Which is the set R = {x : x ∈ N, √x ∈ N, 10 < x < 50}?
Answer and explanation
Correct answer: R = {16, 25, 36, 49}
The governing concept is recognizing that √x ∈ N exactly when x is a perfect square of a natural number. The squares around the stated interval are 9, 16, 25, 36, 49, and 64. Applying the strict condition 10 < x < 50 removes 9 and 64, leaving 16, 25, 36, and 49. Therefore option A is correct. Option B wrongly retains 9, C omits 49, and D includes 11, which is not a perfect square.
Frequently asked questions
What is the correct answer to this question?
R = {16, 25, 36, 49}
Why is this the correct answer?
The governing concept is recognizing that √x ∈ N exactly when x is a perfect square of a natural number. The squares around the stated interval are 9, 16, 25, 36, 49, and 64. Applying the strict condition 10 < x < 50 removes 9 and 64, leaving 16, 25, 36, and 49. Therefore option A is correct. Option B wrongly retains 9, C omits 49, and D includes 11, which is not a perfect square.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
