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
Evaluate: (5^3)^3
Answer:
5^9
When an exponential term is raised to a power, multiply the exponents. Here, multiplying 3 by 3 gives an exponent of 9, leaving us with 5^9.
102
Simplify: (y^5)^2
Answer:
y^10
Applying the power rule, we multiply the exponent inside the parentheses by the exponent outside. The product of 5 and 2 is 10, so the expression simplifies to y^10.
103
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.
104
Simplify the expression: (x^4)^3
Answer:
x^12
The power of a power rule dictates that we multiply the inner and outer exponents. Therefore, 4 multiplied by 3 gives 12, making the simplified form x^12.
105
Simplify using the power of a power rule: (2^3)^2
Answer:
2^6
When raising a power to another power, you multiply the exponents. Multiplying the inside exponent 3 by the outside exponent 2 yields an exponent of 6, resulting in 2^6.
106
Evaluate: 8^4 / 8^4
Answer:
1
Subtracting the exponents gives 8^(4-4) = 8^0. Any non-zero base raised to the power of zero equals 1. Alternatively, any number divided by itself is 1.
107
Simplify: z^12 / z^5
Answer:
z^7
By applying the quotient rule for exponents, we subtract the bottom exponent (5) from the top exponent (12). This operation yields z^7.
108
Simplify the expression: 4^9 / 4^3
Answer:
4^6
Since the bases are the same, we simply subtract the exponents. Subtracting 3 from 9 leaves an exponent of 6, making the simplified form 4^6.
109
Calculate: 10^5 / 10^2
Answer:
10^3
The quotient rule dictates subtracting the denominator's exponent from the numerator's. Performing 5 - 2 yields 3, giving a final simplified expression of 10^3.
110
Simplify: a^8 / a^7
Answer:
a^1
Subtracting the exponents 8 - 7 gives 1. Any variable raised to the power of 1 is just the variable itself, so a^1 is written simply as a.