Relations and Functions Important Questions

10th Standard EM

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Mathematics

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  1. If n(A x B) =6 and A={1,3} then n(B) is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    6

  2. A={a,b,p}, B={2,3}, C={p,q,r,s} then n[(A U C) x B] is

    (a)

    8

    (b)

    20

    (c)

    12

    (d)

    16

  3. Let n(A)= m and n(B) = n then the total number of non-empty relations that can be defined from A to B is

    (a)

    mn

    (b)

    nm

    (c)

    2mn-1

    (d)

    2mn

  4. If {(a,8),(6,b)}represents an identity function, then the value of a and b are respectively

    (a)

    (8,6)

    (b)

    (8,8)

    (c)

    (6,8)

    (d)

    (6,6)

  5. Let A={1,2,3,4} and B={4,8,9,10}. A function f: A ⟶ B given by f={(1,4), (2,8), (3,9), (4,10)} is a

    (a)

    Many-one function

    (b)

    Identity function

    (c)

    One-to-one function

    (d)

    Into function

  6. 6 x 2 = 12
  7. If A x B = {(3,2), (3,4), (5,2), (5,4)} then find A and B.

  8. Find f o g and g o f when f(x)=2x+1 and g(x)=x2-2

  9. Represent the function f(x)=\(\sqrt { 2x^{ 2 }-5x+3 } \) as a composition of two functions.

  10. Find x if gff(x) = fgg(x), given f(x) = 3x+1 and g(x)=x+3.

  11. Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Letf: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as an arrow .

  12. Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Letf: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as a graph.

  13. 6 x 3 = 18
  14. Let A = {1,2,3,4} and B ={2,5,8,11,14} be two sets. Let f: A ⟶ B be a function given by f(x)=3x−1. Represent this function
    (i) by arrow diagram
    (ii) in a table form
    (iii) as a set of ordered pairs
    (iv) in a graphical form

  15. Let f be a function from R to R defined by f(x)=x-5. Find the values of a a and b given that (a,4) and (1,b) belong to f.

  16. The distance S (in kms) travelled by a particle in time ‘t’ hours is given by S(t)=\(\frac { { t }^{ 2 }+t }{ 2 } \). Find the distance travelled by the particle after
    (i) three and half hours.
    (ii) eight hours and fifteen minutes.

  17. A functionf: [-7,6) \(\rightarrow\) R is defined as follows.

    \(\cfrac { 4f(-3)+2f(4) }{ f(-6)-3f(1) } \)

  18. f(x) = (1+ x)
    g(x) = (2x-1)
    Show that fo(g(x)) = gof(x)

  19. Let A = {1, 2, 3, 4, 5}, B = N and f: A \(\rightarrow\)B be defined by f(x) = x2. Find the range of f. Identify the type of function.

  20. 3 x 5 = 15
  21. If A={5,6}, B={4,5,6}, C={5,6,7}, Show that A x A =(B x B) ∩ (C x C)

  22. Let X = {3, 4, 6, 8}. Determine whether the relation R={(x,f(x)) |x\(\in \)X, f(x)=x2+1}. is a function from X to N?

  23. A functionf: (1,6) \(\rightarrow\)R is defined as follows:

    Find the value of f(2) - f( 4).

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