Mathematics - Functions
Practise 23 JEE Advanced previous year questions on Functions, compiled from papers spanning 2007 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Advanced tests.
Functions has been asked in 13 of the 27 years of JEE Advanced papers analysed (2000–2026), with 23 questions in all. 17% of them were easy, 35% moderate and 48% tough. Most of its questions came from 2018, with 3 questions that year. In the last three years (2024–2026) it had 5 questions across 6 papers, about 0.8 per paper.
The chapter's 7 topics are not weighted equally: Types of Function (Mapping) (8 questions, 35%), Number of Solutions (4 questions, 17%), and Functional Equation (4 questions, 17%) have been asked the most. Types of Function (Mapping) has also led over the last five years, with 3 questions. Types of Function (Mapping) has produced the most tough questions (3).
- 1Let denote the set of all positive integers. Consider the sets and . Let be the set of all functions such that and . Consider the set . Then2026 (Paper 2)Types of Function (Mapping)
- 2Let denote the set of all real numbers. Let for . Define the functions , and by If for every , then the coefficient of in is2025 (Paper 1)Composite Function
- 3Let denote the set of all natural numbers, and denote the set of all integers. Consider the functions and defined by And Define for all , an2025 (Paper 1)Types of Function (Mapping)
- 4Let and be functions defined by and Let . Define the function by Match each entry in List-I to the correct entry in List-II. The correct opt2024 (Paper 1)Types of Function (Mapping)
- 5Let be a function such that for all , and be a function such that for all . If and , then the value of is . ________.2024 (Paper 2)Functional Equation
- 6Let S = 0 , 1 1 , 2 3 , 4 and T = 0 , 1 , 2 , 3 . Then which of the following statements is(are) true?2023 (Paper 1)Defintion of Function
- 7If the function f : R R is defined by f x = x x sin x , then which of the following statements is TRUE?2020 (Paper 1)Types of Function (Mapping)
- 8Let the function f : 0 , 1 be defined by f x = 4 x 4 x + 2 . Then the value of f 1 40 + f 2 40 + f 3 40 + + f 39 40 - f 1 2 is_________2020 (Paper 2)Defintion of Function
- 9Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If is the number of one-one functions from X Y and is the num2018 (Paper 2)Types of Function (Mapping)
- 10Let f : R R be a differentiable function with f 0 = 1 and satisfying the equation f x + y = f x f y + f x f y for all x , y R . Then, the va2018 (Paper 2)Functional Equation
- 11Let E 1 = { x : x 1 and x x - 1 0 } and E 2 = { x E 1 : sin - 1 log e x x - 1 is a real number} (Here the inverse trigonometric function sin2018 (Paper 2)Range
- 12Let f x = sin 6 sin 2 sin x , for all x R and g x = 2 sin x , for all x R . Let f o g x denote f g x and g o f x denote g f x . Then which o2015 (Paper 1)Range
- 13Let f : - 2 , 2 R be given by f x = log sec x + tan x 3 . Then2014 (Paper 1)Types of Function (Mapping)
- 14let f 1 : R R , f 2 : 0 , R , f 3 : R R a n d f 4 : R [ 0 , ) be defined by f 1 x = x i f x 0 e x i f x 0 ; f 2 x = x 2 ; f 3 x = sin x i f 2014 (Paper 2)Types of Function (Mapping)
- 15The function , defined by , is2012 (Paper 1)Types of Function (Mapping)
- 16Let for all and let for all . Question: Consider the statements: : There exists some such that : There exists some such that Then2012 (Paper 2)Functional Equation
- 17Let be defined by , where is a constant such that . Then,2011 (Paper 2)Inverse of a Function
- 18Match the statements given in Column I with the intervals/union of intervals given in Column II.2011 (Paper 2)Range
- 19Match the statements/expressions given in Column I with the values given in Column II.2009 (Paper 2)Number of Solutions
- 20Let , where is a twice differentiable positive function on such that . Then, for is equal to2008 (Paper 2)Functional Equation
- 21Paragraph: If a continuous defined on the real line , assume positive and negative values in , then the equation has a root in . For example2007 (Paper 2)Number of Solutions
- 22Paragraph: If a continuous defined on the real line , assume positive and negative values in , then the equation has a root in . For example2007 (Paper 2)Number of Solutions
- 23Paragraph: If a continuous defined on the real line , assume positive and negative values in , then the equation has a root in . For example2007 (Paper 2)Number of Solutions
Frequently Asked Questions
1.How many questions are available for Functions?
This chapter includes 23 questions compiled from JEE Advanced papers spanning 2007 to 2026.
2.Are these questions only from JEE Advanced, or from other exams too?
These are JEE Advanced 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 JEE Advanced Mathematics?
Functions has appeared in 13 of the 21 years of JEE Advanced papers covered here, with 23 questions across 17 papers - about one per paper it appears in.
4.What is the difficulty level of Functions questions in JEE Advanced?
Of the 23 questions analysed for this chapter, 17% are easy, 35% moderate and 48% tough. 2018 had the most, with 3 questions.
5.Which topics in Functions should I focus on?
These topics have carried the most weightage in Functions:
- Types of Function (Mapping) - 8 questions (35%)
- Number of Solutions - 4 questions (17%)
- Functional Equation - 4 questions (17%)
- Types of Function (Mapping) has produced the most tough questions (3).
6.Is Functions's weightage in JEE Advanced going up or down?
Across all 17 papers analysed, Functions has averaged about 1.4 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.8 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.