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1. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships at 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

A) 173 m
B) 200 m
C) 273 m
D) 300 m

Answer: Option C

Explanation:

Let AB be the lighthouse and C and D be the positions of the ships.

Then, AB = 100 m, ∠ACB = 30° and ∠ADB = 45°.

AB/AC = tan 30° = 1/√3 ⇒ AC = AB × √3 = 100/√3 m.

AB/AD = tan 45° = 1 ⇒ AD = AB = 100 m.

∴ CD = (AC + AD) = (100/√3 + 100) m = 273 m.

2. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

A) 120 m
B) 150 m
C) 180 m
D) 160 m

Answer: Option B

Explanation:

The length of the train is determined by multiplying the speed by time. Speed = 60 km/h = 60 × 1000/3600 m/s = 50/3 m/s. Time = 9 seconds. So, Length = Speed × Time = (50/3) × 9 = 150 m.

3. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

A) 120 m
B) 150 m
C) 180 m
D) 160 m

Answer: Option B

Explanation:

The length of the train is determined by multiplying the speed by time. Speed = 60 km/h = 60 × 1000/3600 m/s = 50/3 m/s. Time = 9 seconds. So, Length = Speed × Time = (50/3) × 9 = 150 m.