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
121
An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. What is the height of the tower?
Answer:
30 m
Step 1: Let the tower height above the observer's eye level be x. tan(45°) = x / 28.5. Step 2: 1 = x / 28.5, so x = 28.5 m. Step 3: Total height = x + observer's height = 28.5 + 1.5 = 30 m.
122
A tower is 50√3 m high. The angle of elevation of its top from a point 50 m away from its foot is:
Answer:
60°
Step 1: tan(θ) = Height / Distance = 50√3 / 50. Step 2: tan(θ) = √3. Step 3: θ = 60°.
123
Find the distance of a point from the base of a tower 100 m high if the angle of elevation of the top is 60°.
Answer:
100/√3 m
Step 1: tan(60°) = Height / Distance. Step 2: √3 = 100 / d. Step 3: d = 100 / √3 m.
124
The angle of elevation of the top of a tower from a point 20 m away from its base is 45°. What is the height of the tower?
Answer:
20 m
Step 1: tan(45°) = h / 20. Step 2: 1 = h / 20. Step 3: h = 20 m.
125
From a point 50 m from the base of a building, the angle of elevation to the top is 60°. Find the height of the building.
Answer:
50√3 m
Step 1: tan(60°) = Height / Base. Step 2: √3 = h / 50. Step 3: h = 50√3 m.
126
The angle of elevation of the top of a tower from a point on the ground 30 m away from the foot of the tower is 30°. Find the height of the tower.
Answer:
10√3 m
Step 1: tan(30°) = Height / Base. Step 2: 1/√3 = h / 30. Step 3: h = 30 / √3 = 10√3 m.
127
A string of length 80 m is attached to a kite. If the height of the kite is 40 m, find the angle of elevation.
Answer:
30°
Step 1: sin(θ) = Height / Hypotenuse. Step 2: sin(θ) = 40 / 80 = 1/2. Step 3: Therefore, θ = 30°.
128
If a 100 m string of a kite makes an angle of 60° with the ground, find the height of the kite.
Answer:
50√3 m
Step 1: sin(60°) = h / 100. Step 2: √3/2 = h / 100. Step 3: h = 100 * (√3/2) = 50√3 m.
129
The string of a kite is 120 m long and makes an angle of 45° with the horizontal. Find the height of the kite.
Answer:
60√2 m
Step 1: sin(45°) = Height / Hypotenuse = h / 120. Step 2: 1/√2 = h / 120. Step 3: h = 120 / √2 = 60√2 m.
130
A kite is flying at a height of 75 m. If the string makes an angle of 60° with the ground, what is the length of the string?
Answer:
50√3 m
Step 1: sin(60°) = Height / L. Step 2: √3/2 = 75 / L. Step 3: L = 150 / √3 = 50√3 m.