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JEE Main Sets Relations and Functions questions

42 Mathematics questions on Sets Relations and Functions as asked in JEE Main, newest first. 28 come with a worked solution.

  1. Let f(x) = 2x^n + λ, λ ∈ R, n ∈ N, and f(4) = 133, f(5) = 255. Then the sum of all the positive integer divisors of (f(3) - f(2)) is

    2023 · with solution

  2. The relation R = \(a,b): gcd(a,b) = 1, 2a ≠ b, a, b ∈ Z\ is :

    2023

  3. Let f: R arrow R be a function such that f(x) = (x^2 + 2x + 1)/(x^2 + 1). Then

    2023 · with solution

  4. The number of functions f: \1,2,3,4\ arrow \a ∈ Z : |a| ≤ 8\ satisfying f(n) + 1/n f(n+1) = 1, forall n ∈ \1,2,3\ is

    2023 · with solution

  5. The domain of f(x) = dfraclog_(x+1)(x-2)e^2log_e x - (2x+3), x ∈ R is

    2023 · with solution

  6. The minimum number of elements that must be added to the relation R = \(a, b), (b, c), (b, d)\ on the set \a, b, c, d\ so that it is an equivalence relation, is ______.

    2023

  7. For some a, b, c ∈ N, let f(x) = ax - 3 and g(x) = x^b + c, x ∈ R. If (fog)^-1(x) = ((x-7)/2 )^1/3, then (fog)(ac) + (gof)(b) is equal to __________.

    2023

  8. For x ∈ (0, 3/2 ), let f(x) = √(x), g(x) = tan x and h(x) = (1-x^2)/(1+x^2). If φ(x) = ((hof)og)(x), then φ ((π)/3 ) is equal to

    2019

  9. The domain of the definition of the function f(x) = 1/(4-x^2) + log_10(x^3 - x) is

    2019

  10. If the function f: R - \-1, 1\ → A defined by f(x) = (x^2)/(1 - x^2), is surjective, then A is equal to

    2019

  11. Let f(x) = a^x (a > 0) be written as f(x) = f_1(x) + f_2(x), where f_1(x) is an even function and f_2(x) is an odd function. Then f_1(x + y) + f_1(x - y) equals

    2019 · with solution

  12. Let f(x) = x^2, x ∈ R. For any A ⊂eq R, define g(A) = \x ∈ R : f(x) ∈ A\. If S = [0, 4], then which one of the following statements is not true?

    2019

  13. Let a function f:(0,∞) → (0,∞) be defined by f(x) = |1 - 1/x |. Then, f is

    2019

  14. Let sum_k=1^10 f(a+k) = 16(2^10-1), where the function f satisfies f(x+y) = f(x)f(y) for all natural numbers x, y and f(1) = 2. Then, the natural number 'a' is

    2019 · with solution

  15. Let f: R → R be defined by f(x) = x/(1+x^2), x ∈ R. Then, the range of f is

    2019 · with solution

  16. For x ∈ R - \0, 1\, let f_1(x) = 1/x, f_2(x) = 1 - x and f_3(x) = 1/(1-x) be three given functions. If a function, J(x) satisfies (f_2 circ J circ f_1)(x) = f_3(x), then J(x) is equal to

    2019 · with solution

  17. Let N be the set of natural numbers and two functions f and g be defined as f, g: N → N such that f(n) = begincases (n+1)/2 & if n is odd \ n/2 & if n is even endcases and g(n) = n - (-1)^n. Then, fog is

    2019

  18. Let A = \x ∈ R : x is not a positive integer\. Define a function f : A → R as f(x) = 2x/(x-1), then f is

    2019 · with solution

  19. Let a, b, c ∈ R. If f(x) = ax^2 + bx + c be such that a + b + c = 3 and f(x+y) = f(x) + f(y) + xy, forall x, y ∈ R, and sum_n=1^10 f(n) is equal to

    2017 · with solution

  20. The function f: R → [-1/2, 1/2 ] defined as f(x) = x/(1+x^2) is

    2017 · with solution

  21. The function f: [0, 3] → [1, 29], defined by f(x) = 2x^3 - 15x^2 + 36x + 1, is

    2012 · with solution

  22. Let f(x) = x^2 and g(x) = sin x for all x ∈ R. Then, the set of all x satisfying (fogogof)(x) = (gogof)(x), where (fog)(x) = f(g(x)), is

    2011 · with solution

  23. If X and Y are two non-empty sets where f: X → Y, is function is defined such that f(C) = \f(x) : x ∈ C\ for C ⊂eq X and f^-1(D) = \x : f(x) ∈ D\ for D ⊂eq Y, for any A ⊂eq Y and B ⊂eq Y, then

    2005 · with solution

  24. f(x) = begincases x, & if x is rational \ 0, & if x is irrational endcases, g(x) = begincases 0, & if x is rational \ x, & if x is irrational endcases Then, f - g is

    2005

  25. If f(x) = sin x + cos x, g(x) = x^2 - 1, then g\f(x)\ is invertible in the domain

    2004 · with solution

  26. Domain of definition of the function f(x) = sqrtsin^-1(2x) + (π)/6 for real valued x, is

    2003 · with solution

  27. If f:[0,∞) → [0,∞) and f(x) = x/(1+x), then f is \hfill

    2003 · with solution

  28. Suppose f(x) = (x+1)^2 for x ≥ -1. If g(x) is the function whose graph is reflection of the graph of f(x) with respect to the line y = x, then g(x) equals

    2002

  29. Let function f: R → R be defined by f(x) = 2x + sin x for x ∈ R. Then, f is

    2002 · with solution

  30. If f:[1,∞) → [2,∞) is given by f(x) = x + 1/x, then f^-1(x) equals

    2001 · with solution

  31. Let f(x) = (1 + b^2)x^2 + 2bx + 1 and let m(b) be the minimum value of f(x). As b varies, the range of m(b) is

    2001 · with solution

  32. The domain of definition of f(x) = (log_2(x+3))/(x^2+3x+2) is

    2001

  33. Let f(x) = (α x)/(x+1), x ≠ -1. Then, for what value of α is f[f(x)] = x?

    2001 · with solution

  34. Let E = \1, 2, 3, 4\ and F = \1, 2\. Then, the number of onto functions from E to F is

    2001 · with solution

  35. The domain of definition of the function y(x) is given by the equation 2^x + 2^y = 2, is

    2000 · with solution

  36. If the function f:[1,∞) → [1,∞) is defined by f(x) = 2^x(x-1), then f^-1(x) is

    1999 · with solution

  37. If f(x) = 3x - 5, then f^-1(x)

    1998 · with solution

  38. If g\f(x)\ = |sin x| and f\g(x)\ = (sin √(x))^2, then

    1998 · with solution

  39. Which of the following functions is periodic? (a) f(x) = x - [x] where [x] denotes the greatest integer less than or equal to the real number x (b) f(x) = sin(1/x) for x ≠ 0, f(0) = 0 (c) f(x) = xcos x (d) None of the…

    1983 · with solution

  40. The domain of definition of the function y = dfrac1log_10(1-x) + √(x+2) is

    1983

  41. If f(x) = cos(log x), then f(x) · f(y) - 1/2 [f (x/y ) + f(xy) ] has the value

    1983

  42. Let f(x) = |x - 1|. Then,

    1983 · with solution

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