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R = {(x, y) : y = x + 5 and x < 4} Answer: Is defined on the set {1, 2, 3, 4, 5} by a b = L.C.M. Show that the relation R in the set A of points in a plane given by (b) 3! But no element of {1, 3, 5} is related to any element of {2, 4}. Solution, (7)  Let A = {1, 2} and B = {1, 2, 3, 4} , C = {5, 6} and D = {5, 6 ,7, 8} . Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, (ii) Is commutative? (A) 1 (v) Symmetric and transitive but not reflexive. Let f(x) = x2 – x + 1, x ≥ $$\frac{1}{2}$$, then the solution of the equation f(x) = f-1(x) is R is replaced by N with co-domain being same as R? (iii) On Q, define a b = If the binary operation * is defind on the set Q+ of all positive rational numbers by a * b = $$\frac{a b}{4}$$. Relation and Functions Worksheet and Answer Key. (f + g)oh = foh + goh (iv) Relation R in the set Z of all integers defined as (D) f –1 and show that (f –1)–1 = f. Question 12.Let f : X → Y be an invertible function. operation? Then, $$3 *\left(\frac{1}{5} * \frac{1}{2}\right)$$ is equal to If f(x) = $$1-\frac{1}{x}$$, then f(f($$\frac{1}{x}$$)) 'i.1�wQT_�z�NBy���(͹"�T��q$M��qt��W���#i�� 0000010658 00000 n The function (fog)-1 (x) is equal to If * is a binary operation on set of integers I defined by a * b = 3a + 4b – 2, then find the value of 4 * 5. endobj (a) $$\frac{3+4 x}{6 x-4}$$ (a) injective (d) None of these (b) reflexive, transitive but not symmetric Find Show that f is one-one. (c) 23 Answer: ���n (d) $$\frac{1}{x-1}$$ (b) one-one into, Question 48. <> x3 (B) x3 (C) x (D) (3 – x3), Question 14.Let f : R – 4 B. endobj Here we have covered Important Questions on Relations and Functions for Class 11 Maths subject.. Maths Important Questions Class 11 are given below.. Short Answer Type Questions 0000005345 00000 n Answer: (a) 5x + 3 (c) -1 Find the inverse 11 0 obj (d) None of these (d) Reflexive, transitive but not symmetric with sides 3, 4, 5, T2 with sides 5, 12, 13 and T3 with sides 6, 8,Which (b) $$g(x)=\frac{1}{\left(a x^{2}+b\right)^{3}}$$ (b) {(1, 2), (2, 4), (3, 6), ……..} (b) Many-one (c) f(x) 3 (d) Reflexive, transitive but not symmetric, Question 36. Would a vertical line be a relation, a function, both a relation and a function, or neither a relation nor a function? <> (a) 8 n | m). Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 1 Relations and Functions. 0000011655 00000 n (e) R = {(x, y) : x is father of y}. (b) $$\left(x-\frac{7}{2}\right)^{1 / 3}$$ (a) one-one and onto (c) Both (a) and (b) Answer: Find the set A and the remaining elements of A Ã A. the set of all lines related to the line y = 2x +4. Answer: (c) g is bijective on R (d) none of these (B) Is commutative but not associative? (d) 2106 n n + (iv) Find the identity of in N Math Models Worksheet 4.1 Relations and Functions Answers – math ... #248398 . Identify the domain of this relation. Consider f : R+→ [4, ∞) given by f (x) = x2 +4..Show that f is invertible with the 12 0 obj 2.1 – Represent Relations and Functions. (b) $$\frac{x-5}{3}$$ 0000010679 00000 n one-one nor onto, where [x] denotes the greatest integer less than or equal to x. <> 10 0 obj (v) Which elements of N are invertible for the operation ? (a) $$\frac{2 x-5}{3}$$ Find 2 * $$\frac{1}{3}$$ Functions A function is a relation that satisﬁes the following: each -value is allowed onlyone -value Note: (above) is not a function, because has -values and (violates our condition!) 01 - SETS, RELATIONS AND FUNCTIONS Page 1 ( Answers at the end of all questions ) ( 1 ) Let R = { ( 3, 3 ) ( 6, 6 ) ( ( 9, 9 ) ( 12, 12 ), ( 6, 12 ) ( 3, 9 ) ( 3, 12 ), ( 3, 6 ) } be a relation on the set A = { 3, 6, 9, 12 }. Question 5.State with reason whether following functions have inverse (i) f : {1, 2, 3, 4} → {10} with (a) f is bijective, Question 44. Question 10. Let f : R – {$$\frac{3}{5}$$} → R be defined by f(x) = $$\frac{3 x+2}{5 x-3}$$. (d) f(x) = x2 + 1 (a) 1 (ii) On Q, define a b = ab + 1 (a) 0 (b) f(x) = x + 2 (d) $$\frac{3 x+2}{3}$$ (b) 2, Question 63. (d) 0, Question 21. Answer: (b) 3 Think about the vertical line test and answer the following question. Ê8,10 Ë Á ˆ ¯ ˜, 5,7Ê Ë Á ˆ ¯ ˜, 9,Ê −11 Ë Á ˆ ¯ ˜, 6,Ê −8 Ë Á ˆ ¯ ˜ Ï Ì Ó ÔÔ Ô ¸ ˝ ˛ ÔÔ ÔÔ a. (ii) Transitive but neither reflexive nor symmetric. (b) {nπ + $$\frac{\pi}{4}$$; n ∈ Z} CBSE Syllabus Class 12 Maths Physics Chemistry ... CBSE Syllabus Class 11 