If Q = {x : x ∈ N, 1 ≤ x ≤ 20, and x is a perfect cube}, what is Q?
Answer and explanation
Correct answer: Q = {1, 8}
Perfect cubes in the relevant positive range are obtained from 1³, 2³, 3³, and so on. We have 1³ = 1 and 2³ = 8, both of which lie between 1 and 20. The next cube is 3³ = 27, which is outside the upper limit. Thus the members satisfying every condition are 1 and 8, so Q = {1, 8}. The numbers in option D are perfect squares, not perfect cubes.
Frequently asked questions
What is the correct answer to this question?
Q = {1, 8}
Why is this the correct answer?
Perfect cubes in the relevant positive range are obtained from 1³, 2³, 3³, and so on. We have 1³ = 1 and 2³ = 8, both of which lie between 1 and 20. The next cube is 3³ = 27, which is outside the upper limit. Thus the members satisfying every condition are 1 and 8, so Q = {1, 8}. The numbers in option D are perfect squares, not perfect cubes.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
