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Mathematics - Functions

Practise 87 NTA Abhyas (JEE Main) questions on Functions. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Functions has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 87 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1The range of the function f x = 2 3 x 2 - 4 x + 5 is
  2. 2The domain of the function f x = x - 1 - x 2 4 is
  3. 3sin a x + cos a x and | sin x | + | cos x | are periodic with the same fundamental period, if a equals to
  4. 4For p 2 and x R , if the number of natural numbers in the range of f x = x 2 + 2 x + p x 2 + 2 x + 2 is 3 , then the value of p is equal to
  5. 5If the function f : R A defined as f x = sin - 1 x 1 + x 2 is a surjective function, then the set A is
  6. 6Let a function f : 1 , ∞ → 0 , ∞ be defined by f x = 1 - 1 x . Then f is
  7. 7Let a function f : 2 , ∞ → 0 , ∞ defined as f x = x - 3 x - 2 , then f is
  8. 8If e x + e f x = e , then the domain of the function f is
  9. 9If the range of the function f x = s i n - 1 x + 2 t a n - 1 x + x 2 + 4 x + 1 is [ p , q ] , then the value of p + q is
  10. 10If f tan ⁡ x = cos ⁡ 2 x , x ≠ ( 2 n + 1 ) π 2 , n ∈ I then incorrect statement is
  11. 11The domain of definition of the function f x = log x - 1 x 2 + 4 x + 4 , is
  12. 12Let f : R → R be a periodic function such that f T + x = 1 + 1 - 3 f x + 3 f x 2 - f x 3 1 3 where T is a fixed positive number, then period
  13. 13Let f : R → B be a function defined by f x = t a n - 1 2 x 1 + x 2 , then f is both one-one and onto when B is in the interval
  14. 14A function f : Z → Z is defined as f n = n + 1 n ∈ odd integer n 2 n ∈ even integer . If k ∈ odd integer and f f f k = 33 , then the sum of
  15. 15The minimum value of the function f x = tan ⁡ x 3 + 2 tan ⁡ x , ∀ x ∈ 0 , π 2 is
  16. 16The domain of the function f x = 1 9 - x 2 + l o g 20 x 3 - 3 x is
  17. 17Let f : - 1 , 1 → B be a function defined as f x = cot - 1 ⁡ 2 x 3 1 + x 2 . If f is both one-one and onto, then B is the interval
  18. 18If f : N Z defined as f n = n - 1 2 : if n is o d d - n 2 : if n is e v e n and g : N N defined as g n = n - - 1 n , then f o g is (where, N
  19. 19The domain of definition of the function y = 3 e x 2 - 1 log ⁡ x - 1 is
  20. 20If f : R → 0 , π 2 , f x = s i n - 1 40 x 2 + x + λ is a surjective function, then the value of λ is equal to
  21. 21The domain of the function f x = 4 x 12 - x 9 + x 4 - x + 1 is
  22. 22For the function f x = s i n x c o s - 1 x , choose the correct option. (where . represents the greatest integer function)
  23. 23The domain of the function f x = l o g 2 1 - l o g 12 x 2 - 5 x + 16 is
  24. 24The range of the function f x = sin ⁡ π x + 1 x 4 + 1 (where, · is the greatest integer function) is
  25. 25The function f : - , 1 0 , e 5 defined as f x = e x 3 - 3 x + 2 is
  26. 26If x 2 + m x + 1 x 2 + x + 1 3 for all real x , then
  27. 27Let f x = x 2 - x + 1 , ∀ x ≥ 1 2 , then the solution of the equation f x = f - 1 x is
  28. 28The number of real solutions of cot - 1 ⁡ x x + 3 + sin - 1 ⁡ x 2 + 3 x + 1 = π 2 is/are
  29. 29For real values of x , the value of the expression 11 x 2 - 12 x - 6 x 2 + 4 x + 2
  30. 30If f x = 2 x − sin x , f : R → R and g x = x 1 3 , g : R → R , then
  31. 31If f is a function defined as f ( x ) = x 2 − x + 5 , f : ( 1 2 , ∞ ) → ( 19 4 , ∞ ) , and g ( x ) is its inverse function, then g ' 7 is eq
  32. 32Let f : A B is a function defined by f x = 2 x 1 + x 2 . If the function f x is a bijective function, then the correct statement can be
  33. 33If f : R → R be a function such that f x = x 3 + x 2 + 4 x + sin ⁡ x . Then, the function f x is
  34. 34If f : ( 0 , ∞ ) → ( 0 , ∞ ) and f x = x 1 + x , then f is
  35. 35If f : R - 1,1 be a function defined as f x = sin x 2 8 x 2 + 2 , then f is
  36. 36Let f : R → R be a function defined as f x = x 2 - 6 x 2 + 2 , then f is
  37. 37The domain of the function f x = log 3 ⁡ 1 - log 6 ⁡ x 2 - 7 x + 16 is
  38. 38The domain of f x = x 16 - x 2 + l o g 2 x 3 - 2 x is
  39. 39The function f x = s i n - 1 2 x - x 2 + 2 - 1 x + 1 x 2 is defined in the interval (where is the greatest integer function)
  40. 40For x - 2 , 2 , the range of values of f x = 2 + sin x + sin 3 x + sin 5 x . . is
  41. 41If f x + y, x - y = xy, then the arithmetic mean of f x , y and f y , x is
  42. 42If f x = x 2 - x 2 x 2 - x 2 - 2 (where, ⋅ represents the greatest integer part of x ), then the range of f x is
  43. 43If f : A → B defined by f x = s i n x - c o s x + 3 2 is an invertible function, then the correct statement can be
  44. 44f : R R , f x = x + sin x is onto if is an element of the set P and f x is one-one if is an element of the set Q , then (given, is a real nu
  45. 45If f x = s i n x + c o s x and g x = x 2 - 1 , then g f x is invertible in the domain
  46. 46If f x = x 2 - x 2 1 + x 2 - x 2 (where . represents the greatest integer part of x ), then the range of f x is
  47. 47The function f : R R defined as f x = x 2 - x + 1 x 2 + x + 1 is
  48. 48If f : R → π 3 , π defined by f x = c o s - 1 λ - x 2 x 2 + 2 is a surjective function, then the value of λ is equal to
  49. 49The range of the function f x = tan x + 1 x 4 + 1 (where, is the greatest integer function) is
  50. 50The function f : 0 ,7 0 , 70 where f x = x 3 - 12 x 2 + 45 x , is

Frequently Asked Questions

1.How many questions are available for Functions?

This chapter includes 87 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

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

3.What is the difficulty level of Functions questions in NTA Abhyas (JEE Main)?

Of the 87 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Functions should I focus on?

All of this chapter's questions come from a single topic: Uncategorized.