Relations & Functions Class 12 Chpater - 1 Important Extra Practice Questions For 2022-23 Exam - GMS - Learning Simply
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# Relations & Functions Class 12 Chpater - 1 Important Extra Practice Questions For 2022-23 Exam

Here we are providing Class 12 Maths Important Extra Questions and Answers Chapter 1 Relations and Functions.
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# Class 12 Chpater - 1 Relations & Functions Practice Questions

## Relation and function individually are defined as:Relations - A relation R from a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.Functions - A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, no two distinct elements of B have the same pre-image.Access Class 12 Chpater - 1 Relations & Functions Practice QuestionsVery Short (Objective type)/ Short Answer Type Questions1. Let Z be the set of integers and R be a relation defined in Z such aRb if (a - b) is divisible by 5. Then number of equivalence classes are23452. Let R be a relation defined as R = {(x, x), (y, y), (z, z), (x, z)} in set A = {x, y, z} then relation R isreflexivesymmetrictransitiveequivalence3. If R = {(x, y) : x + 2y = 8} is a relation on N, then range of R is     [AI 2014]{3}{1, 2, 3}{1, 2, 3, ....8}{1, 2}4. Let A = {a, b, c}, then the what is the total numeber of ditinct relations in set A?5. Consider set A = {1, 2, 3} and the relation R = {(1, 2)}, then R is a transitive relation. State true or false and justify your answer.6. Every relation which is symmetric and transitive is reflexive also. State true or false and justify your answer.7. Let R  be a relation in set N, given by R = {(a, b) : a = b - 2, b > 6} then (3, 8) ∈ R. State true or false with reason.8. For the set A = {1, 2, 3}, define a relation R in the set A as follows: R = {(1, 1), (2, 2), (3, ,3), (1, 3)}. Write the ordered pairs to be added to R  to make it the smallest equivalence relation. [NCERT Exemplar]9. Let R  = {(a, a³) : a is a prime number less than 5} be a relation. Find the range of R. [Foriegn 2014]10. A relation in a set A is called ________ relation, if each element of A is related to itself. [CBSE 2020]11. Let set A = {1, 2 ,3 }, define relation R  on A as R  = {(a, b) ∈  A X  A : a + b > 6}. Show that R is a universal relation.12. Check whether the relation R defined on the set {1, 2, 3, 4} as R = {(a, b) : b = a + 1} is transitive.Justify your answer. [2021 (C)]Long Answer I / Long Answer II Type Questions13. Prove that the relation R in the set A = {5, 6, 7, 8, 9} given by R = {(a, b) : |a - b| is divisible by 2}, is an equivalence realtion. Find all the elements related to the element 6. [Foriegn 2013]14.  If the relation R on the set A = {x : 0 ≤  x ≤ 12} given by R = {(a, b) : a = b} is an equivalence relation, then find the set of all elements related to 1.

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