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
21
In how many ways can 6 distinct keys be arranged on a key ring?
Answer:
60
Step 1: A key ring can be flipped over, making clockwise and anti-clockwise arrangements identical. Step 2: Formula is (n - 1)! / 2. Step 3: (6 - 1)! / 2 = 5! / 2 = 120 / 2 = 60.
22
In how many ways can 4 married couples sit around a circular table if every husband and wife sit together?
Answer:
96
Step 1: Treat each couple as a unit. 4 units arranged in a circle = (4-1)! = 3! = 6 ways. Step 2: Within each unit, the husband and wife can swap places (2! ways each). Since there are 4 couples, internal arrangements = 2⁴ = 16. Step 3: Total ways = 6 × 16 = 96.
23
In how many ways can 8 people be seated around a circular table if A and B must sit exactly opposite each other?
Answer:
720
Step 1: Fix person A. B must sit opposite to A. This takes 1 way. Step 2: There are 6 remaining seats for the 6 remaining people. Step 3: The 6 people can arrange themselves in these fixed 6 seats in 6! ways. 6! = 720.
24
In how many ways can a president and 4 committee members sit around a circular table?
Answer:
24
Step 1: There are 5 people in total. Step 2: For a regular circular arrangement of n distinct people, the number of ways is (n - 1)!. Step 3: (5 - 1)! = 4! = 24 ways.
25
How many garlands can be formed using 10 different flowers?
Answer:
181440
Step 1: A garland can be flipped over, making clockwise and anti-clockwise arrangements identical. Step 2: Formula is (n - 1)! / 2. Step 3: (10 - 1)! / 2 = 9! / 2 = 362880 / 2 = 181440.
26
How many different necklaces can be made using 7 distinct beads?
Answer:
360
Step 1: For a necklace, turning it over does not create a new arrangement (clockwise and anti-clockwise are identical). Step 2: The formula is (n - 1)! / 2. Step 3: (7 - 1)! / 2 = 6! / 2 = 720 / 2 = 360.
27
In how many ways can 5 men and 5 women sit around a circular table such that no two men sit together?
Answer:
2880
Step 1: First, seat the 5 women in a circle: (5-1)! = 4! = 24 ways. Step 2: This creates 5 gaps between the women. Step 3: Seat the 5 men in these 5 gaps in a linear fashion: 5! = 120 ways. Total = 24 × 120 = 2880.
28
In how many ways can 6 people sit around a round table so that two specific people DO NOT sit together?
Answer:
72
Step 1: Total ways for 6 people in a circle = (6-1)! = 5! = 120. Step 2: Ways they sit together = 48 (from previous calculation). Step 3: Ways they do not sit together = Total - Together = 120 - 48 = 72.
29
In how many ways can 6 people sit around a circular table if 2 specific people insist on sitting next to each other?
Answer:
48
Step 1: Treat the 2 specific people as a single unit. Total units = 5. Step 2: Arrange 5 units in a circle: (5 - 1)! = 4! = 24 ways. Step 3: The 2 specific people can swap places internally in 2! = 2 ways. Total = 24 × 2 = 48.
30
In how many ways can 5 people sit around a circular table?
Answer:
24
Step 1: For a circular arrangement, the relative position matters, not the absolute position. Step 2: The formula for n distinct objects in a circle is (n - 1)!. Step 3: (5 - 1)! = 4! = 24.