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
81
Calculate 125^(2/3).
Answer:
25
Rewrite the expression as (125^(1/3))^2. The cube root of 125 is 5. Raising 5 to the second power gives 5^2 = 25.
82
Evaluate 32^(2/5).
Answer:
4
This is equivalent to finding the 5th root of 32 and then squaring it. The 5th root of 32 is 2 (2^5 = 32). Squaring 2 gives 2^2 = 4.
83
Find the value of 81^(3/4).
Answer:
27
Express as (81^(1/4))^3. The 4th root of 81 is 3 (since 3^4 = 81). Next, cube the result: 3^3 = 27.
84
Evaluate 64^(5/6).
Answer:
32
Rewrite 64^(5/6) as (64^(1/6))^5. The 6th root of 64 is 2 (since 2^6 = 64). Then, raise 2 to the 5th power: 2^5 = 32.
85
Calculate 8^(2/3).
Answer:
4
A fractional exponent m/n means the nth root raised to the mth power. So, 8^(2/3) = (8^(1/3))^2. The cube root of 8 is 2, and 2^2 = 4.
86
What is the value of 27^(1/3)?
Answer:
3
An exponent of 1/3 means finding the cube root. The cube root of 27 is the number that multiplied by itself three times equals 27. Since 3 * 3 * 3 = 27, the answer is 3.
87
Evaluate 16^(1/2).
Answer:
4
An exponent of 1/2 is equivalent to taking the square root. The square root of 16 is 4, since 4 * 4 = 16.
88
Evaluate (-2)^-3.
Answer:
-1/8
Apply the negative exponent rule to rewrite as 1 / (-2)^3. Cubing -2 yields -8. Therefore, the result is 1 / -8, which is -1/8.
89
Find the value of (1/5)^-1.
Answer:
5
The exponent -1 simply requires taking the reciprocal of the base. The reciprocal of 1/5 is 5/1, which is just 5.
90
Evaluate 4^-1 + 4^-1.
Answer:
1/2
First, convert negative exponents to fractions: 4^-1 = 1/4. The expression becomes 1/4 + 1/4. Adding these fractions gives 2/4, which simplifies to 1/2.