Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
111
If the height of a pole is √3 times the length of its shadow, what is the angle of elevation of the sun?
Answer:
60°
Step 1: Let the shadow length be x. Then the height of the pole is x√3. Step 2: tan(θ) = height / shadow = (x√3) / x = √3. Step 3: Since tan(60°) = √3, the angle of elevation is 60°.
112
The length of the shadow of a vertical pole is √3 times its height. Find the angle of elevation of the sun.
Answer:
30°
Step 1: Let the height of the pole be h. The shadow is h√3. Step 2: The tangent of the angle of elevation θ is height / shadow = h / (h√3) = 1 / √3. Step 3: We know that tan(30°) = 1 / √3. Hence, the angle is 30°.
113
If the height of a vertical pole is equal to the length of its shadow on the ground, what is the angle of elevation of the sun?
Answer:
45°
Step 1: Let the height of the pole be h and the length of the shadow be x. Given h = x. Step 2: Let the angle of elevation be θ. Then tan(θ) = h / x. Step 3: Since h = x, tan(θ) = 1. Therefore, θ = 45°.
114
A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
Answer:
8√3 m
Step 1: Let the broken part be the hypotenuse (y) and the standing part be the perpendicular (x). tan(30°) = x/8 => x = 8/√3. Step 2: cos(30°) = 8/y => y = 16/√3. Step 3: Total height = x + y = 8/√3 + 16/√3 = 24/√3 = 8√3 m.
115
If the distance of a point from the base of a pole is 20√3 m and the angle of depression from the top of the pole to the point is 30°, find the height of the pole.
Answer:
20 m
Step 1: Angle of elevation = 30°. Step 2: tan(30°) = Height / 20√3. Step 3: 1/√3 = h / 20√3 -> h = 20 m.
116
The angle of depression of a point on the ground from the top of a 30 m monument is 30°. The distance of the point from the base is:
Answer:
30√3 m
Step 1: Angle of elevation is 30°. Step 2: tan(30°) = 30 / d. Step 3: 1/√3 = 30 / d -> d = 30√3 m.
117
From a 100 m high tower, the angle of depression of a car is 60°. Find the distance of the car from the tower.
Answer:
100/√3 m
Step 1: Angle of elevation = 60°. Step 2: tan(60°) = 100 / d -> √3 = 100 / d. Step 3: d = 100 / √3 m.
118
A lighthouse is 120 m tall. The angle of depression to a ship is 45°. How far is the ship from the lighthouse?
Answer:
120 m
Step 1: Angle of elevation from ship is 45°. Step 2: tan(45°) = Height / Distance = 120 / d. Step 3: 1 = 120 / d, so d = 120 m.
119
From the top of a 50 m high cliff, the angle of depression of a boat is 30°. Find the distance of the boat from the base of the cliff.
Answer:
50√3 m
Step 1: The angle of depression equals the angle of elevation from the boat to the cliff top (30°). Step 2: tan(30°) = Height / Distance = 50 / d. Step 3: 1/√3 = 50 / d, so d = 50√3 m.
120
An observer 2 m tall is 10√3 m away from a building. The angle of elevation from his eye to the top is 60°. Find the building's height.
Answer:
32 m
Step 1: Height above eye level x = Distance * tan(60°) = 10√3 * √3 = 30 m. Step 2: Total height = x + 2. Step 3: Total height = 30 + 2 = 32 m.