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Class 10MathematicsSetsPower Set and SubsetsMediumLevel 10

If n(P(A)) = 512, what is the value of n(A)?

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Answer and explanation

Correct answer: 9

If A has n elements, then its power set P(A) has 2ⁿ elements. The given information is 2ⁿ = 512. Since 512 = 2⁹, comparing powers of 2 gives n = 9. The nearby values confirm this: 2⁸ = 256 and 2¹⁰ = 1024, so neither 8 nor 10 can be correct. Hence option C is the answer.

Tags

setspower setcardinalityexponentsMathematicsPower Set and SubsetsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

9

Why is this the correct answer?

If A has n elements, then its power set P(A) has 2ⁿ elements. The given information is 2ⁿ = 512. Since 512 = 2⁹, comparing powers of 2 gives n = 9. The nearby values confirm this: 2⁸ = 256 and 2¹⁰ = 1024, so neither 8 nor 10 can be correct. Hence option C is the answer.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.

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