{
  "title": "Angle of Depression - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "The angle of depression from the top of a 30m tower to a point on the ground is 45°. What is the distance of the point from the base of the tower?", "options": {"A": "15 m", "B": "30 m", "C": "40 m", "D": "20 m"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "If the angle of depression from a lighthouse to a boat is 30° and the lighthouse height is 60m, how far is the boat from the base?", "options": {"A": "30√3 m", "B": "60√3 m", "C": "30 m", "D": "120 m"}, "correct_answer": "B"},
   {
  "id": 3,
  "difficulty": "easy",
  "question": "From a point 20m above ground, the angle of depression of an object on ground is 60°. What is the horizontal distance between the point and the object?",
  "options": {"A": "20/√3 m", "B": "20√3 m", "C": "40 m", "D": "10√3 m"},
  "correct_answer": "A"
},  {"id": 4, "difficulty": "easy", "question": "The angle of depression of a car from the top of a 50m building is 45°. How far is the car from the building?", "options": {"A": "25 m", "B": "50 m", "C": "75 m", "D": "100 m"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "From an airplane flying at 1000m, the angle of depression to a runway is 30°. What is the horizontal distance to the runway?", "options": {"A": "500 m", "B": "1000√3 m", "C": "2000 m", "D": "1500 m"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "If angle of depression equals angle of elevation, what can you say about the positions?", "options": {"A": "Objects are at same height", "B": "Objects are symmetric", "C": "Line of sight is horizontal", "D": "They are equal when observer and object are at same horizontal level"}, "correct_answer": "D"},
    {"id": 7, "difficulty": "easy", "question": "From a cliff 80m high, the angle of depression of a boat is 60°. How far is the boat from the cliff?", "options": {"A": "80/√3 m", "B": "80√3 m", "C": "160 m", "D": "40√3 m"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "What is the angle of depression if a 10m tall building casts a 10m long shadow directly below?", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "0°"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "From top of a pole, the angle of depression to a point on ground is 30°. If point is 20√3m from pole base, find pole height.", "options": {"A": "10 m", "B": "20 m", "C": "30 m", "D": "40 m"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "Angle of depression is always measured from which direction?", "options": {"A": "Horizontal downward", "B": "Vertical downward", "C": "Horizontal upward", "D": "At any angle"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "If height is 40m and angle of depression is 30°, horizontal distance = ?", "options": {"A": "40√3 m", "B": "40/√3 m", "C": "80 m", "D": "20√3 m"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "From a window 15m high, angle of depression to foot of building opposite is 45°. Distance between buildings?", "options": {"A": "7.5 m", "B": "15 m", "C": "30 m", "D": "22.5 m"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "What is true about angle of depression?", "options": {"A": "It can be >90°", "B": "It's always acute", "C": "It equals complementary angle of elevation", "D": "It's measured from vertical"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "From a hilltop, angle of depression to a car is 60°. If hill height=150m, car distance=?", "options": {"A": "50√3 m", "B": "150/√3 m", "C": "75√3 m", "D": "100√3 m"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "If distance=height, angle of depression=?", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "Observer at 100m sees object at 45° depression. Object distance?", "options": {"A": "50 m", "B": "100 m", "C": "141 m", "D": "200 m"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Angle of depression and elevation are equal when:", "options": {"A": "Heights are equal", "B": "In right triangle", "C": "Observer and object at same level", "D": "Always equal"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "From 25m tower, depression angle to nearby building's top is 30°. If buildings are 25√3m apart, other building height?", "options": {"A": "25 m", "B": "50 m", "C": "75 m", "D": "100 m"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "If tan(θ)=1 for depression angle, what is θ?", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "0°"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "Depression angle from 40m cliff to boat is 30°. Boat distance?", "options": {"A": "40√3 m", "B": "80 m", "C": "40/√3 m", "D": "20√3 m"}, "correct_answer": "A"},

    {"id": 21, "difficulty": "medium", "question": "From the top of a 90m cliff, angles of depression of two boats in same line are 30° and 60°. Distance between boats?", "options": {"A": "60√3 m", "B": "90√3 m", "C": "120 m", "D": "60(√3-1) m"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "A man on cliff observes boat at 30° depression. After boat moves 100m toward cliff, depression becomes 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": "From 75m tower, depression angles to two cars on opposite sides are 30° and 45°. Distance between cars?", "options": {"A": "75(√3+1) m", "B": "75(3+√3) m", "C": "75√3 m", "D": "150 m"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Two poles 18m and 12m tall. From top of taller, depression to top of shorter is 45°. Distance between poles?", "options": {"A": "6 m", "B": "12 m", "C": "18 m", "D": "24 