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Free download in PDF Class 12 Maths Chapter 1 Relations and Functions Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries. These will help the students for preparation of their examination./p>
(1)
Let E = {1, 2, 3, 4} and F = {1, 2} Then, the number of onto functions from E to F is
[A]
14
[B]
16
[C]
12
[D]
8
(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
[A]
Reflexive and symmetric
[B]
Transitive and symmetric
[C]
Equivalence
[D]
Reflexive, transitive but not symmetric
Answer: Reflexive, transitive but not symmetric
(3)
The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R-1 is given by
[A]
{(2, 1), (4, 2), (6, 3),….}
[B]
{(1, 2), (2, 4), (3, 6),….}
[C]
R-1 is not defined
[D]
None of these
Answer: {(1, 2), (2, 4), (3, 6),….}
[A]
f-1(x) = f(x)
[B]
f-1(x) = -f(x)
[C]
(f o f)x = -x
[D]
f-1(x) = 1/19 f(x)
(5)
Let P = {(x, y) | x² + y² = 1, x, y ∈ R]. Then, P is
[A]
Reflexive
[B]
Symmetric
[C]
Transitive
[D]
Anti-symmetric
(6)
Let R be a relation on the set N be defined by {(x, y) | x, y ∈ N, 2x + y = 41}. Then R is
[A]
Reflexive
[B]
Symmetric
[C]
Transitive
[D]
None of these
(7)
If f(x) + 2f (1 – x) = x² + 2 ∀ x ∈ R, then f(x) =
[A]
x² – 2
[B]
1
[C]
1/3 (x – 2)²
[D]
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
(9)
The domain of sin-1 (log (x/3)] is. .
[A]
[1, 9]
[B]
[-1, 9]
[C]
[-9, 1]
[D]
[-9, -1]
(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
[A]
reflexive but-not transitive
[B]
transitive but not symmetric
[C]
equivalence
[D]
None of these
(11)
Let us define a relation R in R as aRb if a ≥ b. Then R is
[A]
an equivalence relation
[B]
reflexive, transitive but not symmetric
[C]
neither transitive nor reflexive but symmetric
[D]
symmetric, transitive but not reflexive
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
[A]
720
[B]
120
[C]
0
[D]
None of these
(13)
Which of the following functions from Z into Z are bijective?
[A]
f(x) = x³
[B]
f(x) = x + 2
[C]
f(x) = 2x + 1
[D]
f{x) = x² + 1
(14)
For real numbers x and y, we write xRy ⇔ x – y + √2 is an irrational number. Then, the relational R is
[A]
Reflexive
[B]
Symmetric
[C]
Transitive
[D]
None of these
(15)
Let R be an equivalence relation on a finite set A having n elements. Then, the number of ordered pairs in R is
[A]
Less than n
[B]
Greater than or equal to n
[C]
Less than or equal to n
[D]
None of these
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
[A]
Reflexive but not symmetric
[B]
Reflexive but not transitive
[C]
Symmetric and transitive
[D]
Neither symmetric nor transitive
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
[C]
does not exist
[D]
None of these
(18)
Let f: R → R be defined by
then f(- 1) + f (2) + f (4) is
[A]
9
[B]
14
[C]
5
[D]
None of these
(19)
Let f : R → R be defined by f (x) = 1/x ∀ x ∈ R. Then f is
[A]
one-one
[B]
onto
[C]
bijective
[D]
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}
[A]
Reflexive
[B]
Transitive
[C]
Symmetric
[D]
None of these
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