Sets, Relations and Functions Book Back Questions

11th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 30
    5 x 1 = 5
  1. 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

  2. Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4),(4, 1)}. Then R is

    (a)

    reflexive

    (b)

    symmetric

    (c)

    transitive

    (d)

    equivalence

  3. The range of the function \({1\over 1-2sinx}\) is

    (a)

    \((-∞,-1)\cup\left( {1\over 3},\infty\right)\)

    (b)

    \(\left( -1,{1\over 3}\right)\)

    (c)

    \(\left[ -1,{1\over 3}\right]\)

    (d)

    \((-∞,-1]\cup [\frac { 1 }{ 3 } ,∞)\)

  4. The range of the function \(f(x) = \left| \left\lfloor x \right\rfloor - x \right| ,x \in R\)  is 

    (a)

    [0, 1]

    (b)

    [0, ∞)

    (c)

    [0, 1)

    (d)

    (0, 1)

  5. The rule f(x) =x2 is a bijection if the domain and the co-domain are given by

    (a)

    R, R

    (b)

    R, (0, ∞)

    (c)

    (0, ∞); R

    (d)

    [0, ∞); [0,∞)

  6. 3 x 2 = 6
  7. If n(A) = 10 and \(n(A\cap B)=3,\) find \(n((A\cap B')\cap A).\)

  8. If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find \(n((A\cup B)\times(A\cap B)\times(A \triangle B))\)

  9. If p(A) denotes the power set of A, then find \(n(P(P(P(\phi)))).\)

  10. 3 x 3 = 9
  11. Compare and contrast the graph y = x2 - 1, y = 4(x2 - 1) and y = (4x)2 = 1.

  12. By using the same concept applied in previous example, graphs of y = sin x and y = sin 2x, and also their combined graphs are given figures (a), (b) and (c). The minimum and maximum values of sin x and sin 2x are the same. But they have different x-intercepts. The x-intercepts for y = sin x are \(\pm n\pi\) and for y = sin 2x are \(\pm{1\over 2}n\pi,\ n\in Z.\) ​​​

  13. Let us now draw the graph of y = 2 sin ( x - 1 ) + 3.

  14. 2 x 5 = 10
  15. Let f, g: \(R \rightarrow R\) be defined as f (x) = 2x -|x| and g(x) = 2x + |x|. find fog.

  16. If \(f:R\rightarrow R\)  is defined by f(x) = 2x- 3, prove that f is a bijection and find its inverse

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