#### Relations and Functions Model Question Paper

10th Standard EM

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Maths

Time : 01:30:00 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. If the ordered pairs (a+2,4) and (5,2a+b) are equal then (a,b) is

(a)

(2,-2)

(b)

(5,1)

(c)

(2,)

(d)

(3,-2)

3. If f(x)=2x2 and g(x)=$\frac{1}{3x}$, then f o g is

(a)

$\\ \frac { 3 }{ 2x^{ 2 } }$

(b)

$\\ \frac { 2 }{ 3x^{ 2 } }$

(c)

$\\ \frac { 2 }{ 9x^{ 2 } }$

(d)

$\\ \frac { 1 }{ 6x^{ 2 } }$

4. If f: A ⟶ B is a bijective function and if n(B) =8, then n(A) is equal to

(a)

7

(b)

49

(c)

1

(d)

14

5. f(x) = (x+1)3 - (x-1)3 represents a function which is

(a)

linear

(b)

cubic

(c)

reciprocal

(d)

6. 7 x 2 = 14
7. If A = {1,3,5} and B = {2,3} then
(i) find A x B and B x A
(ii) Is A x B = B x A? If not why?
(iii) Show that n(A×B) = n(B×A) = n(A)× n(B)

8. Let X={1,2,3,4} and Y={2,4,6,8,10} and R={(1,2),(2,4),(3,6),(4,8)} Show that R is a function and find its domain, co-domain and range?

9. Given f(x) =2x-x2, find
(i) f (1)
(ii) f (x+1)
(iii) f (x) + f (1)

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

11. Find k if f o g(k) = 5 where f(k)=2k-1.

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 set of ordered pairs.

13. 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 .

14. 3 x 5 = 15
15. Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
(i) R1={(3,7), (4,7), (7,10), (8,1)}
(ii) R2= {(3,1), (4,12)}
(iii) R3= {(3,7), (4,10), (7,7), (7,8), (8,11), (8,7), (8,10)}

16. Let A={1,2,3}, B={4,5,6,7}, and f={(1,4),(2,5),(3,6)}  be a function from A to B. Show that f is one – one but not onto function.

17. 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.

18. 2 x 8 = 16
19. If A={5,6}, B={4,5,6}, C={5,6,7}, Show that A x A =(B x B) ∩ (C x C)

20. A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provide Rs.10,000, Rs.25,000, Rs.50,000 and Rs.1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. If A1, A2, A3, A4 and A5 were Assistants; C1, C2, C3, C4 were Clerks; M1, M2, M3 were managers and E1, E2 were Executive officers and if the relation R is defined by xRy, where x is the salary given to person y, express the relation R through an ordered pair and an arrow diagram.