100m building, depression to car=θ. After car moves 100m closer, depression=45°. tanθ:", "options": {"A": "1", "B": "2", "C": "√3", "D": "1/√3"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "Man on cliff sees boat at 60° depression. After boat moves 40m toward cliff, depression=45°. Cliff height:", "options": {"A": "20(3+√3) m", "B": "40(√3+1) m", "C": "60√3 m", "D": "80/(√3-1) m"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "From tower, depression to car=30°. After car travels 100m toward tower, depression=45°. Initial distance:", "options": {"A": "50(√3+1) m", "B": "100√3 m", "C": "150 m", "D": "200 m"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Two vertical poles 20m apart. From midpoint, depressions to tops=45° and 30°. Height difference:", "options": {"A": "20(√3-1) m", "B": "10(3-√3) m", "C": "20/√3 m", "D": "10√3 m"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "From hill, depression to town=30°. After descending 500m vertically, depression=60°. Hill height above town:", "options": {"A": "250√3 m", "B": "500 m", "C": "750 m", "D": "1000 m"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "From 150m tower, depression to object=45°. After height increased to 200m, depression=θ. tanθ:", "options": {"A": "4/3", "B": "3/2", "C": "2", "D": "5/3"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Two observers 100m apart see same cloud. Depression angles=30° and 45°. Cloud height:", "options": {"A": "50(√3+1) m", "B": "100/(√3-1) m", "C": "50√3 m", "D": "100 m"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "From top of 75m tower, depression to bottom of second tower=45° and to top=30°. Second tower height:", "options": {"A": "25(3-√3) m", "B": "75(√3-1) m", "C": "50 m", "D": "75(2-√3) m"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "medium", "question": "Man 1.8m tall observes shadow end at 60° depression. If sun elevation=30°, shadow length:", "options": {"A": "1.8√3 m", "B": "3.6 m", "C": "5.4 m", "D": "2.4√3 m"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "From airplane at 6000m, depression to airport=30°. After flying horizontally, depression=45°. Distance flown:", "options": {"A": "2000√3 m", "B": "6000(√3-1) m", "C": "3000 m", "D": "6000(3-√3) m"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "Two towers equal height. From midpoint, depressions to tops=30° and 60°. Ratio height:distance between:", "options": {"A": "√3:4", "B": "1:2", "C": "√3:2", "D": "2:√3"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "medium", "question": "From 120m tower, depression to car=30°. After car moves toward tower, depression=45°. Distance moved:", "options": {"A": "40(3-√3) m", "B": "120(√3-1) m", "C": "80√3 m", "D": "60(√3-1) m"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "medium", "question": "Balloon rises vertically. From point, elevation changes 30° to 60° in 10min. If depression from balloon to point was 45° initially, ascent speed:", "options": {"A": "10√3 m/min", "B": "20(√3-1) m/min", "C": "15 m/min", "D": "30/√3 m/min"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "medium", "question": "From hill top, depressions to two consecutive km stones=45° and 30°. Hill height:", "options": {"A": "500(√3+1) m", "B": "1000/(√3+1) m", "C": "500√3 m", "D": "1000(√3-1) m"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Two buildings facing. From top of 40m building, depression to top of other=30°. If distance=40√3m, other building height:", "options": {"A": "20 m", "B": "30 m", "C": "50 m", "D": "60 m"}, "correct_answer": "D"},
    {"id": 48, "difficulty": "medium", "question": "From tower, depression to A=30°. From A, depression to B=45°. If AB=100m, tower height:", "options": {"A": "50(√3+1) m", "B": "100√3 m", "C": "150 m", "D": "200/(√3+1) m"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Man on 90m cliff sees boat at 60° depression. After boat sails 30√3m, depression=45°. Initial distance:", "options": {"A": "30√3 m", "B": "60√3 m", "C": "90 m", "D": "120 m"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "medium", "question": "From 50m tower, depression to car=α. After car moves 50m toward tower, depression=45°. tanα:", "options": {"A": "1/2", "B": "2", "C": "√3", "D": "1/√3"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "Two