Sets, Relations and Functions Important Question Paper

11th Standard

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Mathematics

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  1. The number of constant functions from a set containing m elements to a set containing n elements is

    (a)

    mn

    (b)

    m

    (c)

    n

    (d)

    m+n

  2. 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

  3. If the function f:[-3,3]➝S defined by f(x)=x2 is onto, then S is

    (a)

    [-9,9]

    (b)

    R

    (c)

    [-3,3]

    (d)

    [0,9]

  4. Given A={5,6,7,8}. Which one of the following is incorrect?

    (a)

    Ø⊆A

    (b)

    A⊆A

    (c)

    {7,8,9}⊆A

    (d)

    {5}⊆A

  5. The shaded region in the adjoining diagram represents.

    (a)

    A\B

    (b)

    B\A

    (c)

    AΔB

    (d)

    A'

  6. 5 x 2 = 10
  7. Write the following in roster form.{x \(\in \)N:4x+9<52}

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

  9. The total cost of airfare on a given route is comprised of the base cost C and the fuel surcharge S in rupee. Both C and S functions of the mileage m; C(m)=0.4m + 50 and S(m)=0.03m. Determine a function for the total cost of a ticket in terms of the mileage and find the airfare for flying 1600 miles.

  10. Check whether the following sets are disjoint where p={x:x is a prime<15} and Q={x:x is a multiple of 2 and x<16}

  11. 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'.

  12. 5 x 3 = 15
  13. Graph the function f(x)=x3 and \(g(x)\sqrt[3]x\) on the same co-ordinate plane. Find fog and graph it on the plane as well. Explain your results.

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

  15. By taking suitable sets A, B, C, verify the following results:
    \(\times\) (B\(\cap \)C)=(A\(\times\)B) \(\cap \) (A\(\times\)C)

  16. Find the pairs of equal sets from the following sets. A = {0}, B = {x: x > 15 and x < 5}, C = {x: x - 5 = 0}, D = {x: x2 = 25}, E = {x: x is an integral positive root of the equation x2 - 2x - 15 = 0}.

  17. Which of the following sets are finite and which are infinite?
    Set of concentric circles in a plane.

  18. 4 x 5 = 20
  19. The formula for converting from Fahrenheit to Celsius temperatures is \(y={5x\over 9}-{160\over 9}\). Find the inverse of this function and determine whether the inverse is also a function.

  20. A simple cipher takes a number and codes it, using the function f(x)=3x-4. Find the inverse of this function, determine whether the inverse is also a function and verify the symmetrical property about the line y=x(by drawing the lines)

  21. The cartesian product A x A has 9 elements among which are found (-1, 0) and (0, 1).Find the set A and the remaining elements of A x A.

  22. Show that the relation R on the set R of all real numbers defined as R = {(a, b): a < b2} is neither reflexive, nor symmetric nor transitive.

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