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
61
Calculate 2 sqrt(3) + 4 sqrt(3) - sqrt(3).
Answer:
5 sqrt(3)
Combine the coefficients of the like surds: 2 + 4 - 1 = 5. Therefore, the expression simplifies to 5 sqrt(3).
62
Evaluate sqrt(45) - sqrt(20).
Answer:
sqrt(5)
Simplify the surds first. sqrt(45) = sqrt(9 * 5) = 3 sqrt(5). sqrt(20) = sqrt(4 * 5) = 2 sqrt(5). Subtracting them yields 3 sqrt(5) - 2 sqrt(5) = sqrt(5).
63
Simplify sqrt(50) + sqrt(18).
Answer:
8 sqrt(2)
First, simplify both surds. sqrt(50) = 5 sqrt(2) and sqrt(18) = 3 sqrt(2). Now add the like surds: 5 sqrt(2) + 3 sqrt(2) = 8 sqrt(2).
64
Calculate 5 sqrt(5) - 2 sqrt(5).
Answer:
3 sqrt(5)
These are like surds, so you just subtract the coefficients. 5 - 2 = 3, so the result is 3 sqrt(5).
65
Evaluate sqrt(27) - sqrt(12).
Answer:
sqrt(3)
Simplify each surd first. sqrt(27) = 3 sqrt(3) and sqrt(12) = 2 sqrt(3). Subtract the two expressions: 3 sqrt(3) - 2 sqrt(3) = 1 sqrt(3) or simply sqrt(3).
66
Simplify the expression: sqrt(8) + sqrt(2).
Answer:
3 sqrt(2)
First, simplify sqrt(8) to 2 sqrt(2). Substitute this back into the expression: 2 sqrt(2) + sqrt(2). Adding these like terms gives 3 sqrt(2).
67
Add the surds: sqrt(2) + sqrt(2).
Answer:
2 sqrt(2)
When adding like surds, treat them as variables (e.g., x + x = 2x). Therefore, 1 sqrt(2) + 1 sqrt(2) = 2 sqrt(2).
68
Simplify sqrt(27).
Answer:
3 sqrt(3)
Identify 9 as the largest perfect square factor. Rewrite sqrt(27) as sqrt(9 * 3). The square root of 9 is 3, resulting in 3 sqrt(3).
69
What is the simplified form of sqrt(80)?
Answer:
4 sqrt(5)
The highest perfect square factor of 80 is 16. Break the surd into sqrt(16 * 5). Taking the square root of 16 yields 4, leaving 4 sqrt(5).
70
Simplify sqrt(108).
Answer:
6 sqrt(3)
The largest perfect square factor of 108 is 36. Rewrite as sqrt(36 * 3). The square root of 36 is 6, so the result is 6 sqrt(3).