Page 21 - Mathematics Class - XII

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 the 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 pairs 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
f : A → B or A B and it read as f is a function from A to B or f maps A to B.
Based on the above topic, answer the following questions.

1. The given curve is a 2. The given curve is a
Y (a) function Y (a) function
(b) relation (b) relation
X′ X
O (c) both a & b X′ O X (c) both a & b
Y′ (d) none Y′ (d) none

3. If fx() 1 , then range (f) is equal to
2 sin x 3
(a) [–1, 1] (b) 1 1 (c) 1 1 , (d) 1
1,

,

3 3 3 3
4. 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
Assertion-Reason Based Questions
Assertion-Reason Based Questions
Directions for Questions 1 to 3: 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) : A relation R = {(1, 1), (1, 3), (3, 1), (3, 3), (3, 5)} defined on the set A = {1, 3, 5}
is reflexive.

Reason (R) : A relation R on the set A is said to be transitive if for (a, b) ∈ R and (b, c) ∈ R,
we have (a, c) ∈ R.
Q. 2. Assertion (A) : A relation R = {(x, y) : | x–y | = 0} defined on the set A = {3, 5, 7} is symmetric.
Reason (R) : A relation R on the set A is said to be symmetric if for (a, b) ∈ R, we have (b, a) ∈ R.

Q. 3. Assertion (A) : A relation R = {(1, 1), (1, 2), (2, 2), (2, 3), (3, 3)} is symmetric.
Reason (R) : A relation R on the set A is said to be symmetric if (a, b) ∈ R then (b, a) ∈ R.

Answers

Case-Study Based Questions: 1. (b) 2. (a) 3. (c) 4. (a)
Assertion-Reason Based Questions: 1. (d) 2. (a) 3. (d)

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