m"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "From a point on ground, elevation to tower top is 60°. From point 40m away, depression to same point is 30°. Tower height?", "options": {"A": "20√3 m", "B": "40√3 m", "C": "60 m", "D": "80 m"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "A man 1.5m tall observes cloud at 30° elevation. Cloud reflection in water has 60° depression. Cloud height?", "options": {"A": "3.0 m", "B": "4.5 m", "C": "6.0 m", "D": "7.5 m"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "From hill top, depression angles to two milestones on road are 30° and 45°. If milestones are 1km apart, 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": 28, "difficulty": "medium", "question": "From 60m tower, depression to car is 45°. After car moves, depression becomes 30°. Distance car moved?", "options": {"A": "60(√3-1) m", "B": "60√3 m", "C": "120 m", "D": "60(3-√3) m"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Two ships observed from 100m lighthouse. Their depression angles are 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": 30, "difficulty": "medium", "question": "From tower top, depression to foot of building is 60° and to its top is 30°. If tower is 60m tall, building height?", "options": {"A": "20 m", "B": "30 m", "C": "40 m", "D": "50 m"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "A plane flying at 3000√3m observes two ships ahead with depressions 60° and 30°. Distance between ships?", "options": {"A": "2000 m", "B": "3000 m", "C": "4000 m", "D": "6000 m"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "From 50m tower, depression to point A is 45°. From point A, depression to point B is 30°. If A to B distance=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": 33, "difficulty": "medium", "question": "Two towers height 30m and 40m. From top of shorter, depression to foot of taller is 45°. Distance between towers?", "options": {"A": "10 m", "B": "20 m", "C": "30 m", "D": "40 m"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "From top of 100m building, depression to car is θ. After car moves 100m closer, depression becomes 45°. tanθ=?", "options": {"A": "1", "B": "2", "C": "√3", "D": "1/√3"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "A man on cliff sees boat at 60° depression. When boat moves 40m toward cliff, depression becomes 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": 36, "difficulty": "medium", "question": "From tower, depression to car is 30°. After car travels 100m toward tower, depression becomes 45°. Initial distance car to tower?", "options": {"A": "50(√3+1) m", "B": "100√3 m", "C": "150 m", "D": "200 m"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Two vertical poles 20m apart. From midpoint, depression to tops are 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": 38, "difficulty": "medium", "question": "From hilltop, depression to town is 30°. After descending 500m vertically, depression becomes 60°. Hill height above town?", "options": {"A": "250√3 m", "B": "500 m", "C": "750 m", "D": "1000 m"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "From 150m tower, depression to object is 45°. After tower height increased to 200m, depression becomes θ. tanθ=?", "options": {"A": "4/3", "B": "3/2", "C": "2", "D": "5/3"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Two observers 100m apart see same cloud. Depression angles are 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": 41, "difficulty": "medium", "question": "From top of 75m tower, depression to bottom of second tower is 45° and to its top is 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": 42, "difficulty": "medium", "question": "A man 1.8m tall observes his shadow end at 60° depression. If sun elevation is 30°, his 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": 43, "difficulty": "medium", "question": "From airplane at 6000m, depression to airport is 30°. After flying horizontally for time t, depression becomes 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": 44, "difficulty": "medium", "question": "Two towers of equal height. From midpoint between them, depression to tops are 30° and 60°. Ratio of tower height to distance between them?", "options": {"A": "√3:4", "B": "1:2", "C": "√3:2", "D": "2:√3"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "From 120m tower, depression to car is 30°. After car moves toward tower, depression becomes 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": 46, "difficulty": "medium", "question": "A balloon rises vertically. From point on ground, elevation changes from 30° to 60° in 10min. If depression from balloon to point was 45° at first instant, speed of ascent?", "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": 47, "difficulty": "medium", "question": "From hilltop, depression to two consecutive km stones are 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": 48, "difficulty": "medium", "question": "Two buildings facing each other. From top of 40m building, depression to top of other is 30°. If distance between=40√3m, other building height?", "options": {"A": "20 m", "B": "30 m", "C": "50 m", "D": "60 m"}, "correct_answer": "D"},
