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
241
What is the value of 100^0?
Answer:
1
Regardless of how large the base is, any non-zero number raised to the zero power equals 1. Therefore, 100^0 evaluates to 1.
242
Simplify the expression: sqrt(72)
Answer:
6*sqrt(2)
Find the highest perfect square factor of 72, which is 36. Since 72 = 36 * 2, we take the square root of 36 to get 6 outside, leaving 6*sqrt(2).
243
Determine the result of: 11.71 - 0.86 + 1.78 - 9.20
Answer:
3.43
Combine the positive numbers (11.71 + 1.78 = 13.49) and combine the negative numbers (0.86 + 9.20 = 10.06). Evaluating 13.49 - 10.06 results in 3.43.
244
Simplify the expression: 2^3 * 2^4
Answer:
2^7
When multiplying terms with the same base, you add the exponents according to the product rule. Here, the base is 2, so 2^3 * 2^4 becomes 2^(3+4), which equals 2^7.
245
Calculate: (3^2)^4
Answer:
3^8
To simplify a base raised to a power and then raised to another power, multiply the two exponents together. Multiplying 2 and 4 gives 8, resulting in 3^8.
246
Simplify the expression: (a^2)^6
Answer:
a^12
The rule for a power raised to a power requires multiplying the exponents. Calculating 2 times 6 gives 12, so the expression becomes a^12.
247
Calculate: sqrt(64)
Answer:
8
The principal square root of 64 is the positive number that yields 64 when squared. Since 8^2 is 64, sqrt(64) equals 8.
248
Simplify the division: 2^8 / 2^3
Answer:
2^5
When dividing exponential terms with the same base, you subtract the exponent of the denominator from the exponent of the numerator. Here, 8 - 3 equals 5, resulting in 2^5.
249
Simplify the expression: a^-5
Answer:
1/a^5
By the rules of negative exponents, moving the base to the denominator makes the exponent positive. Thus, a^-5 is rewritten as 1/a^5.
250
Out of the fractions 9/31, 3/17, 6/23, 4/11, 7/25 which is the largest?
Answer:
4/11
Computing approximate decimal values: 9/31 ≈ 0.290, 3/17 ≈ 0.176, 6/23 ≈ 0.261, 4/11 ≈ 0.364, 7/25 = 0.280. The maximum value among these corresponds to 4/11.