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
131
A kite is flying at a height of 50 m above the ground. The string is inclined at 30° to the ground. Find the length of the string assuming there is no slack.
Answer:
100 m
Step 1: The height is the perpendicular (50 m) and the string is the hypotenuse (L). Step 2: sin(30°) = Height / L. Step 3: 1/2 = 50 / L, so L = 100 m.
132
The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
Answer:
9.2 m
Step 1: cos(60°) = Base / Hypotenuse. Step 2: 1/2 = 4.6 / L. Step 3: L = 4.6 * 2 = 9.2 m.
133
A ladder is leaning against a vertical wall. The angle of elevation is 45° and the foot of the ladder is 5 m away from the wall. What is the length of the ladder?
Answer:
5√2 m
Step 1: The base is 5 m and the angle is 45°. Step 2: cos(45°) = Base / Hypotenuse = 5 / L. Step 3: 1/√2 = 5 / L, so L = 5√2 m.
134
A 15 m long ladder makes an angle of 60° with the wall. Find the distance of the foot of the ladder from the wall.
Answer:
7.5√3 m
Step 1: The angle with the WALL is 60°, meaning the angle with the ground is 30°. Step 2: The distance from the wall is the base. cos(30°) = Base / Hypotenuse. Wait, if angle with wall is 60°, sin(60°) = Perpendicular (distance from wall) / Hypotenuse. Step 3: sin(60°) = x / 15 -> √3/2 = x / 15 -> x = 7.5√3 m.
135
A 20 m long ladder rests against a wall. It makes an angle of 60° with the ground. How far is the foot of the ladder from the wall?
Answer:
10 m
Step 1: The ladder is the hypotenuse (20 m), and the distance from the wall is the base (x). Step 2: cos(60°) = Base / Hypotenuse = x / 20. Step 3: 1/2 = x / 20, so x = 10 m.
136
If the shadow of a tree is 1/√(3) times its height, the angle of elevation is:
Answer:
60°
Step 1: Let height = h. Shadow = h / √3. Step 2: tan(θ) = Height / Shadow = h / (h / √3) = √3. Step 3: Since tan(60°) = √3, the angle is 60°.
137
If the angle of elevation of the sun is 60°, find the length of the shadow of a 30 m tall building.
Answer:
10√3 m
Step 1: Let shadow length be x. tan(60°) = Height / x. Step 2: √3 = 30 / x. Step 3: x = 30 / √3 = (30√3) / 3 = 10√3 m.
138
A pole 15 m high casts a shadow of 15 m. What is the angle of elevation of the sun?
Answer:
45°
Step 1: The height is 15 m and the base (shadow) is 15 m. Step 2: tan(θ) = 15 / 15 = 1. Step 3: Therefore, θ = 45°.
139
The shadow of a tower is √3 times its height. Find the angle of elevation of the source of light.
Answer:
30°
Step 1: Let height = h. Shadow = h√3. Step 2: tan(θ) = h / (h√3) = 1/√3. Step 3: The angle θ whose tangent is 1/√3 is 30°.
140
If the length of the shadow of a vertical pole is equal to its height, what is the angle of elevation of the sun?
Answer:
45°
Step 1: Let the height of the pole be h. Then the length of the shadow is also h. Step 2: tan(θ) = Height / Shadow = h / h = 1. Step 3: Since tan(45°) = 1, the angle of elevation is 45°.