    {"id": 49, "difficulty": "medium", "question": "From tower, depression to point A is 30°. From A, depression to point B is 45°. If AB=100m and all points collinear, tower height?", "options": {"A": "50(√3+1) m", "B": "100√3 m", "C": "150 m", "D": "200/(√3+1) m"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "A man on 90m cliff sees boat at 60° depression. After boat sails 30√3m, depression becomes 45°. Initial distance boat to cliff?", "options": {"A": "30√3 m", "B": "60√3 m", "C": "90 m", "D": "120 m"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "From 50m tower, depression to car is α. After car moves 50m toward tower, depression becomes 45°. tanα=?", "options": {"A": "1/2", "B": "2", "C": "√3", "D": "1/√3"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "Two poles 16m and 9m high. From top of shorter, depression to top of taller is θ. If tanθ=7/24, distance between poles?", "options": {"A": "12 m", "B": "18 m", "C": "24 m", "D": "30 m"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "medium", "question": "From airplane at height h, depression to island is 45°. After flying 1000m horizontally, depression becomes 30°. h=?", "options": {"A": "500(√3+1) m", "B": "1000/(√3-1) m", "C": "500√3 m", "D": "1000 m"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "From 75m tower, depression angles to two cars are 30° and 45°. If cars are on opposite sides, distance between cars?", "options": {"A": "75(√3+1) m", "B": "150 m", "C": "75√3 m", "D": "225 m"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "A man 2m tall observes cloud at elevation 30°. Cloud reflection shows depression 60°. Cloud height above ground?", "options": {"A": "6 m", "B": "8 m", "C": "10 m", "D": "12 m"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "From lighthouse 100m high, depression to ship changes from 45° to 30° as ship approaches. Distance traveled by ship?", "options": {"A": "100(√3-1) m", "B": "100 m", "C": "200 m", "D": "100√3 m"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Two vertical towers. From point midway, depression to tops are 30° and 60°. If towers are 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": 58, "difficulty": "medium", "question": "From hill, depression to town is 30°. After walking 500m down slope at 30° incline, depression becomes 45°. Initial height above town?", "options": {"A": "250(3+√3) m", "B": "500√3 m", "C": "750 m", "D": "1000 m"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "From 80m tower, depression to object is 45°. If tower height doubled, new depression angle θ satisfies?", "options": {"A": "tanθ=2", "B": "tanθ=4/3", "C": "θ=60°", "D": "tanθ=3/2"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "Two observers 200m apart see same balloon. Depression angles are 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": 61, "difficulty": "medium", "question": "From top of 120m tower, depression to car is 30°. After some time, depression becomes 45°. If car moved toward tower, distance moved?", "options": {"A": "40(3-√3) m", "B": "120(√3-1) m", "C": "80 m", "D": "60√3 m"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "A man on cliff sees boat at 30° depression. After boat sails 100m parallel to cliff, depression becomes 60°. Cliff height?", "options": {"A": "50√3 m", "B": "100√3 m", "C": "150 m", "D": "200/√3 m"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Two buildings of height 40m and 60m. From top of shorter, depression to foot of taller is 45°. Distance between buildings?", "options": {"A": "20 m", "B": "40 m", "C": "60 m", "D": "80 m"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "From airplane at 6000m, depression to point A is 30°. After flying 2000√3m, depression to same point is θ. tanθ=?", "options": {"A": "√3", "B": "1", "C": "1/√3", "D": "2/√3"}, "correct_answer": "B"},
    {"id": 65, "difficulty": "medium", "question": "From 90m tower, depression to two points on ground are 30° and 60°. If points are on same side, distance between them?", "options": {"A": "60√3 m", "B": "90(√3-1) m", "C": "120 m", "D": "180 m"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "A man 1.5m tall observes reflection of pole in water. Depression to reflection is 60°, elevation to top is 30°. Pole height?", "options": {"A": "3 m", "B": "4.5 m", "C": "6 m", "D": "7.5 m"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "From hill, depression angles to two towns are 45° and 30°. If towns are 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": 68, "difficulty": "medium", "question": "From 150m tower, depression to car is α. After car moves 50m toward tower, depression becomes 45°. tanα=?", "options": {"A": "2", "B": "3", "C": "1.5", "D": "2.5"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "Two poles 25m apart. From point between them, depression to tops are complementary angles. If one pole is 20m, other pole height?", "options": {"A": "15 m", "B": "20 m", "C": "25 m", "D": "30 m"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "From lighthouse 80m high, depression to ship changes from 60° to 45°. Distance ship sailed?", "options": {"A": "80(√3-1)/√3 m", "B": "80(3-√3) m", "C": "160/√3 m", "D": "80 m"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "A balloon rises at constant speed. From point, elevation changes from 30° to 60° in 5min. If depression from balloon to point was 45° initially, height gained in 5min?", "options": {"A": "50(√3-1) m", "B": "100(2-√3) m", "C": "75 m", "D": "120/√3 m"}, "correct_answer": "B"},
    {"id": 72, "difficulty": "medium", "question": "From 100m cliff, depression to boat is 30°. After boat sails 100m, depression becomes 45°. If boat sailed directly toward cliff, initial distance?", "options": {"A": "100√3 m", "B": "200 m", "C": "150 m", "D": "250 m"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "Two towers equal height. From point on line joining bases, depression to tops are 30° and 60°. If point is 60m from one tower, tower height?", "options": {"A": "20√3 m", "B": "30√3 m", "C": "40√3 m", "D": "60√3 m"}, "correct_answer": "B"},
