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
71
Find the simplified form of sqrt(200).
Answer:
10 sqrt(2)
Find the largest perfect square in 200, which is 100. Write as sqrt(100 * 2). Since sqrt(100) is 10, the simplified surd is 10 sqrt(2).
72
Simplify the expression sqrt(32).
Answer:
4 sqrt(2)
The largest perfect square factor of 32 is 16. Express it as sqrt(16 * 2). Extract the square root of 16 to get 4, leaving 4 sqrt(2).
73
What is the simplified form of sqrt(12)?
Answer:
2 sqrt(3)
The highest perfect square factor of 12 is 4. Rewrite as sqrt(4 * 3). Separate into sqrt(4) * sqrt(3), which evaluates to 2 sqrt(3).
74
Evaluate and simplify sqrt(75).
Answer:
5 sqrt(3)
The largest perfect square factor of 75 is 25. Break it down into sqrt(25 * 3). Taking the square root of 25 leaves 5 outside the root, resulting in 5 sqrt(3).
75
Simplify sqrt(48).
Answer:
4 sqrt(3)
Identify the largest perfect square dividing 48, which is 16. Rewrite sqrt(48) as sqrt(16 * 3). This simplifies to sqrt(16) * sqrt(3) = 4 sqrt(3).
76
What is the simplified form of sqrt(50)?
Answer:
5 sqrt(2)
The largest perfect square factor of 50 is 25. Rewrite as sqrt(25 * 2) = sqrt(25) * sqrt(2). The square root of 25 is 5, giving 5 sqrt(2).
77
Simplify the surd: sqrt(18).
Answer:
3 sqrt(2)
Find the largest perfect square factor of 18, which is 9. Rewrite sqrt(18) as sqrt(9 * 2). Using the multiplication property of surds, split it into sqrt(9) * sqrt(2). This simplifies to 3 sqrt(2).
78
Calculate 16^(-1/4).
Answer:
1/2
First, handle the negative exponent by taking the reciprocal: 1 / (16^(1/4)). Then, find the 4th root of 16, which is 2. The expression simplifies to 1/2.
79
Evaluate (1/8)^(1/3).
Answer:
1/2
Apply the exponent to both the numerator and the denominator. The cube root of 1 is 1, and the cube root of 8 is 2. Thus, the result is 1/2.
80
What is the value of 10000^(1/4)?
Answer:
10
The exponent 1/4 indicates the 4th root. We are looking for a number that multiplied by itself four times equals 10,000. 10 * 10 * 10 * 10 = 10,000, so the answer is 10.