Jamia Millia Islamia MCA 2017
Let 10 is the cardinality of set A. The number of bijective mappings from set A to itself is
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Answer: Option D ā 3628800
Detailed Solution
A bijection from to assigns the 10 elements distinct images, i.e. it is an arrangement of the 10 elements.
The first element has 10 choices, the next 9, and so on: .
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For a 3-element set there are bijections: 123, 132, 213, 231, 312, 321.ā Common trap
(C) 100 is ; even the number of all functions is , and only of them are bijections.Quick tip
Bijections on an -element set
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Relations & Mappings ā Preparation
This question tests your understanding of Relations & Mappings, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
A relation from set A to set B is a subset of the Cartesian product A x B. A mapping, or function, is a special relation in which every element of A is related to exactly one element of B. This topic covers types of relations (reflexive, symmetric, transitive and equivalence relations), domain, codomain and range, and types of functions such as one-one (injective), onto (surjective) and bijective functions, along with composition and inverse functions. Exam questions test identifying the type of a given relation or function, counting the number of relations or functions between two sets, and finding the domain or range of a function. Useful counting facts: if A has m elements and B has n elements, there are 2^(mn) relations and n^m functions from A to B. Practise the relations and mappings questions below, each with a step-by-step solution.