#### Sets, Relations and Functions Important Questions

11th Standard

Reg.No. :
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Maths

Time : 02:00:00 Hrs
Total Marks : 50
10 x 1 = 10
1. 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

2. Let f:R➝R be defined by f(x)=1-|x|. Then the range of f is

(a)

R

(b)

(1,∞)

(c)

(-1,∞)

(d)

(-∞,1]

(a)

A\B

(b)

B\A

(c)

AΔB

(d)

A'

4. Let R be the set of all real numbers. Consider the following subsets of the plane R x R: S = {(x, y) : y =x + 1 and 0 < x < 2} and T = {(x,y) : x - y is an integer} Then which of the following is true?

(a)

T is an equivalence relation but S is not an equivalence relation

(b)

Neither S nor T is an equivalence relation

(c)

Both S and T are equivalence relation

(d)

S is an equivalence relation but T is not an equivalence relation.

5. If f:R➝R is given by f(x)=3x-5, then f-1(x) is

(a)

$\frac{1}{3x-5}$

(b)

$\frac{x+5}{3}$

(c)

does not exist since f is not one-one

(d)

does not exists since f is not onto

6. 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

7. $n(p(A))=512,n(p(B))=32,n(A\cup B)=16,$ find $n(A\cap B):$

(a)

2

(b)

9

(c)

4

(d)

5

8. The range of the function is $f(x)=\sqrt{3x^2-4x+5}$ is

(a)

$\left( -\infty,\sqrt{11\over 3}\right)$

(b)

$\left( -\infty,-\sqrt{11\over 3}\right)$

(c)

$\left( \sqrt{11\over 3},-\infty\right)$

(d)

none

9. If A and B are any two finite sets having m and n elements respectively then the cardinality of the power set of A x B is

(a)

2m

(b)

2n

(c)

mn

(d)

2mn

10. The domain and range of the function $f(x)={|x-4|\over x-4}$

(a)

R, [-1, 1]

(b)

R \ {4};{-1,1}

(c)

R \ {4};{-1,l}

(d)

R, (-1,1)

11. 5 x 2 = 10
12. Write the following in roster form.
$\left\{ x:\frac { x-4 }{ x+2 } =3,x\in R-\{ -2\} \right\}$

13. Let A and B be two sets such that n(A)=3 and n(B)=2. If (x, 1) (y, 2) (z, 1) are in A$\times$B, find A and B, where x, y, z are distinct elements.

14. Let A = {a, b, c}, and R = {(a, a) (b, b) (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it
Equivalence.

15. 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'.

16. Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A$\rightarrow$B for each of the following:
neither one- to -one and nor onto.

17. 5 x 3 = 15
18. Write the steps to obtain the graph of the function y=3(x-1)2+5 from the graph y=x2

19. Show that the function f: R ⟶ R given by f(x) = cos x for all x ∈ R is neither one-one nor onto.

20. If A = {x: x = 3n, n ∈ Z} and B = {x: x = 4n, n ∈ Z} then find A ∩ B.

21. Check the relation R = {(1, 1) (2, 2) (3, 3) ... (n, n)} defined on the set S = {1, 2,3, .. n} for the three basic relations.

22. See the figure below, here letters of the English alphabets are mapped onto.

23. 3 x 5 = 15
24. For the given curve y=x3 given in figure draw, try to draw with the same scale
(i) y=-x3
(ii) y= x3+1
(iii) y=x3-1
(iv) y=(x+1)3

25. Show that the relation R defined on the set A of all polygons as R = {(P1 P2): P1 and P2 have same number of sides} is an equivalence relation.

26. Let f: R ⟶ R be the signum function defined as $f(x)=\begin{cases} 1,\ x>0\\0, x=0 \\-1, x<0 \end{cases}$and g: R ⟶ R to the greatest integer function given by g(x) = [x]. Then prove that fog and gof coincide in [-1,0).