    {"id": 74, "difficulty": "medium", "question": "From airplane, depression to airport is 30°. After flying 3000m horizontally, depression becomes 60°. Initial height?", "options": {"A": "1500√3 m", "B": "3000 m", "C": "4500 m", "D": "6000 m"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "From 120m tower, depression to car is 45°. After car moves, depression becomes 30°. If car moved away from tower, distance moved?", "options": {"A": "120(√3-1) m", "B": "120 m", "C": "240 m", "D": "120√3 m"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Two buildings 50m apart. From top of 40m building, depression to top of other is 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": 77, "difficulty": "medium", "question": "From hill, depression to car changes from 45° to 30° as car approaches. If hill height=150m, distance car traveled?", "options": {"A": "150(√3-1) m", "B": "150 m", "C": "300 m", "D": "150√3 m"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "A man on 60m cliff sees two boats in line. Depression angles are 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": 79, "difficulty": "medium", "question": "Two poles 12m and 20m high. From top of shorter, depression to top of taller gives tanθ=2/3. Distance between poles?", "options": {"A": "10 m", "B": "12 m", "C": "15 m", "D": "18 m"}, "correct_answer": "B"},
    {"id": 80, "difficulty": "medium", "question": "From 200m tower, depression to object is 45°. If object moves 100m toward tower, new depression angle θ satisfies?", "options": {"A": "tanθ=2", "B": "θ=60°", "C": "tanθ=4/3", "D": "θ=30°"}, "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 respectively. If AB:BC=2:3 and tanα=1, tanβ=2, tanγ=3, find 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": "A man on cliff observes boat at 30° depression. Boat sails toward cliff for 10min at constant speed, then depression becomes 45°. If boat then takes 5min more to reach cliff foot, find cliff height to 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 is 60°. From point Q vertically above P, depression to same point is 30°. If PQ=40m, find 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 of heights h1 and h2. From midpoint of line joining bases, depression to tops are complementary. Prove h1h2 equals square of half distance between towers.", "options": {"A": "Always true", "B": "True only if h1=h2", "C": "Never true", "D": "True only for specific angles"}, "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": "A man on cliff observes boat at depression α. After boat sails d meters toward cliff, depression becomes β. Prove cliff height h = d/(cotβ - cotα).", "options": {"A": "True statement", "B": "False, should be d/(tanα - tanβ)", "C": "True only for α=30°, β=45°", "D": "Never true"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "From point on ground, depression to bottom of window is 30° and to top is 60°. If window height is 2m, find 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, depression to tops are θ and (90°-θ). If poles heights are a and b, distance from point to poles are in 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 is 45°. From point 100m vertically above, depression to same cloud is 30°. Cloud height above ground?", "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 are three points on straight road. From tower top, depressions are 30°,45°,60°. If AB=BC, find ratio of tower height to 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 is α. After time t flying horizontally at speed v, depression becomes β. Prove h = vt/(cotβ - cotα).", "options": {"A": "True", "B": "False", "C": "True only if α+β=90°", "D": "True only for v constant"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "Two towers of equal height. From point on line joining bases, depression to tops are tan⁻¹(1/2) and tan⁻¹(1/3). If point divides distance between towers in ratio 2:3, find ratio of tower height to distance between towers.", "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 point A is 30°. From A, depression to point B is 45°. From B, depression to point C is 60°. If AB=BC and tower height=100m, find 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": "A man on cliff observes boat sailing toward cliff. Depression changes from 60° to 45° in 5min, then to 30° in next 5min. If speed constant, find 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, depression to tops are complementary. If one pole is twice other, find ratio of 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 of height h, depression to foot of building is α and to top is 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 A and C. From tower top, depression to A,B,C are 30°,45°,60°. If AB=100m, find 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, depression to tops are complementary. Find ratio of distance between towers to 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 is 45° and to top is 30°. From point 100m above, depression to cloud bottom is 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, depression to tops of others are 30° and 60°. If middle tower is 60m and others equal height, find their height.", "options": {"A": "30 m", "B": "40 m", "C": "45 m", "D": "50 m"}, "correct_answer": "B"}
  ]
}