If a set A has 2048 total subsets, how many elements does A have?
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Answer and explanation
Correct answer: 11
For a finite set with n elements, every element has two choices in a subset: it is either included or excluded. Therefore, the total number of subsets is 2^n. Here 2^n = 2048, and 2048 = 2^11. Thus n = 11, so option C is correct. The neighboring powers confirm this: 2^10 = 1024 and 2^12 = 4096.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
For a finite set with n elements, every element has two choices in a subset: it is either included or excluded. Therefore, the total number of subsets is 2^n. Here 2^n = 2048, and 2048 = 2^11. Thus n = 11, so option C is correct. The neighboring powers confirm this: 2^10 = 1024 and 2^12 = 4096.
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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