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One-one, into and onto functions Concepts for JEE

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Quick answer

Master One-one, into and onto functions by understanding definitions, standard results, and typical JEE question patterns — then practise with syllabus-aligned MCQs on Goodmarks.

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Concept explainer

One-one, into and onto functions is a core JEE Main Mathematics subtopic under Sets, Relations and Functions. Master the definitions, standard results, and typical MCQ patterns tested in JEE Main and Advanced.

Key points

  • Understand the definition and scope of One-one, into and onto functions in the JEE syllabus
  • Memorise key formulas and standard results linked to One-one, into and onto functions
  • Practise 20–40 syllabus-aligned MCQs with step-by-step solutions

JEE tips

  • Revise One-one, into and onto functions with a one-page formula sheet before attempting mixed tests
  • After each practice set, log mistakes specific to One-one, into and onto functions and reattempt after 48 hours

Common trap

Students often rush One-one, into and onto functions questions without checking units, sign conventions, or boundary conditions — always verify assumptions before calculating.

Syllabus context

Part of Sets, Relations and Functions in JEE Main Mathematics.

Free sample questions

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Q1MathsUnit 1: Sets, Relations and Functions
If f:[0,∞)→[0,∞),\mathbf{f}:[\mathbf{0}, \infty) \rightarrow[\mathbf{0}, \infty), and f(x)=x1+x\mathbf{f}(\mathbf{x})=\frac{\mathbf{x}}{\mathbf{1}+\mathbf{x}} then f\boldsymbol{f} is
Q2MathsUnit 1: Sets, Relations and Functions
The function f:(−∞,−1)→(0,e5]\boldsymbol{f}:(-\infty,-1) \rightarrow\left(\mathbf{0}, e^{5}\right] defined by f(x)=ex3−3x+2f(x)=e^{x^{3}-3 x+2} is
Q3MathsUnit 1: Sets, Relations and Functions
If a function f:(2,∞)→B\boldsymbol{f}:(2, \infty) \rightarrow \boldsymbol{B} defined by f(x)=x2−4x+5f(x)=x^{2}-4 x+5 is a bijection, then B=\boldsymbol{B}=
Q4MathsUnit 1: Sets, Relations and Functions
Let A={x,y,z},B={a,b,c}\boldsymbol{A}=\{\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z}\}, \boldsymbol{B}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\} and f\boldsymbol{f} A→BA \rightarrow B be defined by f(x)=a,f(y)=f(x)=a, f(y)= b,f(z)=c.\boldsymbol{b}, \boldsymbol{f}(\boldsymbol{z})=\boldsymbol{c} . This function is
Q5MathsUnit 1: Sets, Relations and Functions
If f(A)f(A) is a proper subset of BB, then ff A→BA \rightarrow B is called a/an ……..\ldots \ldots . . function
Q6MathsUnit 1: Sets, Relations and Functions
An identity function is a?
Q7MathsUnit 1: Sets, Relations and Functions
f:Q→Q\boldsymbol{f}: \boldsymbol{Q} \rightarrow \boldsymbol{Q} is defined by f(x)=15x+7\boldsymbol{f}(\boldsymbol{x})=\mathbf{1 5} \boldsymbol{x}+\mathbf{7} is
Q8MathsUnit 1: Sets, Relations and Functions
The function f:R→R\boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} defined by f(x)=x21+x2∀x∈Rf(x)=\frac{x^{2}}{1+x^{2}} \forall x \in R is

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