poles 16m and 9m. From top of shorter, depression to top of taller gives tanθ=7/24. Distance:", "options": {"A": "12 m", "B": "18 m", "C": "24 m", "D": "30 m"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "medium", "question": "From airplane at height h, depression to island=45°. After flying 1000m horizontally, depression=30°. h:", "options": {"A": "500(√3+1) m", "B": "1000/(√3-1) m", "C": "500√3 m", "D": "1000 m"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "From 75m tower, depression angles to two cars=30° and 45°. If cars opposite sides, distance between:", "options": {"A": "75(√3+1) m", "B": "150 m", "C": "75√3 m", "D": "225 m"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Man 2m tall observes cloud at elevation 30°. Reflection shows depression 60°. Cloud height:", "options": {"A": "6 m", "B": "8 m", "C": "10 m", "D": "12 m"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "From lighthouse 100m high, depression to ship changes 45° to 30°. Distance traveled:", "options": {"A": "100(√3-1) m", "B": "100 m", "C": "200 m", "D": "100√3 m"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Two vertical towers. From point midway, depressions to tops=30° and 60°. If towers 60m apart, height difference:", "options": {"A": "20√3 m", "B": "40√3 m", "C": "60√3 m", "D": "80√3 m"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "medium", "question": "From hill, depression to town=30°. After walking 500m down slope at 30° incline, depression=45°. Initial height:", "options": {"A": "250(3+√3) m", "B": "500√3 m", "C": "750 m", "D": "1000 m"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "From 80m tower, depression to object=45°. If height doubled, new depression angle satisfies:", "options": {"A": "tanθ=2", "B": "tanθ=4/3", "C": "θ=60°", "D": "tanθ=3/2"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Two observers 200m apart see same balloon. Depression angles=45° and 30°. Balloon height:", "options": {"A": "100(√3-1) m", "B": "200/(√3+1) m", "C": "100√3 m", "D": "200 m"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "From 120m tower, depression to car=30°. After some time, depression=45°. If car moved toward, distance moved:", "options": {"A": "40(3-√3) m", "B": "120(√3-1) m", "C": "80 m", "D": "60√3 m"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "Man on cliff sees boat at 30° depression. After boat sails 100m parallel to cliff, depression=60°. Cliff height:", "options": {"A": "50√3 m", "B": "100√3 m", "C": "150 m", "D": "200/√3 m"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "Two buildings 40m and 60m. From top of shorter, depression to foot of taller=45°. Distance:", "options": {"A": "20 m", "B": "40 m", "C": "60 m", "D": "80 m"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "From airplane at 6000m, depression to point A=30°. After flying 2000√3m, depression to same point=θ. tanθ:", "options": {"A": "√3", "B": "1", "C": "1/√3", "D": "2/√3"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "From 90m tower, depressions to two points=30° and 60°. If points same side, distance between:", "options": {"A": "60√3 m", "B": "90(√3-1) m", "C": "120 m", "D": "180 m"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Man 1.5m tall observes reflection of pole in water. Depression to reflection=60°, elevation to top=30°. Pole height:", "options": {"A": "3 m", "B": "4.5 m", "C": "6 m", "D": "7.5 m"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "From hill, depression angles to two towns=45° and 30°. If towns 10km apart, hill height:", "options": {"A": "5(√3+1) km", "B": "10/(√3+1) km", "C": "5√3 km", "D": "10(√3-1) km"}, "correct_answer": "B"},
