Set, Relations and FunctionsPYQ Nov. 20Question 1891 of 217
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The set of cubes of the natural number is:

Options

AA null set
BA finite set
CAn infinite set
DA finite set of three numbers
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Correct Answer

✅ Option c — An infinite set

All Options:

  • AA null set
  • BA finite set
  • CAn infinite set
  • DA finite set of three numbers

Detailed Solution & Explanation

Let the set of natural numbers be N={1,2,3,4,… }\displaystyle \mathbb{N} = \{1, 2, 3, 4, \dots\}.
The set of cubes of natural numbers, say S\displaystyle S, can be written as:
S={n3∣n∈N}={13,23,33,43,… }={1,8,27,64,… }S = \{n^3 \mid n \in \mathbb{N}\} = \{1^3, 2^3, 3^3, 4^3, \dots\} = \{1, 8, 27, 64, \dots\}
Since there are infinitely many natural numbers, we can find a unique cube for each natural number.
Thus, the set S\displaystyle S has infinitely many elements, making it an infinite set.
Hence, **Option C** is the correct answer.

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