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
91
What is the angular speed of the hour hand of a clock in radians per hour?
Answer:
π/6
The hour hand completes one full revolution (2π radians) in exactly 12 hours. Therefore, its angular speed is 2π / 12 = π/6 radians per hour.
92
What is the angular speed of the minute hand of a clock in radians per minute?
Answer:
π/30
The minute hand completes one full revolution (2π radians) in exactly 60 minutes. Therefore, its angular speed is 2π / 60 = π/30 radians per minute.
93
What is the angular speed of the second hand of a standard clock in radians per second?
Answer:
π/30
The second hand completes one full revolution (2π radians) in exactly 60 seconds. Therefore, its angular speed is 2π / 60 = π/30 radians per second.
94
Convert 40° 30' into radians.
Answer:
9π/40
First, convert to decimal degrees: 40° + (30/60)° = 40.5° = 81/2 degrees. Now, multiply by π/180: (81/2) * (π/180) = 81π / 360. Dividing by 9 gives 9π/40 radians.
95
Convert 1 minute into seconds.
Answer:
60"
In the sexagesimal system, one minute of arc is subdivided into exactly 60 seconds (60").
96
Convert 1 degree into minutes.
Answer:
60'
In the sexagesimal system of angular measurement, one degree is defined as being exactly equal to 60 minutes (60').
97
If the perimeter of a circular sector is equal to half the circumference of the circle, what is the central angle in radians?
Answer:
π - 2
The perimeter of a sector is r + r + l = 2r + rθ. Half the circumference is πr. So, 2r + rθ = πr. Dividing by r gives 2 + θ = π, meaning θ = π - 2 radians.
98
What is the area of a sector of a circle of radius 10 m, bounded by an arc of length 5 m?
Answer:
25 m²
We can use the alternative formula for sector area: A = (1/2) * l * r, where l is the arc length. Substituting the given values: A = (1/2) * 5 * 10 = 25 m².
99
Find the radius of a circle in which a central angle of 45° intercepts an arc of length 11 cm. (Use π ≈ 22/7)
Answer:
14 cm
Convert 45° to radians: 45° = π/4 radians. Using l = rθ, we have 11 = r * (π/4). Using π ≈ 22/7, 11 = r * (22/28). Therefore, r = (11 * 28) / 22 = 28 / 2 = 14 cm.
100
A wheel has a radius of 0.5 m. How far does it travel in one complete revolution?
Answer:
π m
One complete revolution corresponds to 2π radians. The distance traveled is the arc length of one full circle. l = rθ = 0.5 * 2π = π meters. This is also known as the circumference.