    {"id": 67, "difficulty": "medium", "question": "From 150m tower, depression to car=α. After car moves 50m toward, depression=45°. tanα:", "options": {"A": "2", "B": "3", "C": "1.5", "D": "2.5"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "Two poles 25m apart. From point between, depressions to tops complementary. If one pole 20m, other:", "options": {"A": "15 m", "B": "20 m", "C": "25 m", "D": "30 m"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "From lighthouse 80m high, depression to ship changes 60° to 45°. Distance sailed:", "options": {"A": "80(√3-1)/√3 m", "B": "80(3-√3) m", "C": "160/√3 m", "D": "80 m"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "Balloon rises at constant speed. From point, elevation changes 30° to 60° in 5min. If depression from balloon to point was 45° initially, height gained:", "options": {"A": "50(√3-1) m", "B": "100(2-√3) m", "C": "75 m", "D": "120/√3 m"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "From 100m cliff, depression to boat=30°. After boat sails 100m, depression=45°. If boat sailed directly toward, initial distance:", "options": {"A": "100√3 m", "B": "200 m", "C": "150 m", "D": "250 m"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Two towers equal height. From point on line joining bases, depressions to tops=30° and 60°. If point 60m from one, height:", "options": {"A": "20√3 m", "B": "30√3 m", "C": "40√3 m", "D": "60√3 m"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "From airplane, depression to airport=30°. After flying 3000m horizontally, depression=60°. Initial height:", "options": {"A": "1500√3 m", "B": "3000 m", "C": "4500 m", "D": "6000 m"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "From 120m tower, depression to car=45°. After car moves, depression=30°. If car moved away, distance moved:", "options": {"A": "120(√3-1) m", "B": "120 m", "C": "240 m", "D": "120√3 m"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Two buildings 50m apart. From top of 40m building, depression to top of other=30°. Other building height:", "options": {"A": "10(4-√3) m", "B": "40-50/√3 m", "C": "50/√3 m", "D": "40-25√3 m"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "From hill, depression to car changes 45° to 30° as car approaches. If hill height=150m, distance traveled:", "options": {"A": "150(√3-1) m", "B": "150 m", "C": "300 m", "D": "150√3 m"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "Man on 60m cliff sees two boats in line. Depression angles=45° and 30°. Distance between boats:", "options": {"A": "60(√3-1) m", "B": "60 m", "C": "120 m", "D": "60√3 m"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Two poles 12m and 20m. From top of shorter, depression to top of taller gives tanθ=2/3. Distance:", "options": {"A": "10 m", "B": "12 m", "C": "15 m", "D": "18 m"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "From 200m tower, depression to object=45°. If object moves 100m toward, new depression satisfies:", "options": {"A": "tanθ=2", "B": "θ=60°", "C": "tanθ=4/3", "D": "θ=30°"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "From point on bridge over river, depression to near bank=45°, to far bank=30°. If bridge 30m above water, river width:", "options": {"A": "30(√3+1) m", "B": "60 m", "C": "30√3 m", "D": "45 m"}, "correct_answer": "A"},

    {"id": 81, "difficulty": "hard", "question": "From top of tower, depression angles to three collinear points A,B,C are α,β,γ. If AB:BC=2:3 and tanα=1, tanβ=2, tanγ=3, ratio of distances from tower foot to A,B,C:", "options": {"A": "1:2:3", "B": "1:3:6", "C": "1:√2:√3", "D": "2:3:5"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "Man on cliff observes boat at 30° depression. Boat sails toward cliff for 10min at constant speed, then depression=45°. If boat then takes 5min more to reach cliff foot, cliff height:speed ratio:", "options": {"A": "15(√3+1)", "B": "10(2+√3)", "C": "5(3√3+1)", "D": "20(√3-1)"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "From point P on ground, elevation to tower top=60°. From point Q vertically above P, depression to same point=30°. If PQ=40m, tower height:", "options": {"A": "30√3 m", "B": "40(√3+1) m", "C": "60 m", "D": "80/√3 m"}, "correct_answer": "C"},
    {"id": 84, "difficulty": "hard", "question": "Two towers heights h1 and h2. From midpoint of line joining bases, depressions to tops complementary. Then h1h2 equals:", "options": {"A": "Square of half distance", "B": "Square of distance", "C": "Product of distances", "D": "Sum of heights squared"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "From top of tower 100m high, depression angles to two cars on opposite sides are θ and φ. If tanθ=3/4 and tanφ=5/12, distance between cars:", "options": {"A": "240 m", "B": "300 m", "C": "360 m", "D": "420 m"}, "correct_answer": "C"},
