1) The document is a mathematics worksheet for class 11 that contains 9 multiple choice questions about relations and functions. 2) The questions cover topics like determining the domain and range of various functions, identifying which sets of ordered pairs represent functions, and properties of relations such as the inverse of a relation. 3) The worksheet is intended to test students' understanding of key concepts in relations and functions through multiple choice problems.

1. RYAN INTERNATIONAL SCHOOL, GHAZIABAD
WORKSHEET (CLASS XI)
SUB:MATHEMATICS
2012-2013
TOPIC:RELATIONS AND FUNCTIONS
Choose the correct option for the following MCQ’s
 2 x, x > 3
 2
1) Let f : R → R be defined by f(x) =  x ,1 < x ≤ 3 then f ( −1) + f (2) + f (4) =
 3 x, x ≤ 1

(a) 9 (b) 5 (c) 14 (d) None of these
2) The domain of the function f(x) = 2 x − x 2 is
(a) [0, ∞ ) (b) (- ∞ ,2] (c) [0,2] (d) (0,2)
3) If R is a relation on set A,then
(a) R=A × A (b) R ⊂ A × A (c) R ⊂ P ( A) (d) None of these
ax − b
4) If y = f(x) = , then f(y) is equal to
bx − a
(a) x (b) y (c) 2y (d) None of these
5) A relation R is defined from { 2,3,4,5} to { 3,6,7,10} by x R y if and only if x is
relatively prime to y.Then the domain of R is
(a) { 3,5} (b) { 2,3,5} (c) { 2,3,4} (d) { 2,3,4,5}
6) If A= {1,2,3,4} ,then which of the following are functions from A to itself
(a) f 1 = { ( x, y ) : y = x + 1} (b) f 2 = { ( x, y ) : x + y > 4} (c) f 3 = { ( x, y ) : y < x}
(d) f 4 = { ( x, y ) : x + y = 5}
x
7) The range of f ( x) = when x ≠ 0 is
x
(a) [-1,1] (b) (-1,1) (c) { − 1,1} (d) (-1,0) ∪ (0,1)
8) R = { (a, b) : a = 2b} where R is defined on the set of natural numbers.Then R −1
is given by (a) None of these (b) { (1,2), (2,4), (3,6),........} (c) { (2,1), (4,2), (6,3),.......}
(d) R −1 is not defined
2x
9) The range of the function f(x) = , x ∈ R is
x +1
2
(a) (-1,1) (b) [-1,1] (c) (- ∞ ,-1) ∪ (1, ∞ ) (d) (- ∞ ,1)