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Q. A tower is 120 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 degrees. How far is the point from the base of the tower? (2020)

A. 60 m
B. 120 m
C. 90 m
D. 30 m

Solution

Distance = Height / tan(45) = 120 / 1 = 120 m.

Correct Answer: B — 120 m

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Q. A tower is 40 meters high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower?

A. 20√3 meters
B. 40 meters
C. 20 meters
D. 30 meters

Solution

Distance = height / tan(angle) = 40 / tan(60°) = 40 / √3 = 20√3 meters.

Correct Answer: A — 20√3 meters

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Q. A tower is 50 meters high. From a point on the ground, the angle of elevation to the top of the tower is 30 degrees. What is the distance from the point to the base of the tower?

A. 25√3 m
B. 50 m
C. 25 m
D. 50√3 m

Solution

Using tan(30°) = height/distance, we have distance = height/tan(30°) = 50/√3 = 25√3 m.

Correct Answer: A — 25√3 m

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Q. A tower is 60 m high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower? (2023)

A. 30 m
B. 40 m
C. 50 m
D. 60 m

Solution

Distance = height / tan(angle) = 60 / tan(60) = 60 / √3 ≈ 30 m.

Correct Answer: A — 30 m

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Q. A tower is 60 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 degrees. How far is the point from the base of the tower?

A. 30 meters
B. 60 meters
C. 45 meters
D. 75 meters

Solution

Distance = height / tan(angle) = 60 / 1 = 60 meters.

Correct Answer: B — 60 meters

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Q. A tower is 80 meters high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower?

A. 40 m
B. 80 m
C. 20 m
D. 60 m

Solution

Distance = height / tan(angle) = 80 / √3 = 40 m.

Correct Answer: A — 40 m

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Q. A tower is standing on a horizontal ground. The angle of elevation of the top of the tower from a point on the ground is 30 degrees. If the height of the tower is 10√3 meters, how far is the point from the base of the tower?

A. 10 m
B. 20 m
C. 30 m
D. 40 m

Solution

Using tan(30°) = height/distance, we have 1/√3 = 10√3/distance. Therefore, distance = 10√3 * √3 = 30 m.

Correct Answer: B — 20 m

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Q. A tower is standing on a horizontal ground. The angle of elevation of the top of the tower from a point on the ground is 30 degrees. If the height of the tower is 10√3 m, how far is the point from the base of the tower?

A. 10 m
B. 5 m
C. 15 m
D. 20 m

Solution

Using tan(30°) = height/distance, we have 1/√3 = 10√3/distance. Therefore, distance = 10√3 * √3 = 30 m.

Correct Answer: A — 10 m

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Q. A tower is standing on a horizontal ground. The angle of elevation of the top of the tower from a point on the ground is 30 degrees. If the height of the tower is 50 meters, how far is the point from the base of the tower?

A. 50√3 m
B. 100 m
C. 50 m
D. 100√3 m

Solution

Using tan(30°) = height/distance, we have distance = height/tan(30°) = 50/(1/√3) = 50√3 m.

Correct Answer: A — 50√3 m

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Q. A trade agreement between two countries is expected to increase trade by 25%. If the current trade volume is $200 million, what will be the new trade volume?

A. $220 million
B. $250 million
C. $275 million
D. $300 million

Solution

New trade volume = $200 million + (25% of $200 million) = $200 million + $50 million = $250 million.

Correct Answer: B — $250 million

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Q. A trade agreement was signed between 4 countries. If each country can trade with every other country, how many unique trade pairs can be formed? (2020)

A. 4
B. 6
C. 8
D. 12

Solution

Unique trade pairs = C(4, 2) = 4! / (2!(4-2)!) = 6.

Correct Answer: B — 6

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Q. A trade agreement was signed between 8 countries. If each country can form a partnership with every other country, how many unique partnerships can be formed?

A. 28
B. 56
C. 36
D. 64

Solution

Number of unique partnerships = C(8, 2) = 8! / (2!(8-2)!) = 28.

Correct Answer: A — 28

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Q. A train covers a distance of 300 km in 4 hours. What is its average speed? (2020)

A. 60 km/h
B. 70 km/h
C. 75 km/h
D. 80 km/h

Solution

Average speed = Total distance / Total time = 300 km / 4 hours = 75 km/h.

Correct Answer: A — 60 km/h

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Q. A train covers a distance of 300 km in 4 hours. What is its speed in km/h? (2020)

A. 70 km/h
B. 75 km/h
C. 80 km/h
D. 85 km/h

Solution

Speed = Distance / Time = 300 km / 4 hours = 75 km/h.

Correct Answer: C — 80 km/h

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Q. A train is moving at 72 km/h and a bird flies in the opposite direction at 18 km/h. What is the speed of the bird relative to the train?

A. 54 km/h
B. 72 km/h
C. 90 km/h
D. 18 km/h

Solution

Relative speed = Speed of train + Speed of bird = 72 km/h + 18 km/h = 90 km/h.

Correct Answer: A — 54 km/h

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Q. A train is moving at 72 km/h and passes a platform in 20 seconds. What is the length of the train?

A. 100 m
B. 200 m
C. 300 m
D. 400 m

Solution

Length of train = Speed × Time = (72 km/h × (1000 m/1 km) / (3600 s/1 h)) × 20 s = 400 m.

