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NDA 1 2025 Maths, question 88

Topic: Algebra

Passage · Q87 to Q88

Let f={(1,1),(2,4),(3,7),(4,10)}f = \{(1,1),(2,4),(3,7),(4,10)\}.

Q88

Consider the following statements:

I. f is one-one function.

II. f is onto function if the codomain is the set of natural numbers.

Which of the statements given above is/are correct?

  1. (a) I onlyCorrect answer
  2. (b) II only
  3. (c) Both I and II
  4. (d) Neither I nor II

Solution.

Answer: (a) I only

  1. The distinct inputs 1, 2, 3 and 4 have distinct outputs 1, 4, 7 and 10, so ff is one-one.
  2. Its range is only {1,4,7,10}\{ 1,4,7,10\}.
  3. Natural numbers such as 2 have no preimage, so it is not onto the natural numbers.