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
101
Simplify (-3^2)^3.
Answer:
-729
First, note the order of operations: -3^2 means -(3^2) = -9. Then, cube it: (-9)^3 = -729. A negative number raised to an odd power remains negative.
102
Evaluate (2^-2)^2.
Answer:
1/16
Multiply the exponents: -2 * 2 = -4. This gives 2^-4. A negative exponent means taking the reciprocal, so 2^-4 = 1 / (2^4) = 1/16.
103
What is the value of (10^2)^3?
Answer:
1,000,000
Multiply the exponents: 2 * 3 = 6. This gives 10^6. 10^6 is equal to 1 followed by 6 zeros, which is 1,000,000.
104
Calculate (5^1)^4.
Answer:
625
Multiply the powers: 1 * 4 = 4, resulting in 5^4. Evaluating 5^4 gives 5 * 5 * 5 * 5 = 625.
105
Simplify (x^4)^2.
Answer:
x^8
Applying the power rule of indices, you multiply the inner exponent by the outer exponent. 4 * 2 = 8, so the simplified expression is x^8.
106
Evaluate (3^2)^3.
Answer:
729
Multiply the exponents together: 2 * 3 = 6. The expression becomes 3^6. Calculating 3^6 (3 * 3 * 3 * 3 * 3 * 3) gives 729.
107
Simplify (2^3)^2.
Answer:
64
According to the power of a power rule, multiply the exponents: 3 * 2 = 6. This gives 2^6. Expanding 2^6 yields 64.
108
Express a^x / a^y as a single power.
Answer:
a^(x-y)
This represents the general quotient rule of indices. When dividing terms with the same base 'a', the exponent of the denominator is subtracted from the exponent of the numerator, giving a^(x-y).
109
What is the value of 9^4 / 9^3?
Answer:
9
Subtract the powers: 4 - 3 = 1. This leaves 9^1. Any number raised to the power of 1 is the number itself, which is 9.
110
Calculate 4^5 / 4^3.
Answer:
16
Applying the division rule of indices, 4^5 / 4^3 = 4^(5-3) = 4^2. Expanding this gives 4 * 4 = 16.