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
231
Identify the property: a(b + c) = ab + ac
Answer:
Distributive property
Step 1: Multiplication is distributed over addition. Step 2: This is the distributive property. Step 3: It is not commutative (order change) nor associative (grouping change), and identity involves 1 or 0.
232
Simplify: (a^2)^3
Answer:
a^6
Step 1: Use the power of a power rule: (a^m)^n = a^(m*n). Step 2: Here (a^2)^3 = a^(2*3) = a^6.
233
Compute: -| -4 | + 3
Answer:
-1
Step 1: | -4 | = 4. Step 2: -| -4 | = -4. Step 3: -4 + 3 = -1.
234
Which is greater: 8.90 or 8.11?
Answer:
8.90
Step 1: Normalize to the same number of decimal places: 8.90 and 8.11. Step 2: Compare digit by digit: at the tenths place both are 8. At the hundredths place 9 > 1. Step 3: Therefore 8.90 > 8.11.
235
Which of the following is a rational number?
Answer:
0.333... (repeating)
Step 1: A rational number can be written as a ratio a/b of integers. Step 2: 0.333... repeating equals 1/3, which is rational. Step 3: sqrt(2), sqrt(5), and pi are irrational.
236
Which statement is true about the number line positions of -3, 0, and 4?
Answer:
-3 < 0 < 4
Step 1: On the number line, negative numbers are left of 0 and positive numbers are right of 0. Step 2: Therefore -3 is left of 0 and 4 is right of 0, giving -3 < 0 < 4.
237
Solve for x: |x| = 7
Answer:
x = 7 or x = -7
Step 1: By the definition of absolute value, |x| = 7 means the distance of x from 0 is 7. Step 2: There are two solutions: x = 7 and x = -7.
238
Simplify the radical: sqrt(50)
Answer:
5*sqrt(2)
Step 1: Factor inside the root: sqrt(50) = sqrt(25*2). Step 2: sqrt(25) = 5. Step 3: Therefore sqrt(50) = 5*sqrt(2) in simplest radical form.
239
Simplify: sqrt(81)
Answer:
9
Step 1: 81 is a perfect square: 81 = 9*9. Step 2: Therefore sqrt(81) = 9.
240
Compute: (5/6) / (1/3)
Answer:
5/2
Step 1: Division by a fraction equals multiplication by its reciprocal: (5/6)*(3/1). Step 2: Multiply: 15/6. Step 3: Simplify 15/6 by dividing by 3: 5/2.