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Relations and Functions - Set 3

This document is a test paper for Class XI Mathematics focusing on relations and functions. It includes various questions related to Cartesian products, finite sets, functions, and their properties, requiring students to find domains, ranges, and express relations in different forms. The test assesses understanding through both theoretical and practical applications of mathematical concepts.

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Jacob Chakola
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125 views1 page

Relations and Functions - Set 3

This document is a test paper for Class XI Mathematics focusing on relations and functions. It includes various questions related to Cartesian products, finite sets, functions, and their properties, requiring students to find domains, ranges, and express relations in different forms. The test assesses understanding through both theoretical and practical applications of mathematical concepts.

Uploaded by

Jacob Chakola
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.

in
Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks
TEST PAPER-02
CLASS - XI MATHEMATICS (Relations and functions)


1.
If { } , , P a b c = and { }, Q d = form the sets P Q andQ P are these two
Cartesian products equal?
[1]
2.
If A and B are finite sets such that ( ) n A m = and ( ) n B k = find the number of
relations from A to B
[1]
3.
Let ( ) ( ) ( ) ( ) { }
1,1 , 2, 3 , 0, 1 , 1, 3 ,...... f = be a function from z to z defined by
( ) , f x ax b = + for same integers a and b determine a and b.
[1]
4.
Express ( ) { }
, : 2 5, x y y x xy w + = as the set of ordered pairs
[1]
5.
Let a relation ( ) ( ) ( ) ( ) ( ) { }
0, 0 , 2, 4 , 1, 2 , 3, 6 , 1, 2 R = then
(i) write domain of R (ii) write range of R
(iii) write R the set builder form (iv) represent R by an arrow diagram
[4]
6.
Let { } { } 1, 2, 3 , 1, 2, 3, 4 A B = = and ( ) ( ) { }
, : , , 1 R x y x y A B y x = = +
(i) find A B (ii) write R in roster form
(iii) write domain & range of R (iv) represent R by an arrow diagram
[4]
7. The cartesian product A A has a elements among which are found
( ) 1, 0 and ( ) 0,1 . find the set and the remaining elements of A A
[4]
8.
Find the domain and the range of the following functions ( )
1
5
f x
x
=


[4]
9.
Let ( ) 1 f x x = + and ( ) 2 3 g x x = be two real functions. Find the following
functions ( ) ( ) ( ) ( ) ( )
2
3
f
i f g ii f g iii fg iv v f g
g
+
[4]
10. Find the domain and the range of the following functions
( ) ( ) ( ) ( ) ( ) ( )
2
2 2
3 1
2 1 1 1
x x
i f x ii f x iii f x
x x x

= = =
+ +

[4]
11. Draw the graphs of the following real functions and hence find their range
( ) ( ) ( ) ( )
2
1
2 1
1
x
i f x x ii f x
x

= =


[6]
12.
Let f be a function defined by
2
: 5 2, F x x x R +
(i) find the image of 3 under f (ii) find ( ) ( ) 3 2 f f +
(iii) find x such that ( ) 22 f x =
[6]

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