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
121
What is the simplified form of 5^2 * 5^5?
Answer:
5^7
To multiply expressions with identical bases, you must add the exponents while keeping the base unchanged. Adding 2 and 5 gives an exponent of 7, resulting in 5^7.
122
Simplify: y^6 * y
Answer:
y^7
A variable without a visible exponent has an implicit exponent of 1. So, y^6 * y^1 means we add the exponents 6 and 1 together, resulting in y^7.
123
Calculate the value of: 3^4 * 3^2
Answer:
3^6
Using the law of exponents for multiplication, we keep the base the same and add the powers. For 3^4 * 3^2, adding the powers 4 and 2 gives us 3^6.
124
Simplify the expression: x^5 * x^2
Answer:
x^7
According to the product rule for exponents, when you multiply two terms with the same base, you add their exponents together. Therefore, x^5 * x^2 is equal to x^(5+2), which simplifies to x^7.
125
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.