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Hard One-one, into and onto functions MCQs for JEE

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Hard One-one, into and onto functions MCQs train multi-concept problem solving — attempt after mastering easy and medium sets (13+ on Goodmarks).

Push your limits with hard One-one, into and onto functions MCQs designed for JEE Advanced-level thinking. 13+ questions with detailed solutions.

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

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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
Let f:R→R\boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} where f(x)=2∣x∣−2−x\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2}^{|\boldsymbol{x}|}-\boldsymbol{2}^{-\boldsymbol{x}} then f(x)f(x) is
Q3MathsUnit 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
Q4MathsUnit 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}=
Q5MathsUnit 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
Q6MathsUnit 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
Q7MathsUnit 1: Sets, Relations and Functions
An identity function is a?
Q8MathsUnit 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

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After 70%+ accuracy on medium MCQs and once core formulas are automatic.

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