If U = {1, 2, ..., 49} and A = {x : x ∈ U, x is a perfect square}, how many numbers divisible by 7 are in A′?
Answer and explanation
Correct answer: 6
The numbers from 1 to 49 that are divisible by 7 are 7, 14, 21, 28, 35, 42, and 49, giving seven numbers in total. Among them, only 49 is a perfect square because 49 = 7², so 49 belongs to A and is excluded from A′. The other six numbers are not perfect squares and therefore belong to the complement A′. Hence, the correct answer is 6, option D.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The numbers from 1 to 49 that are divisible by 7 are 7, 14, 21, 28, 35, 42, and 49, giving seven numbers in total. Among them, only 49 is a perfect square because 49 = 7², so 49 belongs to A and is excluded from A′. The other six numbers are not perfect squares and therefore belong to the complement A′. Hence, the correct answer is 6, option D.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
