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
211
Compute: (1/2)^3
Answer:
1/8
Step 1: Raise numerator and denominator: (1^3)/(2^3) = 1/8. Step 2: Therefore (1/2)^3 = 1/8.
212
Simplify: 3^4 / 3^2
Answer:
3^2
Step 1: Use exponent quotient rule: a^m / a^n = a^(m - n). Step 2: 3^4 / 3^2 = 3^(4 - 2) = 3^2. Step 3: 3^2 = 9; the simplest exponential form is 3^2.
213
Compute: (-8) - 6
Answer:
-14
Step 1: Subtracting 6 from -8 moves further left. Step 2: -8 - 6 = -14.
214
Compute: (-5) + 12
Answer:
7
Step 1: Adding a positive to a negative moves right on the number line. Step 2: 12 - 5 = 7. Step 3: Therefore (-5) + 12 = 7.
215
Evaluate: 15 - 4*2 + 3
Answer:
10
Step 1: Apply order of operations: multiply first. Step 2: 4*2 = 8. Step 3: Compute 15 - 8 + 3 = 7 + 3 = 10. Step 4: Therefore the correct answer is 10, so option B.
216
Classify the number 0.25
Answer:
Rational
Step 1: 0.25 = 25/100 = 1/4. Step 2: Since it can be expressed as a fraction of integers, it is rational. Step 3: It is not an integer or natural.
217
Solve for x: 3x = 18
Answer:
6
Step 1: Divide both sides by 3: x = 18/3. Step 2: Compute 18/3 = 6.
218
Compute: 3/4 of 2/3 of 18
Answer:
9
Step 1: Multiply fractions first: (3/4)*(2/3) = 6/12 = 1/2. Step 2: Then 1/2 of 18 = 18*(1/2) = 9.
219
Is 0 prime, composite, neither, or both?
Answer:
Neither
Step 1: A prime has exactly two distinct positive divisors. Step 2: A composite has more than two. Step 3: 0 has infinitely many divisors and does not meet either definition. Step 4: Therefore 0 is neither prime nor composite.
220
Find the GCD of 0 and 14.
Answer:
14
Step 1: By convention, GCD(0, n) = n for n != 0. Step 2: Therefore GCD(0, 14) = 14. Step 3: Reason: any number divides 0, so the greatest common divisor with 14 is 14.