[Solved] Let R be the set of real numbers. If f:R R is a function defined by f(x)=x^2. then f is | Practice

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Q1. $R_{1} = (x, y) ∣ x, y \in R, x^{2} + y^{2} \leq 25$ and $R_{2} = (x, y) ∣ x, y \in R, 9 y \geq 4 x^{2}$ . Then $R_{1} \cap R_{2}$ is
Q2.Define a relation $\sim$ on the set $1, 2, 3, 4, 5, 6, 7, 8, 9, 10$ by $a \sim b$ if $a - 2 b$ is divisible by 3. Then:
Q3.Let R be a reflexive relation on a finite set A having 10 elements, and let m be the number of ordered pairs in R. Then
Q4.The total number of relations that exist from a set $A$ with $m$ elements into the set $A \times A$ is:
Q5.Let $A = 1, 2, 3, \dots, 20$ . Let $R \subseteq A \times A$ such that $R = (x, y) : y = 2 x - 7$ . Then the number of elements in $R$ is equal to

Relations & Mappings — 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.

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Let R be the set of real numbers. If $f : R \to R$ is a function defined by $f (x) = x^{2}$ . then $f$ is

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Relations & Mappings — Preparation

Let R be the set of real numbers. If f:R→R is a function defined by f(x)=x2. then f is

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More Relations & Mappings Questions

More Quantitative Aptitude Questions

Relations & Mappings — Preparation

Let R be the set of real numbers. If $f : R \to R$ is a function defined by $f (x) = x^{2}$ . then $f$ is