Set, Relations and FunctionsPYQ Nov 20, PYQ Jan 21Question 1892 of 217
All Questions

The set of cubes of natural number is

Options

ANull set
BA finite set
CAn infinite set
DSingleton set
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Correct Answer

✅ Option c — An infinite set

All Options:

  • ANull set
  • BA finite set
  • CAn infinite set
  • DSingleton set

Detailed Solution & Explanation

The set of natural numbers is defined as N={1,2,3,4,… }\displaystyle \mathbb{N} = \{1, 2, 3, 4, \dots\}, which is an infinite set.
The set of cubes of natural numbers is defined as:
S={x∣x=n3,n∈N}={1,8,27,64,… }S = \{x \mid x = n^3, n \in \mathbb{N}\} = \{1, 8, 27, 64, \dots\}
Since the mapping f(n)=n3\displaystyle f(n) = n^3 from N\displaystyle \mathbb{N} to S\displaystyle S is one-to-one and N\displaystyle \mathbb{N} is an infinite set, the set of cubes S\displaystyle S is also an infinite set.
Hence, **Option C** is the correct answer.

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