Mathematics biology chemistry ... CBSE Syllabus Class 10 Maths Science Hindi English ... CBSE Syllabus Class 9 Mathematics Science English Hindi ... Revised Syllabus for Class 12 Mathematics. Answer: Consider three right angle triangles T1 Let f : R → R be given by f(x) = tan x. Let be the binary operation on N given by a b = L.C.M. (c) equivalence, Question 25. (a) $$\log _{10}(2-x)$$ (b) f-1(x) = -f(x) Choose the correct answer. In each of the following cases, state whether the function is one-one, onto or R = {(P, Q) : distance of the point P from the origin is same as the distance of the [U6��Ue�����:�}�a���u&+�X�[f]�Ơp��2n�3&\� 爊_ (ii) If is a commutative binary operation on N, then a (b c) = (c b) a. stream (a) Onto 0000007380 00000 n • Solution A is 30% acid by volume. (a) f-1(x) = f(x) 0000009963 00000 n Consider the function f : A → B defined by Question 5. %S%��m�7$3g3: \$ ���Y�m�k�Ѽ�� Xv�H3�a,�� @~^�6����=��X��f�����w�5q�@S3��J�����QFL͐���fȂ��4 ��yy�E �j�|8���� ����]� �p����q� H����a����� L�8��DC�sK4��rqf���.�,Ѱjng�hC�-ʧ���S��߿_�J���h. (a) $$\frac{\pi}{4}$$ Then the number of surjections from A into B is (a) f-1(x) = f(x), Question 34. The number of binary operations that can be defined on a set of 2 elements is (a) Commutative Question 4.Consider a binary operation on the set {1, 2, 3, 4, 5} given by the following (Hint: use the following table). Answer: (d) None of these 2 C. Testing Relations To See If They Are Functions We make a “mapping table”. (iii) Compute (2 3) (4 5). (iv) Reflexive and transitive but not symmetric. bijective. (d) none of these (d) neither one-one nor onto <> R = {(x, y) : 3x – y = 0} Copyright @ ncerthelp.com A free educational website for CBSE, ICSE and UP board. Relations, Functions, and Graphs-A Review - YouTube #248397. Consider the binary operation * on Q defind by a * b = a + 12b + ab for a, b ∈ Q. n} and B = {a, b}. 9 0 obj 7�.�L��p/��; ��)�ᖡQ[.�[��m�ɇJ�-y)��ߖeUt��� ���=�PK�j~8�2��%.s*�4F�Ն��/�\�.�{�f3�O�)���r����Qy�l8�q3�ay�[���Tƙ SC�� ��~���Gh������̷ (a) reflexive but not symmetric Solution (2) The Cartesian product A×A has 9 elements among which (–1, 0) and (0,1) are found. (c) 7 Then (a) {(2, 1), (4, 2), (6, 3),….} Answer: (b) Not onto (ii) On Z+, define by a b = ab 2.1 – Represent Relations and Functions. Multiple choice and true or false type questions are also provided. all points related to a point P ≠ (0, 0) is the circle passing through P with origin as 0000016338 00000 n (c) -1 Question 1.Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} be given by (d) -f(x) (a) $$g(x)=\left(\frac{b-x^{1 / 3}}{a}\right)^{1 / 2}$$ Answer: (a) $$\frac{3}{160}$$, Question 14. Answer: R = {(x, y) : x – y is an integer} (c) $$\frac{x}{x-1}$$, Question 11. (a) Reflexive and symmetric 4 (c) symmetric, transitive but not reflexive (d) (0, 2) Verify whether A Ã C is a subset of B Ã D? Let f : R → R be a function defined by f(x) = x3 + 4, then f is (c) $$\left(\frac{x-2}{7}\right)^{1 / 3}$$ The function f : R → R given by f(x) = x3 – 1 is (B) f is many-one onto A, if any. (c) bijective (c) R = {(x, y) : x is exactly 7 cm taller than y} (1 ) of the function f : [–1, 1] → Range f. Free PDF Download of JEE Main Sets Relations and Functions Important Questions of key topics. (b) onto but not one-one (a) f is bijective The function f : R → R defined by f(x) = 3 – 4x is Functions A function is a relation that satisﬁes the following: each -value is allowed onlyone -value Note: (above) is not a function, because has -values and (violates our condition!) Answer: (ii) Is commutative? Chapter 1 Relations and Functions Download NCERT Solutions for Class 12 Mathematics (Link of Pdf file is given below at the end of the Questions List) In this pdf file you can see answers of following Questions EXERCISE 1.1 . Question 4. 13 0 obj Answer: (B) R is reflexive and transitive but not symmetric. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. f = {(1, 10), (2, 10), (3, 10), (4, 10)} Answer: (b) associative (c) many-one onto, Question 41. (a) one-one onto of a and b. point Q from the origin}, is an equivalence relation. (iv) On Z+, define a b = 2ab triangles among T1, T2 and T3 are related? > (d) None of these x (c) Both (a) & (b) (d) $$1+\sqrt{x^{2}-4}$$ (c) $$g(x)=\left(a x^{2}+b\right)^{1 / 3}$$ (a) commutative, Question 19. Answer: Question 8. n n 0000003690 00000 n Record your answer neatly on the Answer …