NCERT Solutions for class 12 Maths | Chapter 1 - Relations and Functions
Questions
1
Let E = {1, 2, 3, 4} and F = {1, 2} Then, the number of onto functions from E to F is
Answer:14
2
Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). Then, R is
Answer:Reflexive, transitive but not symmetric
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3
The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R-1 is given by
Answer:{(1, 2), (2, 4), (3, 6),….}
then
6
Let R be a relation on the set N be defined by {(x, y) | x, y ∈ N, 2x + y = 41}. Then R is
Answer:None of these
8
Let function R → R is defined as f(x) = 2x³ – 1, then ‘f’ is
A
2x³ + 1
B
(2x)³ + 1
C
(1 – 2x)³
D
1/3
1/3Answer:
10
Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a congruent to b ∀ a, b ∈ T. Then R is
Answer:equivalence
11
Let us define a relation R in R as aRb if a ≥ b. Then R is
Answer:reflexive, transitive but not symmetric
12
If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is
Answer:0
13
Which of the following functions from Z into Z are bijective?
Answer:f(x) = x + 2
14
For real numbers x and y, we write xRy ⇔ x – y + √2 is an irrational number. Then, the relational R is
Answer:Reflexive
15
Let R be an equivalence relation on a finite set A having n elements. Then, the number of ordered pairs in R is
Answer:Greater than or equal to n
16
The relation R = {(1,1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is
Answer:Reflexive but not symmetric
17
Let f : R → R be given by f (,v) = tan x. Then f-1(1) is
A
π/4
B
C
does not exist
D
None of these
Answer:
19
Let f : R → R be defined by f (x) = 1/x ∀ x ∈ R. Then f is
Answer:f is not defined
20
What type of a relation is R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} on the set A – {1, 2, 3, 4}
Answer:None of these
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