Page 26 - Mathematics Class - XI

Case-Study Based Questions
Case-Study Based Questions

A relation f from a non-empty set A to a non-empty set B is said to be a function, if every element of set A has
one and only one image in set B. In other words, we can say that a function f is a relation from a non-empty
set A to a non-empty set B such that the domain of f is A and no two distinct ordered pair in f have the same
first element or component.
If f is a function from a set A to a set B then we write
f
fA: Bor A B
and it is read as f is a function from A to B or f maps A to B.
Based upon the above theory, answer the following questions.

1. The given curve is a y
(a) Function

(b) Relation x' o x
(c) Cannot say anything
(d) Data is inappropriate y'

2. If f (x) = x + 2x + 3, then among f (1), f (2) and f (3) which one gives maximum value
2
(a) f (1) (b) f (2) (c) f (3) (d) f (1) = f (2) = f (3)
3. If f (1 + x) = x + 1, then f (2–h) is
2
(a) h – 2h + 2 (b) h – 2h + 1 (c) h – 2h – 2 (d) h + 2h + 2
2
2
2
2
4. If f (x) = 1 , then range (f) is equal to
2 −sin 3x
(a) [–1, 1] (b) 1 1 (c) 1 1 , (d) 1, 1
,

3 3 3 3

Assertion-Reason Based Questions
Assertion-Reason Based Questions
Directions for Questions 1 to 2: In each of the questions given below, there are two statements marked as
Assertion (A) and Reason (R). Mark your answer as per the codes provided below:
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.

(c) A is true but R is false. (d) A is false but R is true.
Q. 1. Assertion (A) : The domain of the relation R = {(x +2, x + 4) : x ∈ N, x < 8} is {3, 4, 5, 6, 7, 8, 9}
Reason (R) : The range of the relation R = {(x +2, x + 4) : x ∈ N, x < 8} is {1, 2, 3, 4, 5, 6, 7}
Q. 2. Assertion (A) : Let A = {1, 2} and B = {3, 4} then number of relations from A to B is 16.
Reason (R) : If n(A) = P and n(B) = q, then number of relations is 2 .
pq

Answers

1
Case-Study Based Questions: 1. (b) Relation 2. (c) f (3) 3. (a) h – 2h + 2 4. (c) 3 1 ,
2

Assertion-Reason Based Questions: 1. (c) 2. (a)

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