#### Relations and Functions Important Questions

10th Standard EM

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Mathematics

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. If n(A x B) =6 and A={1,3} then n(B) is

(a)

1

(b)

2

(c)

3

(d)

6

2. A={a,b,p}, B={2,3}, C={p,q,r,s} then n[(A U C) x B] is

(a)

8

(b)

20

(c)

12

(d)

16

3. Let n(A)= m and n(B) = n then the total number of non-empty relations that can be defined from A to B is

(a)

mn

(b)

nm

(c)

2mn-1

(d)

2mn

4. If {(a,8),(6,b)}represents an identity function, then the value of a and b are respectively

(a)

(8,6)

(b)

(8,8)

(c)

(6,8)

(d)

(6,6)

5. Let A={1,2,3,4} and B={4,8,9,10}. A function f: A ⟶ B given by f={(1,4), (2,8), (3,9), (4,10)} is a

(a)

Many-one function

(b)

Identity function

(c)

One-to-one function

(d)

Into function

6. 6 x 2 = 12
7. If A x B = {(3,2), (3,4), (5,2), (5,4)} then find A and B.

8. Find f o g and g o f when f(x)=2x+1 and g(x)=x2-2

9. Represent the function f(x)=$\sqrt { 2x^{ 2 }-5x+3 }$ as a composition of two functions.

10. Find x if gff(x) = fgg(x), given f(x) = 3x+1 and g(x)=x+.

11. Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Letf: A $\rightarrow$B be a function given by  f(x) = 2x + 1. Represent this function as an arrow .

12. Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Letf: A $\rightarrow$B be a function given by  f(x) = 2x + 1. Represent this function as a graph.

13. 6 x 3 = 18
14. Let A = {1,2,3,4} and B ={2,5,8,11,14} be two sets. Let f: A ⟶ B be a function given by f(x)=3x−1. Represent this function
(i) by arrow diagram
(ii) in a table form
(iii) as a set of ordered pairs
(iv) in a graphical form

15. Let f be a function from R to R defined by f(x)=x-5. Find the values of a a and b given that (a,4) and (1,b) belong to f.

16. The distance S (in kms) travelled by a particle in time ‘t’ hours is given by S(t)=$\frac { { t }^{ 2 }+t }{ 2 }$. Find the distance travelled by the particle after
(i) three and half hours.
(ii) eight hours and fifteen minutes.

17. A functionf: [-7,6) $\rightarrow$ R is defined as follows.

$\cfrac { 4f(-3)+f2(4) }{ f(-6)-3f(1) }$

18. f(x) = (1+ x)
g(x) = (2x-1)
Show that fo(g(x)) = gof(x)

19. Let A = {1, 2, 3, 4, 5}, B = N and f: A $\rightarrow$B be defined by f(x) = x2. Find the range of f. Identify the type of function.

20. 3 x 5 = 15
21. If A={5,6}, B={4,5,6}, C={5,6,7}, Show that A x A =(B x B) ∩ (C x C)

22. Let X = {3, 4, 6, 8}. Determine whether the relation R={(x,f(x)) |x$\in$X, f(x)=x2+1}. is a function from X to N?

23. A functionf: (1,6) $\rightarrow$R is defined as follows:

Find the value of f(2) - f( 4).