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
111
Evaluate: 5^6 / 5^4
Answer:
5^2
Applying the exponent rule for division, subtract the exponent 4 from the exponent 6 while maintaining the base of 5. This results in 5^2.
112
Simplify: y^10 / y^3
Answer:
y^7
For division of terms with identical bases, subtract the lower power from the upper power. Taking 3 away from 10 gives an exponent of 7, making the answer y^7.
113
Calculate: 3^7 / 3^2
Answer:
3^5
Using the quotient rule, we keep the base of 3 and subtract the denominator's exponent from the numerator's exponent. The calculation 7 - 2 leaves us with 3^5.
114
Simplify the expression: x^9 / x^4
Answer:
x^5
According to the quotient rule for exponents, we subtract the bottom exponent from the top exponent when bases are the same. Subtracting 4 from 9 gives us x^5.
115
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.
116
Simplify: 7^1 * 7^6
Answer:
7^7
The product rule tells us to add the exponents when the base is identical. Adding the exponent 1 to the exponent 6 gives a final power of 7, so the answer is 7^7.
117
Multiply the terms: z^2 * z^8
Answer:
z^10
Since the bases are identical, the exponents are simply added together. Taking the sum of 2 and 8 yields 10, resulting in the simplified term z^10.
118
Simplify: 4^2 * 4^3
Answer:
4^5
By applying the fundamental rule of exponents for multiplication, we add the exponents 2 and 3. The base remains 4, which gives us 4^5.
119
Evaluate: 10^3 * 10^4
Answer:
10^7
When multiplying powers of 10, the base remains 10 and the exponents are summed. The sum of 3 and 4 is 7, making the final expression 10^7.
120
Simplify the multiple terms: a^3 * a^4 * a
Answer:
a^8
The product rule applies to any number of terms with the same base. Adding the exponents 3, 4, and the implicit 1 gives 3 + 4 + 1 = 8, yielding a^8.