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NDA 2025
Exam
NDA
Year
2025
Subject
Mathematics
Chapter
Functions

NDA 2025 · Mathematics · Functions

Consider the following for the two (02) items that follow: Let f =...

Consider the following for the two (02) items that follow:
Let f={(1,1),(2,4),(3,7),(4,10)}f = \{(1,1), (2,4), (3,7), (4,10)\}.

Consider the following statements:
I. ff is one-one function.
II. ff is onto function if the codomain is the set of natural numbers.
Which of the statements given above is/are correct?

Options

  1. AI only
  2. BII only
  3. CBoth I and II
  4. DNeither I nor II

Correct answer

A. I only

Step-by-step solution

The given function is f={(1,1),(2,4),(3,7),(4,10)}f = \{(1,1), (2,4), (3,7), (4,10)\}.

The domain of ff is {1,2,3,4}\{1, 2, 3, 4\} and the range of ff is {1,4,7,10}\{1, 4, 7, 10\}.

Since each element in the domain has a distinct image in the range, ff is a one-one function. Statement I is correct.

If the codomain is the set of natural numbers, the range {1,4,7,10}\{1, 4, 7, 10\} is a proper subset of the codomain. Since the range is not equal to the codomain, ff is not an onto function. Statement II is incorrect.

Therefore, only Statement I is correct.

Answer: I only
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