#### Sets, Relations and Functions Important Questions

11th Standard

Reg.No. :
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Maths

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. Let A and B be subsets of the universal set N, the set of natural numbers. Then A'∪[(A⋂B)∪B'] is

(a)

A

(b)

A'

(c)

B

(d)

N

4. If n(A) = 2 and n(B ∪ C) = 3, then n[(A x B) ∪ (A x C)] is

(a)

23

(b)

32

(c)

6

(d)

5

5. If two sets A and B have 17 elements in common, then the number of elements common to the set A x B and B x A is

(a)

217

(b)

172

(c)

34

(d)

insufficient data

6. 5 x 2 = 10
7. State whether the following sets are finite or infinite.
{x $\in$ N:x is an odd prime number}

8. State whether the following sets are finite or infinite.
{x $\in$ Z:x is even and less than 10}

9. Discuss the following relations for reflexivity, symmetricity and transitivity:
Let A be the set consisting of all the members of a family. The relation R defined by "aRb if a is not a sister of b".

10. Discuss the following relations for reflexivity, symmetricity and transitivity :
Let A be the set consisting of all the female members of a family. The relation R defined by "aRb if a is not a sister of b".

11. Show that the relation R on R defined as R={(a,b):a≤b} is reflexive and transitive but not symmetric.

12. 5 x 3 = 15
13. If n(A$\cap$B)=3 and n(A$\cup$B) = 10 then find n(P(A$\Delta$B))

14. For a set A, A$\times$A contains 16 elements and two of its elements are (1,3) and (0,2). Find the elements of A.

15. Which of the following sets are finite and which are infinite?
{x ∈ R: 0 < x < 1}

16. If R is the set of all real numbers, what do the cartesian products R x Rand R x R x R represent?

17. Find the domain and range of the function f(x)=$\frac { 1 }{ \sqrt { x-5 } }$.

18. 4 x 5 = 20
19. 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)

20. 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.

21. Let A = R - [2] and B = R - [1].If f : A ⟶ B is a mapping defined by $f(x)={x-1\over x-2}$Show thatfis one-one and onto.

22. A relation R is defined on the set z of integers as follows:
(x, Y) ∈ R⇔x2 + y2 = 25. Express R and R-1 as the set of ordered pairs and hence find their respective domains.