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NCERT Solutions for class 12 Maths | Chapter 1 - Relations and Functions

(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
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
[A] Reflexive and symmetric
[B] Transitive and symmetric
[C] Equivalence
[D] Reflexive, transitive but not symmetric
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
[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),….}
(4) Let f: R then
[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)
Answer: f-1(x) = 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
Answer: 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
Answer: 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
Answer: 1/3 (x – 2)²
(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
Answer: 1/3
(9) The domain of sin-1 (log (x/3)] is. .
[A] [1, 9]
[B] [-1, 9]
[C] [-9, 1]
[D] [-9, -1]
Answer: [1, 9]
(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
Answer: equivalence
(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
Answer: 0
(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
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
[A] Reflexive
[B] Symmetric
[C] Transitive
[D] None of these
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
[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
[B]
[C] does not exist
[D] None of these
Answer:
(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
Answer: 9
(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
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}
[A] Reflexive
[B] Transitive
[C] Symmetric
[D] None of these
Answer: None of these

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