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
91
What is the value of (-5)^0?
Answer:
1
Any non-zero number raised to the power of zero is always equal to 1. The negative sign is inside the parentheses, meaning the entire base of -5 is raised to the zero power, resulting in 1.
92
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.
93
Calculate: (2xy)^0 (assuming x and y are not zero)
Answer:
1
Because the entire expression (2xy) is enclosed in parentheses and raised to the power of zero, the zero exponent rule applies to the whole term, resulting in 1.
94
Simplify: x^0 (assuming x is not zero)
Answer:
1
Any non-zero variable or number raised to the zero power simplifies to exactly 1. Thus, as long as x is not zero, x^0 = 1.
95
Evaluate the expression: 5^0
Answer:
1
According to the zero exponent rule, any non-zero real number raised to the power of zero is always equal to 1. Therefore, 5^0 equals 1.
96
Evaluate: (7^2)^2
Answer:
7^4
Using the power rule, multiply the inner exponent 2 by the outer exponent 2. This gives an exponent of 4, keeping the base 7 intact to form 7^4.
97
Simplify: (z^3)^5
Answer:
z^15
When a term with an exponent is raised to an additional power, the exponents are multiplied. Multiplying 3 by 5 yields 15, making the simplified term z^15.
98
Calculate: (4^5)^3
Answer:
4^15
Multiplying the exponent 5 by the outer exponent 3 gives 15. The base remains 4, so the final simplified answer is 4^15.
99
Simplify: (10^4)^2
Answer:
10^8
By multiplying the exponents according to the power of a power rule, we calculate 4 * 2 = 8. The base stays the same, resulting in 10^8.
100
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.