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
51
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.
52
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).
53
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.
54
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.
55
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.
56
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.
57
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.
58
How many 3-digit numbers can be formed using 0, 1, 2, 3, 4 if repetition is allowed?
Answer:
100
Step 1: A 3-digit number cannot begin with 0. So, the hundreds place has 4 options (1,2,3,4). Step 2: The tens and units places can each take any of the 5 digits (0,1,2,3,4). Step 3: Total ways = 4 × 5 × 5 = 100.
59
How many 4-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if repetition is allowed?
Answer:
1296
Step 1: There are 4 positions to fill. Step 2: Since repetition is allowed, any of the 6 digits can go into any position. Step 3: Total ways = 6 × 6 × 6 × 6 = 1296.
60
How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 if repetition is allowed?
Answer:
125
Step 1: There are 3 spots to fill. Step 2: Each spot can be filled in 5 ways since repetition is allowed. Step 3: Total ways = 5 × 5 × 5 = 125.