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#### Sets, Relations and Functions Book Back Questions

11th Standard

Reg.No. :
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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