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
Evaluate log9(3).
Answer:
1/2
Step 1: Let x = log9(3). In exponential form, 9^x = 3. Step 2: Express base 9 as 3^2. This gives (3^2)^x = 3^1, meaning 3^(2x) = 3^1. Step 3: Equating exponents gives 2x = 1, resulting in x = 1/2.
122
What is the value of log4(2)?
Answer:
1/2
Step 1: Let log4(2) = x. Convert to exponential form: 4^x = 2. Step 2: Express both sides with the same base (base 2). Since 4 = 2^2, we have (2^2)^x = 2^1, or 2^(2x) = 2^1. Step 3: Equate the exponents: 2x = 1, so x = 1/2.
123
Evaluate log10(0.01).
Answer:
-2
Step 1: Let x = log10(0.01). Convert to exponential form: 10^x = 0.01. Step 2: Write 0.01 as a fraction: 1/100, which is 10^-2. Step 3: So, 10^x = 10^-2, which implies x = -2.
124
Find the value of log2(1/16).
Answer:
-4
Step 1: Let x = log2(1/16). Convert to exponential form: 2^x = 1/16. Step 2: Express 1/16 as a power of 2: 1/16 = 1/(2^4) = 2^-4. Step 3: Equating the exponents in 2^x = 2^-4 gives x = -4.
125
Evaluate log7(7).
Answer:
1
Step 1: Use the identity log_a(a) = 1. Step 2: Let log7(7) = x. In exponential form, 7^x = 7. Step 3: Since 7^1 = 7, it follows that x = 1.
126
Find the value of log10(1000).
Answer:
3
Step 1: Write the equation log10(1000) = x. Step 2: Convert to exponential form: 10^x = 1000. Step 3: Since 1000 is 10 cubed (10^3), we get 10^x = 10^3, so x = 3.
127
Evaluate log3(81).
Answer:
4
Step 1: Set the expression equal to x: log3(81) = x. Step 2: Rewrite in exponential form: 3^x = 81. Step 3: Recognize that 3^4 = 81. Thus, 3^x = 3^4, which means x = 4.
128
What is the value of log2(8)?
Answer:
3
Step 1: Let x = log2(8). Step 2: Convert the logarithmic equation to its exponential form: 2^x = 8. Step 3: Since 8 can be written as 2^3, we have 2^x = 2^3. Therefore, x = 3.