frequently asked five mark questions chapter one

10th Standard EM

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Maths

Do not involve in any malpractices
Time : 01:15:00 Hrs
Total Marks : 75

    Part - A

    Answer all the questions

    15 x 5 = 75
  1. 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

  2. Using horizontal line test (Fig.1.35(a), 1.35(b), 1.35(c)), determine which of the following functions are one – one.

  3. Let A={1,2,3}, B={4,5,6,7}, and f={(1,4),(2,5),(3,6)}  be a function from A to B. Show that f is one – one but not onto function.

  4. If A={-2,-1,0,1,2} and f: A ⟶ B is an onto function defined by f(x)=x2+x+1 then find B.

  5. Let f be a function f:N ⟶ N be defined by f(x) = 3x+2, x\(\in \)N
    (i) Find the images of 1, 2, 3
    (ii) Find the pre-images of 29, 53
    (ii) Identify the type of function

  6. Forensic scientists can determine the height (in cms) of a person based on the length of their thigh bone. They usually do so using the function h(b)=2.47b+54.10 where b is the length of the thigh bone.
    (i) Check if the function h is one – one
    (ii) Also find the height of a person if the length of his thigh bone is 50 cms.
    (iii) Find the length of the thigh bone if the height of a person is 14796 cms.

  7. 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.

  8. 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.

  9. If the function f: R⟶ R defined by 

    (i) f(4)
    (ii) f(-2)
    (iii) f(4)+2f(1)
    (iv) \(\frac { f(1)-3f(4) }{ f(-3) } \)

  10. Let f = {(2, 7); (3, 4), (7, 9), (-1, 6), (0, 2), (5,3)} be a function from A = {-1,0, 2, 3, 5, 7} to B = {2, 3, 4, 6, 7, 9}. Is this (i) an one-one function (ii) an onto function, (iii) both oneone and onto function?

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

    find 2f(-4) + 3f(2)

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

    f(-7) -f(-3)

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

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

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

  15. 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.

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