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
What is the probability that a randomly chosen leap year contains both 53 Sundays AND 53 Mondays?
Answer:
1/7
Step 1: A leap year has 2 extra days. Step 2: The possible consecutive day pairs are 7. The only pair containing both Sunday and Monday is (Sunday, Monday). Step 3: There is 1 favorable outcome out of 7. Probability = 1/7.
52
What is the probability that an ordinary (non-leap) year contains exactly 53 Mondays?
Answer:
1/7
Step 1: An ordinary year has 365 days, which is 52 weeks and 1 extra day. Step 2: The extra day can be any of the 7 days of the week. Step 3: For there to be 53 Mondays, the extra day must be a Monday. Probability = 1/7.
53
What is the probability that a leap year, selected at random, will contain 53 Sundays?
Answer:
2/7
Step 1: A leap year has 366 days, which is 52 complete weeks (364 days) and 2 extra days. Step 2: The 2 extra days can be (Sun-Mon, Mon-Tue, Tue-Wed, Wed-Thu, Thu-Fri, Fri-Sat, Sat-Sun). There are 7 pairs. Step 3: Sundays appear in 2 pairs (Sat-Sun and Sun-Mon). Probability = 2/7.
54
If a two-digit number is chosen at random, find the probability that both its digits are the same.
Answer:
1/10
Step 1: Total two-digit numbers = 90. Step 2: Numbers with identical digits are 11, 22, 33, 44, 55, 66, 77, 88, 99. Total = 9. Step 3: Probability = 9/90 = 1/10.
55
What is the probability that a randomly chosen two-digit number is a multiple of 10?
Answer:
1/10
Step 1: Total two-digit numbers = 90. Step 2: Multiples of 10 are 10, 20, 30, ..., 90. There are 9 such numbers. Step 3: Probability = 9/90 = 1/10.
56
What is the probability that a randomly chosen two-digit positive integer has a sum of digits equal to 9?
Answer:
1/10
Step 1: Total two-digit numbers (10 to 99) = 90. Step 2: Numbers with sum 9: 18, 27, 36, 45, 54, 63, 72, 81, 90. Total = 9 outcomes. Step 3: Probability = 9/90 = 1/10.
57
A number is picked from 1 to 20. Find the probability that it is divisible by both 4 and 6.
Answer:
1/20
Step 1: A number divisible by both 4 and 6 must be divisible by their LCM, which is 12. Step 2: Multiples of 12 between 1 and 20 is just 12 (1 outcome). Step 3: Probability = 1/20.
58
A number is chosen from 1 to 50. What is the probability that it is a multiple of either 3 or 5?
Answer:
23/50
Step 1: Multiples of 3 = int(50/3) = 16. Multiples of 5 = int(50/5) = 10. Step 2: Multiples of both 3 and 5 (i.e., 15) = int(50/15) = 3. Step 3: Total favorable = 16 + 10 - 3 = 23. Probability = 23/50.
59
If a number is selected at random from the integers 1 to 50, what is the probability that it is a multiple of 5?
Answer:
1/5
Step 1: Total numbers = 50. Step 2: Multiples of 5 up to 50 are 5, 10, ..., 50. There are 50/5 = 10 multiples. Step 3: Probability = 10/50 = 1/5.
60
A number is chosen from 1 to 100. What is the probability that it is a perfect square?
Answer:
1/10
Step 1: Total numbers = 100. Step 2: Perfect squares from 1 to 100 are 1², 2², ..., 10² (1, 4, 9, 16, 25, 36, 49, 64, 81, 100). Total 10. Step 3: Probability = 10/100 = 1/10.