Relations and Functions Book Back Questions

10th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    4 x 1 = 4
  1. If f: A ⟶ B is a bijective function and if n(B) =8, then n(A) is equal to

    (a)

    7

    (b)

    49

    (c)

    1

    (d)

    14

  2. Let f(x) = \(\sqrt { 1+x^{ 2 } } \) then

    (a)

    f(xy) = f(x).f(y)

    (b)

    f(xy) ≥ f(x).f(y)

    (c)

    f(xy) ≤ f(x).f(y)

    (d)

    None of these

  3. If g={(1,1), (2,3), (3,5), (4,7)} is a function givrn by g(x)=αx+β then the values of α and β are

    (a)

    (-1,2)

    (b)

    (2,-1)

    (c)

    (-1,-2)

    (d)

    (1,2)

  4. f(x) = (x+1)3 - (x-1)3 represents a function which is

    (a)

    linear

    (b)

    cubic

    (c)

    reciprocal

    (d)

    quadratic

  5. 4 x 2 = 8
  6. Represent the function f(x)=\(\sqrt { 2x^{ 2 }-5x+3 } \) as a composition of two functions.

  7. If f(x)=3x-2, g(x)=2x+k and if f o g = f o f, then find the value of k..

  8. Find k if f o g(k) = 5 where f(k)=2k-1.

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

  10. 2 x 5 = 10
  11. 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.

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

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

  13. 1 x 8 = 8
  14. 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?

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