    {"id": 86, "difficulty": "hard", "question": "Man on cliff observes boat at depression α. After boat sails d meters toward cliff, depression becomes β. Then cliff height h = ?", "options": {"A": "d/(cotβ - cotα)", "B": "d/(tanα - tanβ)", "C": "d sinα sinβ/sin(β-α)", "D": "All equivalent"}, "correct_answer": "D"},
    {"id": 87, "difficulty": "hard", "question": "From point on ground, depression to bottom of window=30° and to top=60°. If window height=2m, height of point above ground:", "options": {"A": "1 m", "B": "√3 m", "C": "2 m", "D": "3 m"}, "correct_answer": "B"},
    {"id": 88, "difficulty": "hard", "question": "Two vertical poles. From point on line joining bases, depressions to tops are θ and (90°-θ). If poles heights a and b, distance from point to poles ratio:", "options": {"A": "a:b", "B": "√a:√b", "C": "a²:b²", "D": "b:a"}, "correct_answer": "D"},
    {"id": 89, "difficulty": "hard", "question": "From top of tower, depression to cloud=45°. From point 100m vertically above, depression to same cloud=30°. Cloud height:", "options": {"A": "50(3+√3) m", "B": "100(√3+1) m", "C": "150 m", "D": "200/√3 m"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "A,B,C on straight road. From tower top, depressions=30°,45°,60°. If AB=BC, ratio tower height:AB:", "options": {"A": "√3-1:1", "B": "2-√3:1", "C": "√3:2", "D": "1:√3-1"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "From airplane at height h, depression to point P=α. After time t flying horizontally at speed v, depression=β. Then h = ?", "options": {"A": "vt/(cotβ - cotα)", "B": "vt sinα sinβ/sin(β-α)", "C": "vt tanα tanβ/(tanβ-tanα)", "D": "All"}, "correct_answer": "D"},
    {"id": 92, "difficulty": "hard", "question": "Two towers equal height. From point on line joining bases, depressions to tops are tan⁻¹(1/2) and tan⁻¹(1/3). If point divides distance in ratio 2:3, ratio height:distance between:", "options": {"A": "1:5", "B": "2:5", "C": "3:10", "D": "1:√13"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "From top of tower, depression to A=30°. From A, depression to B=45°. From B, depression to C=60°. If AB=BC and tower height=100m, AC:", "options": {"A": "100(√3+1) m", "B": "200 m", "C": "150√3 m", "D": "100(3-√3) m"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "Man on cliff observes boat sailing toward cliff. Depression changes 60° to 45° in 5min, then to 30° in next 5min. If speed constant, ratio cliff height:speed:", "options": {"A": "5(3√3+1)", "B": "10(√3+1)", "C": "15(2-√3)", "D": "20/√3"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "Two vertical poles. From point on ground, depressions to tops complementary. If one pole twice other, ratio distances from point to poles:", "options": {"A": "1:√2", "B": "√2:1", "C": "1:2", "D": "2:1"}, "correct_answer": "D"},
    {"id": 96, "difficulty": "hard", "question": "From top of tower height h, depression to foot of building=α and to top=β. Building height = ?", "options": {"A": "h(1 - tanβ/tanα)", "B": "h(tanα - tanβ)/(tanα)", "C": "h(cotβ - cotα)", "D": "h(1 - cotα/cotβ)"}, "correct_answer": "D"},
    {"id": 97, "difficulty": "hard", "question": "A,B,C collinear with B between. From tower top, depressions to A,B,C=30°,45°,60°. If AB=100m, tower height and BC:", "options": {"A": "h=50(√3+1), BC=100√3", "B": "h=100, BC=100(√3-1)", "C": "h=50√3, BC=100", "D": "h=100(√3-1), BC=50√3"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "Two towers heights h and 2h. From midpoint of line joining bases, depressions to tops complementary. Ratio distance between towers:h:", "options": {"A": "2:1", "B": "√2:1", "C": "2√2:1", "D": "√6:1"}, "correct_answer": "C"},
    {"id": 99, "difficulty": "hard", "question": "From point on ground, depression to bottom of cloud=45° and to top=30°. From point 100m above, depression to cloud bottom=30°. Cloud thickness:", "options": {"A": "50(√3-1) m", "B": "100(2-√3) m", "C": "50√3 m", "D": "100/√3 m"}, "correct_answer": "B"},
    {"id": 100, "difficulty": "hard", "question": "Three towers in straight line. From top of middle tower, depressions to tops of others=30° and 60°. If middle tower=60m and others equal height, their height:", "options": {"A": "30 m", "B": "40 m", "C": "45 m", "D": "50 m"}, "correct_answer": "B"}
  ]
}