Sets, Relations and Functions Important Questions

11th Standard

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Maths

Time : 02:00:00 Hrs
Total Marks : 50
    10 x 1 = 10
  1. The function f:[0,2π]➝[-1,1] defined by f(x)=sin x is

    (a)

    one-to-one

    (b)

    on to

    (c)

    bijection

    (d)

    cannot be defined

  2. Let f:R➝R be defined by f(x)=1-|x|. Then the range of f is

    (a)

    R

    (b)

    (1,∞)

    (c)

    (-1,∞)

    (d)

    (-∞,1]

  3. The shaded region in the adjoining diagram represents.

    (a)

    A\B

    (b)

    B\A

    (c)

    AΔB

    (d)

    A'

  4. Let R be the set of all real numbers. Consider the following subsets of the plane R x R: S = {(x, y) : y =x + 1 and 0 < x < 2} and T = {(x,y) : x - y is an integer} Then which of the following is true?

    (a)

    T is an equivalence relation but S is not an equivalence relation

    (b)

    Neither S nor T is an equivalence relation

    (c)

    Both S and T are equivalence relation

    (d)

    S is an equivalence relation but T is not an equivalence relation.

  5. If f:R➝R is given by f(x)=3x-5, then f-1(x) is

    (a)

    \(\frac{1}{3x-5}\)

    (b)

    \(\frac{x+5}{3}\)

    (c)

    does not exist since f is not one-one

    (d)

    does not exists since f is not onto

  6. Let R be the universal relation on a set X with more than one element. Then R is

    (a)

    not reflexive

    (b)

    not symmetric

    (c)

    transitive

    (d)

    none of the above

  7. \(n(p(A))=512,n(p(B))=32,n(A\cup B)=16,\) find \(n(A\cap B):\)

    (a)

    2

    (b)

    9

    (c)

    4

    (d)

    5

  8. The range of the function is \(f(x)=\sqrt{3x^2-4x+5}\) is

    (a)

    \(\left( -\infty,\sqrt{11\over 3}\right)\)

    (b)

    \(\left( -\infty,-\sqrt{11\over 3}\right)\)

    (c)

    \(\left( \sqrt{11\over 3},-\infty\right)\)

    (d)

    none

  9. If A and B are any two finite sets having m and n elements respectively then the cardinality of the power set of A x B is

    (a)

    2m

    (b)

    2n

    (c)

    mn

    (d)

    2mn

  10. The domain and range of the function \(f(x)={|x-4|\over x-4}\)

    (a)

    R, [-1, 1]

    (b)

    R \ {4};{-1,1}

    (c)

    R \ {4};{-1,l}

    (d)

    R, (-1,1)

  11. 5 x 2 = 10
  12. Write the following in roster form.
    \(\left\{ x:\frac { x-4 }{ x+2 } =3,x\in R-\{ -2\} \right\} \)

  13. Let A and B be two sets such that n(A)=3 and n(B)=2. If (x, 1) (y, 2) (z, 1) are in A\(\times\)B, find A and B, where x, y, z are distinct elements.

  14. Let A = {a, b, c}, and R = {(a, a) (b, b) (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it
    Equivalence.

  15. If U={x:1≤x≤10, x∈N}, A={1,3,5,7,9} and B={2,3,5,9,10} then find A'UB'.

  16. Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A\(\rightarrow\)B for each of the following:
    neither one- to -one and nor onto.

  17. 5 x 3 = 15
  18. Write the steps to obtain the graph of the function y=3(x-1)2+5 from the graph y=x2

  19. Show that the function f: R ⟶ R given by f(x) = cos x for all x ∈ R is neither one-one nor onto.

  20. If A = {x: x = 3n, n ∈ Z} and B = {x: x = 4n, n ∈ Z} then find A ∩ B.

  21. Check the relation R = {(1, 1) (2, 2) (3, 3) ... (n, n)} defined on the set S = {1, 2,3, .. n} for the three basic relations.

  22. See the figure below, here letters of the English alphabets are mapped onto.

  23. 3 x 5 = 15
  24. For the given curve y=x3 given in figure draw, try to draw with the same scale
    (i) y=-x3 
    (ii) y= x3+1
    (iii) y=x3-1
    (iv) y=(x+1)3

  25. Show that the relation R defined on the set A of all polygons as R = {(P1 P2): P1 and P2 have same number of sides} is an equivalence relation.

  26. Let f: R ⟶ R be the signum function defined as \(f(x)=\begin{cases} 1,\ x>0\\0, x=0 \\-1, x<0 \end{cases}\)and g: R ⟶ R to the greatest integer function given by g(x) = [x]. Then prove that fog and gof coincide in [-1,0).

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