All Categories MCQs
Topic Notes: All Categories
General Description
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
2581
From a group of 6 men and 5 women, a committee of 4 is to be formed. In how many ways can this be done so that it contains all men?
Answer:
15
Step 1: The committee must consist entirely of men. This means selecting 4 men out of 6. Step 2: Formula is 6C4. Step 3: 6C4 = 6C2 = (6 × 5) / 2 = 15.
2582
From 5 men and 4 women, in how many ways can a committee of 3 be formed if it must consist of exactly 2 men and 1 woman?
Answer:
40
Step 1: Select 2 men from 5: 5C2. Step 2: Select 1 woman from 4: 4C1. Step 3: Total ways = 5C2 × 4C1 = 10 × 4 = 40.
2583
From a group of 5 men and 4 women, in how many ways can a committee of 3 people be formed?
Answer:
84
Step 1: Total number of people = 5 + 4 = 9. We need to select 3 people. Step 2: Use the combination formula 9C3. Step 3: 9C3 = (9 × 8 × 7) / (3 × 2 × 1) = 84.
2584
How many 4-digit numbers can be formed using digits 0-9 such that all digits are distinct?
Answer:
4536
Step 1: The thousands place has 9 options (1-9, no zero). Step 2: The hundreds place has 9 options (any digit except the first one, zero is now included). The tens place has 8 options, and units place has 7 options. Step 3: Total ways = 9 × 9 × 8 × 7 = 4536.
2585
What is the total number of 3-digit numbers possible?
Answer:
900
Step 1: A 3-digit number cannot start with 0. The hundreds place has 9 options (1-9). Step 2: The tens and units places can be any digit (0-9), giving 10 options each. Step 3: Total 3-digit numbers = 9 × 10 × 10 = 900. (Or simply 999 - 99 = 900).
2586
How many different 4-digit PINs can be created using digits 0-9?
Answer:
10000
Step 1: A PIN can start with 0, so there are 10 choices for every position. Step 2: There are 4 positions to fill. Step 3: Total PINs = 10 × 10 × 10 × 10 = 10⁴ = 10,000.
2587
How many license plates can be made consisting of 3 uppercase English letters followed by 3 digits (0-9) with repetition allowed?
Answer:
17576000
Step 1: There are 26 letters and 10 digits. Step 2: The sequence is L-L-L-D-D-D. Step 3: Total plates = 26 × 26 × 26 × 10 × 10 × 10 = 17576 × 1000 = 17,576,000.
2588
How many binary sequences of length 5 can be formed?
Answer:
32
Step 1: A binary sequence uses 0s and 1s. Thus, there are 2 choices for each position. Step 2: The length of the sequence is 5. Step 3: Total sequences = 2 × 2 × 2 × 2 × 2 = 2⁵ = 32.
2589
How many 3-digit numbers divisible by 5 can be formed from 1, 2, 3, 4, 5 if repetition is allowed?
Answer:
25
Step 1: To be divisible by 5, the last digit must be 5 (1 option). Step 2: The first two digits can each be any of the 5 options. Step 3: Total ways = 5 × 5 × 1 = 25.
2590
How many 4-digit even numbers can be formed from 1, 2, 3, 4, 5 if repetition is allowed?
Answer:
250
Step 1: To be even, the last digit must be 2 or 4 (2 options). Step 2: The first three digits can each be any of the 5 options. Step 3: Total ways = 5 × 5 × 5 × 2 = 250.