All Categories MCQs
Topic Notes: All Categories
General Description
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
2001
What is the angle between the hands of a clock at exactly 3:00?
Answer:
90°
At 3:00, the minute hand points to 12 and the hour hand points to 3. This spans 3 hour markings. 3 × 30° = 90°, making it a perfect right angle.
2002
What is the angle between the hands of a clock at exactly 2:00?
Answer:
60°
At 2:00, the minute hand is at 12 and the hour hand is at 2. Since each hour marking represents 30°, the angle between the hands is 2 × 30° = 60°.
2003
What is the angle between the hands of a clock at exactly 1:00?
Answer:
30°
At 1:00, the minute hand is perfectly at 12 and the hour hand is exactly at 1. The clock face is divided into 12 sections, each spanning 360° / 12 = 30°. Therefore, the angle is 30°.
2004
What is the relative speed of the minute hand with respect to the hour hand?
Answer:
5.5° per minute
The minute hand moves at 6° per minute, and the hour hand moves at 0.5° per minute. Because they move in the same direction, the relative speed is 6° - 0.5° = 5.5° per minute.
2005
What is the angle traced by the hour hand of a clock in 1 minute?
Answer:
0.5°
The hour hand completes a full circle of 360° in 12 hours, which equals 720 minutes. Thus, the angle traced by the hour hand in 1 minute is 360° / 720 = 0.5°.
2006
What is the angle traced by the minute hand of a clock in 1 minute?
Answer:
6°
The minute hand completes a full circle of 360° in exactly 60 minutes. Therefore, the angle traced by the minute hand in 1 minute is 360° / 60 = 6°.
2007
What is the value of log(50) + log(2)?
Answer:
2
Step 1: Use the product rule for logarithms: log(A) + log(B) = log(A * B). Step 2: Multiply the arguments: log(50 * 2) = log(100). Step 3: Evaluate log10(100). Since 10^2 = 100, the answer is 2.
2008
If ln(x) + ln(e) = 2, find x.
Answer:
e
Step 1: Evaluate ln(e), which is 1. The equation becomes ln(x) + 1 = 2. Step 2: Subtract 1 from both sides: ln(x) = 1. Step 3: Convert to exponential form: e^1 = x. Thus, x = e.
2009
Solve for x: 10^(x-1) = 1000.
Answer:
4
Step 1: Express both sides with the same base. Since 1000 = 10^3, write the equation as 10^(x-1) = 10^3. Step 2: Equate the exponents: x - 1 = 3. Step 3: Solve for x by adding 1: x = 4. Alternatively, use logs: log(1000) = x-1 => 3 = x-1 => x=4.
2010
Express 3*log(x) - 2*log(y) as a single logarithm.
Answer:
log(x^3 / y^2)
Step 1: Use the power rule to rewrite the terms: log(x^3) - log(y^2). Step 2: Use the quotient rule for logarithms: log(A) - log(B) = log(A / B). Step 3: Combine them to get log(x^3 / y^2).