If V = {x : x ∈ Z and x² < 5}, how many elements are in V?
Answer and explanation
Correct answer: 5
The governing concept is solving an inequality over the integers and then counting the resulting set. Since x²<5, we have -√5<x<√5, so the possible integers are -2,-1,0,1,2. Their squares are 4,1,0,1,4, all less than 5. The next integers, -3 and 3, have square 9 and are excluded. Thus V has five elements, so C is correct.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The governing concept is solving an inequality over the integers and then counting the resulting set. Since x²<5, we have -√5<x<√5, so the possible integers are -2,-1,0,1,2. Their squares are 4,1,0,1,4, all less than 5. The next integers, -3 and 3, have square 9 and are excluded. Thus V has five elements, so C is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Irrational numbers.
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