CBSE Class 12 Mathematics Relation And Function Worksheet Set B

Question. Let f : R → R be defined as f(x) = x4. Choose the correct answer : 
(a) f is one-one onto
(b) f is many-one onto
(c) f is one-one but not onto
(d) f is neither one-one nor onto
Choose the correct option :
(a) Both (A) and (B) are true and R is the correct explanation A.
(b) Both (A) and (R) are true but R is not correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer. D

Question. Assertion (R) : The function f(x) = | x | is not one-one.
Reason (R) : The negative real number are not the images of any real numbers.
Answer. C

Question. Assertion (A) : A function y = f(x) is defined by x² – cos^{– 1} y = π, then domain of f(x) is R.
Reason (R) : cos^–1 y ∈ [0, π].
Answer. D

Question. Assertion (A) : If f(x) is odd function and g(x) is even function, then f(x) + g(x) is neither even nor odd.
Reason (R) : Odd function is symmetrical in opposite quadrants and even function is symmetrical about the y-axis.
Answer. B

Question. Assertion (A) : Every even function y = f(x) is not one-one, ∀ x ∈ D_f .
Reason (R) : Even function is symmetrical about the y-axis.
Answer. A

Question. Assertion (A) : f(x) = sin x + cos ax is a periodic function.
Reason (R) : a is rational number.
Answer. A

Question. Assertion (A) : The least period of the function,f (x) = cos (cos x) + cos (sin x) + sin 4x is π.
Reason (R) : ... f (x + π) = f (x).
Answer. D

Question. Assertion (A) : If f (x + y) + f (x – y) = 2f(x) · f (y) ∀ x, y ∈ R and f (0) ≠ 0, then f(x) is an even function.
Reason (R) : If f (– x) = f (x), then f (x) is an even function.
Answer. B

Question. Assertion (A) : The equation x⁴ = (λx – 1)² has atmost two real solutions (is λ > 0).
Reason (R) : Curves f(x) = x⁴ and g(x) = (λx – 1)² has atmost two points.
Answer. D

Question. Assertion (A) : The domains of f (x) = √cos (sin x) and g(x) = √sin (cosx) are same.
Reason (R) : –1 ≤ cos (sin x) ≤ 1 and – 1 ≤ sin (cos x) ≤ 1
Answer. D

Question. Assertion (A) : If f(x) = x5 – 16x + 2, then f(x) = 0 has only one root in the interval [–1, 1].
Reason (R) : f (– 1) and f (1) are of opposite sign.
Answer. B

Question. Assertion (A) : The domain of the function f (x) = sin^–1 x + cos^–1 x + tan^–1 x is [–1, 1].
Reason (R) : sin^–1 x and cos^–1 x is defined in | x| ≤ 1 and tan^–1 x defined for all x.
Answer. A

Question. Assertion (A) : The period of f(x) = sin 3x cos [3x] – cos 3x sin [3x] is 1/3 where [ ] denotes the greatest integer function ≤ x.
Reason (R) : The period of {x} is 1, where {x} denotes the fractional part function of x.
Answer. A

Question. Assertion (A) : The relation R given by
R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} on a set A = {1, 2,3} is not symmetric.
Reason : For symmetric relation R = R– 1.
Answer. A

Question. The price of the oranges in the market is dependent on the amount of oranges (in kgs) which can be represented as y = 3x + 5. Reema went to buy the oranges for a family function in her house. The total number of oranges she wants to buys is 5 ≤ x ≤ 10 according to her assumption of people coming to the party. Answer the following questions on the basis of the given information.

Question. How many ordered pairs can be represented for the equation y = 3x + 5 for 5 ≤ x ≤ 10 ?
(a) 4
(b) 5
(c) 6
(d) 7
Answer. C

Question. What is the domain of the given relation R = {(5, 20), (6, 23), (7, 26), (8, 29), (9, 32), (10, 35)} ?
(a) {– 5, – 4, 0, 1, 2}
(b) {0, 1, 2, 3, 4, 5}
(c) {4, 5, 6, 7, 8}
(d) {5, 6, 7, 8, 9, 10}
Answer. D

Question. How can range of the relation be represented for the relation R = {(5, 20), (6, 23), (7, 26), (8, 29),(9, 32), (10, 35)} ?
(a) {(x, y) | y = x + 3; 3 : 17 ≤ x ≤ 32}
(b) {(x, y) | y = x + 3 : 20 ≤ x ≤ 35}
(c) {(x, y) | y = x + 3 : 17 < x < 32}
(d) {(x, y) | y = x + 3 : 20 < x < 35}
Answer. A

