Jump to a section

Mathematics - Functions

Practise 10 IAT (IISER) previous year questions on Functions, compiled from papers spanning 2017 to 2025. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty IAT (IISER) tests.

Functions has been asked in 6 of the 9 years of IAT (IISER) papers analysed (2017–2026), with 10 questions in all. 10% of them were easy, 70% moderate and 20% tough. Most of its questions came from 2024, with 2 questions that year. In the last three years (2023–2026) it had 2 questions across 3 papers, about 0.7 per paper.

The chapter's 3 topics are not weighted equally: Types of Function (Mapping) (5 questions, 50%), Composite Function (4 questions, 40%), and Functional Equation (1 question, 10%) have been asked the most. Types of Function (Mapping) has also led over the last five years, with 1 question. Types of Function (Mapping) has produced the most tough questions (1).

  1. 1Let be the function defined by Which one of the following statements is TRUE?2025Types of Function (Mapping)
  2. 2Let be a strictly decreasing function with for all . Let be a function defined by . Which one of the following statements is Correct?2024Composite Function
  3. 3Let be a function such that for all , and . Which one of the following statements is Correct ?2024Functional Equation
  4. 4The number of functions such that for all , is2021Types of Function (Mapping)
  5. 5Let and be two functions such that Then which of the following statements is correct?2020Composite Function
  6. 6Let be a continuous function. Then, is surjective if2019Types of Function (Mapping)
  7. 7Let \(f, g, h\) be functions from \( {R}\) to \( {R}\), with \(f\) and \(g\) invertible. Which of the following is NOT always true?2018Composite Function
  8. 8How many functions \(f: {R} {R}\) satisfy \(f(1)=10\) and \(|f(x)-f(y)|=|x-y|\) for all \(x, y {R}\) ?2018Composite Function
  9. 9For , the number of onto functions from the set to the set is2017Types of Function (Mapping)
  10. 10A function satisfying for all is2017Types of Function (Mapping)

Frequently Asked Questions

1.How many questions are available for Functions?

This chapter includes 10 questions compiled from IAT (IISER) papers spanning 2017 to 2025.

2.Are these questions only from IAT (IISER), or from other exams too?

These are IAT (IISER) questions specifically for the Functions chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Functions an important chapter for IAT (IISER) Mathematics?

Functions has appeared in 7 of the 10 years of IAT (IISER) papers covered here, with 10 questions across 7 papers - about one per paper it appears in.

4.What is the difficulty level of Functions questions in IAT (IISER)?

Of the 10 questions analysed for this chapter, 10% are easy, 70% moderate and 20% tough. 2024 had the most, with 2 questions.

5.Which topics in Functions should I focus on?

These topics have carried the most weightage in Functions:

  • Types of Function (Mapping) - 5 questions (50%)
  • Composite Function - 4 questions (40%)
  • Functional Equation - 1 question (10%)
  • Types of Function (Mapping) has produced the most tough questions (1).
6.Is Functions's weightage in IAT (IISER) going up or down?

Across all 7 papers analysed, Functions has averaged about 1.4 questions per paper. In the last three years (2023–2026), that average has fallen, at about 0.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.