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
Simplify 8^3 / 8^5.
Answer:
1/64
Subtract the exponents: 3 - 5 = -2, giving 8^-2. A negative exponent indicates a reciprocal, so 8^-2 = 1 / (8^2) = 1/64.
112
Evaluate 7^2 / 7^2.
Answer:
1
Subtracting the exponents yields 7^(2-2) = 7^0. Any non-zero base raised to the power of 0 is equal to 1. Alternatively, dividing a number by itself equals 1.
113
Find the value of 3^4 / 3^-1.
Answer:
243
Subtract the exponents: 4 - (-1) = 4 + 1 = 5. The expression becomes 3^5. Evaluating 3^5 gives 3 * 3 * 3 * 3 * 3 = 243.
114
Simplify x^8 / x^3.
Answer:
x^5
When dividing terms with the same base, subtract the bottom exponent from the top exponent. x^(8-3) simplifies to x^5.
115
Calculate 10^5 / 10^2.
Answer:
1,000
Applying the quotient law, 10^5 / 10^2 = 10^(5-2) = 10^3. 10^3 equals 10 * 10 * 10, which is 1,000.
116
What is the value of 5^6 / 5^4?
Answer:
25
Using the division rule for indices, subtract the powers: 6 - 4 = 2. This leaves 5^2. Evaluating 5^2 gives 25.
117
Simplify the expression: 2^5 / 2^2.
Answer:
2^3
According to the quotient law of indices, when dividing expressions with the same base, you subtract the exponent of the denominator from the exponent of the numerator. So, 2^(5-2) = 2^3.
118
Simplify 6^-1 * 6^3.
Answer:
36
Add the exponents: -1 + 3 = 2. The expression simplifies to 6^2. Calculating the square of 6 yields 6 * 6 = 36.
119
Evaluate (-2)^2 * (-2)^3.
Answer:
-32
Using the indices addition rule for the same base (-2), we get (-2)^(2+3) = (-2)^5. A negative number raised to an odd power remains negative, so (-2)^5 = -32.
120
What is the value of 7^1 * 7^2?
Answer:
343
By adding the exponents, 7^1 * 7^2 = 7^(1+2) = 7^3. Calculating 7^3 gives 7 * 7 * 7 = 343.