Question. What is co-domain for the given relation ?
(a) {(x, y) | y = x + 3 : 17 ≤ x ≤ 32}
(b) {(x, y) | y = x + 3 : 20 ≤ x ≤ 35}
(c) {(x, y) | y = x + 3 : 17 < x < 32}
(d) {(x, y) | y = x + 3 : 20 < x < 35}
Answer. A

Question. How many subsets are there for the given relation R = {(5, 20), (6, 23), (7, 26), (9, 29), (9, 32), (10, 35)} ?
(a) 16
(b) 32
(c) 64
(d) 128
Answer. C

There is a circular track in a playground where little kids come to play. Mohan whose son is in the 11th standard had taken him to the park. His son is having the difficulty in grasping the concept of the relations. Mohan saw the track and realised that he can teach his son the concept using the real world example. He asked his son to imagine the playground as the mathematical figure of circle and imagine the equation of the circle to be x² + y² = 8.

Question. What is the relation called ?
(a) Set of ordered pair
(b) Function
(c) x-value
(d) y-value
Answer. A

Question. Which of the following sets will certainly represent the given relation accurately ?
(a) {(0, 8), (1, 7), (2, 2)}
(b) {(0,2 2),(1, 7 ),(2,2)}
(c) {(0,0), (1, 7 ), (2,− 2)}
(d) {(0, 2 3), (1,7), (2, 2)}
Answer. B

Question. From the given graph, what values of the x can be in the given relation ?
(a) Inside the circle
(b) Outside the circle
(c) above half of the circle only
(d) Lower half of the circle only
Answer. A

Question. What is the maximum value of the range of the given relation ?
(a) 0
(b) – 2
(c) −2 2
(d) 2 2
Answer. D

Question. Waht is the co-domain of the given circle ?
(a) (– 2, 2)
(b) (− 2 2, 2 2)
(c) [– 2, 2]
(d) [− 2 2, 2 2]
Answer. D

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1, 2, 3, 4, 5, 6}. Let A be the set of players while B be the set of all possible outcomes.

Question. Let R : B → B be defined by R = {(x, y) : y is disivible by x} is :
(a) Reflexive and transitive but not symmetric
(b) Reflexive and symmetric and not transitive
(c) Not reflexive but symmetric and transitive
(d) Equivalence
Answer. A

Question. Raji wants to know the number of functions from A to B. How many number of functions are possible ?
(a) 62
(b) 26
(c) 6!
(d) 212
Answer. A

Question. Let R be a relation on B defined by R = {(1, 2),
(2, 2), (1,3 ), (3, 4), (3, 1), (4, 3), (5, 5)}. Then R is :
(a) Symmetric
(b) Reflexive
(c) Transitive
(d) None of these three
Answer. D

Question. Raji wants to know the number of relations possible from A to B. How many numbers of relations are possible ?
(a) 62
(b) 26
(c) 6!
(d) 212
Answer. D

Question. Let R : B → be defined by R = {(1, 1), (1, 2), (2, 2),(3, 3), (4, 4), (5, 5), (6, 6)}, then R is :
(a) Symmetric
(b) Reflexive and Transitive
(c) Transitive and symmetric
(d) Equivalence
Answer. B

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x – 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Question. Let relation R be defined by R = {(L₁, L₂) : L₁ || L₂ where L₁, L₂ ∈ L} then R is .................. .
(a) Equivalence
(b) Only reflexive
(c) Not reflexive
(d) Symmetric but not transitive
Answer. A

Question. Let R = {(L₁, L₂) : L₁ + L₂ where L₁, L₂ ∈ L} which of the following is true ?
(a) R is symmetric but neither reflexive nor transitive
(b) R is reflexive and transitive but not symmetric
(c) R is reflexive but neither symmetric nor transitive
(d) R is an equivalence relation
Answer. A

Question. The function f : R → R defined by f(x) = x – 4 is :
(a) Bijective
(b) Surjective but not injective
(c) Injective but not surjective
(d) Neither surjective nor injective
Answer. A

Question. Let f : R → R be defined by f(x) = x – 4. Then the range of f(x) is :
(a) R
(b) Z
(c) W
(d) Q
Answer. A

Question. Let R = {(L₁, L₂) : L1 is parallel to L₂ and L1 : y = x – 4} then which of the following can be taken as L2 ?
(a) 2x – 2y + 5 = 0
(b) 2x + y = 5
(c) 2x + 2y + 7 = 0
(d) x + y = 7
Answer. A

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