Correct Answer: B — 200 m

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Q. A train is moving at 72 km/h and passes a platform in 20 seconds. What is the length of the platform if the train is 180 meters long?

A. 200 m
B. 300 m
C. 400 m
D. 500 m

Solution

Speed of train = 72 km/h = 20 m/s. Time = 20 s. Distance = Speed × Time = 20 m/s × 20 s = 400 m. Length of platform = 400 m - 180 m = 220 m.

Correct Answer: B — 300 m

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Q. A train is moving at 72 km/h and passes a platform in 30 seconds. What is the length of the platform if the train is 200 meters long?

A. 200 m
B. 300 m
C. 400 m
D. 500 m

Solution

Speed in m/s = 72 * (1000/3600) = 20 m/s. Distance = Speed × Time = 20 m/s × 30 s = 600 m. Length of platform = 600 m - 200 m = 400 m.

Correct Answer: B — 300 m

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Q. A train is moving at 90 km/h and a bird flies at 45 km/h in the opposite direction. What is the speed of the bird relative to the train?

A. 135 km/h
B. 45 km/h
C. 90 km/h
D. 135 km/h

Solution

Relative speed = Speed of train + Speed of bird = 90 km/h + 45 km/h = 135 km/h.

Correct Answer: A — 135 km/h

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Q. A train leaves a station and travels at 90 km/h. Another train leaves the same station 30 minutes later and travels at 120 km/h. How far from the station will they meet?

A. 90 km
B. 120 km
C. 150 km
D. 180 km

Solution

Let the distance be d. Time taken by first train = d/90. Time taken by second train = d/120. Setting up the equation gives d = 150 km.

Correct Answer: C — 150 km

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Q. A train leaves a station and travels at a speed of 80 km/h. How far will it travel in 3 hours? (2022)

A. 200 km
B. 240 km
C. 260 km
D. 300 km

Solution

Distance = Speed × Time = 80 km/h × 3 h = 240 km.

Correct Answer: B — 240 km

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Q. A train leaves a station and travels at a speed of 90 km/h. How far will it travel in 2.5 hours?

A. 200 km
B. 225 km
C. 250 km
D. 300 km

Solution

Distance = speed × time = 90 km/h × 2.5 h = 225 km.

Correct Answer: B — 225 km

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Q. A train leaves a station and travels at a speed of 90 km/h. How long will it take to travel 270 km?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours

Solution

Time = Distance / Speed. Here, time = 270 km / 90 km/h = 3 hours.

Correct Answer: B — 3 hours

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Q. A train leaves a station and travels at a speed of 90 km/h. How long will it take to cover 270 km? (2022)

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours

Solution

Time = Distance / Speed = 270 km / 90 km/h = 3 hours.

Correct Answer: B — 3 hours

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Q. A train leaves a station at 2 PM traveling at 80 km/h. If it travels for 3 hours, at what time will it arrive at the next station? (2022)

A. 4 PM
B. 5 PM
C. 6 PM
D. 7 PM

Solution

Departure time = 2 PM, travel time = 3 hours. Arrival time = 2 PM + 3 hours = 5 PM.

Correct Answer: C — 6 PM

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Q. A train leaves a station at 70 km/h. Another train leaves the same station 30 minutes later at 90 km/h. How far from the station will they meet?

A. 70 km
B. 90 km
C. 100 km
D. 110 km

Solution

Let the distance be d. Time taken by first train = d/70, second train = d/90. They meet when d/70 = d/90 + 0.5. Solving gives d = 100 km.

Correct Answer: C — 100 km

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Q. A train leaves a station at 80 km/h and another train leaves the same station 30 minutes later at 100 km/h. How far from the station will they meet?

A. 100 km
B. 120 km
C. 150 km
D. 180 km

Solution

Let the time taken by the first train be t hours. Distance = speed * time. 80t = 100(t - 0.5). Solving gives t = 2 hours, so distance = 80 * 2 = 160 km.

Correct Answer: B — 120 km

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Q. A train moving at 72 km/h applies brakes and comes to a stop in 10 seconds. What is the acceleration of the train?

A. -2 m/s²
B. -3 m/s²
C. -4 m/s²
D. -5 m/s²

Solution

First convert speed to m/s: 72 km/h = 20 m/s. Using the formula: a = (v - u) / t = (0 - 20) / 10 = -2 m/s².

Correct Answer: C — -4 m/s²

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Q. A train moving at 72 km/h applies brakes and comes to a stop in 5 seconds. What is the deceleration? (2023)

A. 2 m/s²
B. 3 m/s²
C. 4 m/s²
D. 5 m/s²

Solution

First convert speed to m/s: 72 km/h = 20 m/s. Deceleration = (final velocity - initial velocity) / time = (0 - 20) / 5 = -4 m/s².

Correct Answer: C — 4 m/s²

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Q. A train moving at 72 km/h applies brakes and comes to a stop in 5 seconds. What is the acceleration of the train?

A. -4 m/s²
B. -5 m/s²
C. -6 m/s²
D. -7 m/s²

Solution

First convert speed to m/s: 72 km/h = 20 m/s. Using the formula: acceleration = (final velocity - initial velocity) / time = (0 - 20) / 5 = -4 m/s².

Correct Answer: B — -5 m/s²

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Major Competitive Exams

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