IIT - JEE Main Important Questions of Relations and Functions | Zigya

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

Advertisement
1.

If the function g(x) =open curly brackets table attributes columnalign left end attributes row cell straight k square root of straight x plus 1 end root comma space space 0 space less or equal than straight x space less or equal than 3 end cell row cell mx plus 2 space comma space 3 space less than straight x less or equal than 5 end cell end table close is differntiable, then the value of k+m is

  • 2

  • 16/5

  • 10/3

  • 10/3

379 Views

2.

If a ε R and the equation - 3(x-[x]2 + 2(x-[x] +a2 = 0(where,[x] denotes the greatest integer ≤ x) has no  integral solution, then all possible value of  lie in the interval

  • (-1,0) ∪ (0,1)

  • (1,2)

  • (-2,-1)

  • (-∞,-2) ∪ (2, ∞)

182 Views

3.

Consider the following relations:
R = {(x, y)| x, y are real numbers and x = wy for some rational number w}; S = {(m/p, p/q)| m, n, p and q are integers such that n, q ≠ 0 and qm = pn}. Then

  • R is an equivalence relation but S is not an equivalence relation

  • neither R nor S is an equivalence relation

  • S is an equivalence relation but R is not an equivalence relation

  • S is an equivalence relation but R is not an equivalence relation

308 Views

4.

Let p(x) be a function defined on R such that limit as straight x space rightwards arrow infinity of space fraction numerator straight f left parenthesis 3 straight x right parenthesis over denominator straight f left parenthesis straight x right parenthesis end fraction = 1, p'(x)  p'(1-x),for all x∈[0,1] p(0) = 1 and p(1) = 41. Then integral subscript 0 superscript straight x space straight p space left parenthesis straight x right parenthesis space dx equals

  • √41

  • 21

  • 41

  • 41

224 Views

Advertisement
5.

The function straight f colon space straight R space rightwards arrow with space on top space open square brackets negative 1 half comma 1 half close square brackets space defined space as space straight f left parenthesis straight x right parenthesis space equals space fraction numerator straight x over denominator 1 plus space straight x squared end fraction comma space is

  • neither injective nor surjective.

  • invertible

  • injective but not surjective.

  • injective but not surjective.

371 Views

6.

Let W denote the words in the English dictionary. Define the relation R by :
R = {(x, y) ∈ W × W | the words x and y have at least one letter in common}. Then R is

  • not reflexive, symmetric and transitive

  • reflexive, symmetric and not transitive

  • reflexive, symmetric and transitive

  • reflexive, symmetric and transitive

141 Views

7.

The graph of the function y = f(x) is symmetrical about the line x = 2, then

  • f(x + 2)= f(x – 2)

  • f(2 + x) = f(2 – x)

  • f(x) = f(-x)

  • f(x) = f(-x)

219 Views

8.

The domain of the function straight f left parenthesis straight x right parenthesis space equals space fraction numerator sin to the power of negative 1 end exponent space left parenthesis straight x minus 3 right parenthesis over denominator square root of 9 minus straight x squared end root end fraction

  • [2, 3]

  • [2, 3)

  • [1, 2]

  • [1, 2]

139 Views

Advertisement
9.

x  R: cosx  sinx  0, 3π2 is equal to

  • 0, π4  3π4, 3π2

  • 0, π4  π2, 3π2

  • 0, π4  5π4, 3π2

  • 0, 3π2


10.

If log0.2x - 1 > log0.04x + 5, then

  • - 1 < x < 4

  • 2 < x < 3

  • 1 < x < 4

  • 1 < x < 3


Advertisement