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
41
A password consists of 3 digits (0-9). What is the probability of guessing the correct password on the first try?
Answer:
1/1000
Step 1: Each digit can be anything from 0 to 9 (10 options). Total combinations = 10 × 10 × 10 = 1000. Step 2: There is only exactly 1 correct password. Step 3: Probability = 1/1000.
42
Five books are placed randomly on a shelf. What is the probability that two specific books are placed next to each other?
Answer:
2/5
Step 1: Total arrangements of 5 books = 5! = 120. Step 2: Treat the two specific books as a single unit. We now arrange 4 units: 4! = 24 ways. The two books can swap places: 2! = 2. Total favorable = 24 × 2 = 48. Step 3: Probability = 48 / 120 = 2/5.
43
Five people sit in a circle. What is the probability that two specific persons sit together?
Answer:
1/2
Step 1: Total circular permutations for 5 people = (5-1)! = 4! = 24. Step 2: Treat the two specific people as a single unit. Total units = 4. Circular permutations = (4-1)! = 3! = 6. Internal arrangements of the two = 2!. Favorable ways = 6 × 2 = 12. Step 3: Probability = 12 / 24 = 1/2.
44
Three boys and two girls sit in a row. What is the probability that the two girls sit together?
Answer:
2/5
Step 1: Total unrestricted arrangements of 5 people = 5! = 120. Step 2: Treat the 2 girls as one unit. Arrangements = 4! × 2! (internal arrangement) = 24 × 2 = 48. Step 3: Probability = 48 / 120 = 2/5.
45
If the letters of the word 'APPLE' are arranged randomly, what is the probability that the two P's are together?
Answer:
2/5
Step 1: Total arrangements of 'APPLE' = 5! / 2! = 120 / 2 = 60. Step 2: Treat 'PP' as a single entity. Entities = (PP), A, L, E. Ways to arrange = 4! = 24. Step 3: Probability = Favorable / Total = 24 / 60 = 2/5.
46
If a letter is chosen at random from the word 'MISSISSIPPI', find the probability that it is an 'S'.
Answer:
4/11
Step 1: Total letters in 'MISSISSIPPI' = 11. Step 2: The letter 'S' appears 4 times. Step 3: Probability = 4/11.
47
A letter is chosen at random from the word 'MATHEMATICS'. What is the probability that it is an 'M'?
Answer:
2/11
Step 1: Count total letters in 'MATHEMATICS' = 11. Step 2: Count the occurrences of 'M', which is 2. Step 3: Probability = 2/11.
48
If a letter is chosen at random from the English alphabet, what is the probability that it is a vowel?
Answer:
5/26
Step 1: Total letters in the English alphabet = 26. Step 2: Vowels are A, E, I, O, U (Total 5). Step 3: Probability = Favorable / Total = 5/26.
49
If a month of the year is selected at random, what is the probability that it has exactly 31 days?
Answer:
7/12
Step 1: Total months in a year = 12. Step 2: Months with 31 days are Jan, Mar, May, Jul, Aug, Oct, Dec. Total = 7. Step 3: Probability = 7/12.
50
What is the probability that a leap year contains 53 Sundays OR 53 Mondays?
Answer:
3/7
Step 1: P(53 Sundays) = 2/7. P(53 Mondays) = 2/7. Step 2: P(Both) = 1/7. Step 3: Using the addition rule: P(Sun OR Mon) = P(Sun) + P(Mon) - P(Both) = 2/7 + 2/7 - 1/7 = 3/7.