If M₁ = {x : x ∈ ℕ, x is a divisor of 100 and x is a square number}, what is M₁?
Answer and explanation
Correct answer: M₁ = {1, 4, 25, 100}
The governing concept is finding the intersection of the divisors of 100 with the perfect squares. The positive divisors are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Among them, 1 = 1², 4 = 2², 25 = 5², and 100 = 10² are squares. Thus M₁ = {1, 4, 25, 100}, so option A is correct. Option C lists all divisors rather than only squares, and 16 in D is square but does not divide 100.
Frequently asked questions
What is the correct answer to this question?
M₁ = {1, 4, 25, 100}
Why is this the correct answer?
The governing concept is finding the intersection of the divisors of 100 with the perfect squares. The positive divisors are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Among them, 1 = 1², 4 = 2², 25 = 5², and 100 = 10² are squares. Thus M₁ = {1, 4, 25, 100}, so option A is correct. Option C lists all divisors rather than only squares, and 16 in D is square but does not divide 100.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
