#### Relations and Functions Model Question Paper

10th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
4 x 1 = 4
1. 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)

2. 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

3. Let f(x) = $\sqrt { 1+x^{ 2 } }$ then

(a)

f(xy) = f(x).f(y)

(b)

f(xy) ≥ f(x).f(y)

(c)

f(xy) ≤ f(x).f(y)

(d)

None of these

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

(a)

linear

(b)

cubic

(c)

reciprocal

(d)

5. 5 x 2 = 10
6. 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?

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

8. 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 table .

9. 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 .

10. 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.

11. 4 x 5 = 20
12. 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

13. 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.

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

f(-7) -f(-3)

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

$\cfrac { 4f(-3)+2f(4) }{ f(-6)-3f(1) }$

16. 2 x 8 = 16
17. Given A={1,2,3}, B = {2,3,5}, C = {3,4} and D = {1,3,5}, check if (A ∩ C) x (B ∩ D) =(A x B) ∩ (C x D) is true?

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

Find the value of f(2) - f( 4).