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Mathematics · JEE

Important Questions: One-one, into and onto functions for JEE

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The most important One-one, into and onto functions questions for JEE cover conceptual traps, standard results, and numerical patterns from One-one, into and onto functions. Goodmarks provides 7+ high-yield MCQs with full solutions.

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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 f(A)f(A) is a proper subset of BB, then ff A→BA \rightarrow B is called a/an ……..\ldots \ldots . . function
Q4MathsUnit 1: Sets, Relations and Functions
An identity function is a?
Q5MathsUnit 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
Q6MathsUnit 1: Sets, Relations and Functions
Let f:N→Nf: N \rightarrow N defined by f(n)=f(n)= {n+12 if n is odd n2 if n is even \left\{\begin{array}{cc}\frac{n+1}{2} & \text { if } n \text { is odd } \\ \frac{n}{2} & \text { if } n \text { is even }\end{array}\right. then f\boldsymbol{f} is.
Q7MathsUnit 1: Sets, Relations and Functions
The function f:N→N\boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N} defined by f(x)=x−5[x5],\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}-\mathbf{5}\left[\frac{\boldsymbol{x}}{\mathbf{5}}\right], where N\mathrm{N} is the set of natural numbers and [x][x] denotes the greatest integer less than or equal to xx is

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What makes a One-one, into and onto functions question "important" for JEE?

Important questions test core concepts that appear frequently across JEE Main and Advanced papers — definitions, standard formulas, and classic problem types.

Which subtopics in Sets, Relations and Functions are high-weightage?

Key areas include One-one, into and onto functions. Prioritise these before moving to edge cases.

How many important questions should I revise?

Revise 30–50 important MCQs per unit in the last month before JEE. Focus on questions you got wrong at least once.

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