Mathematics · JEE

Sets, Relations and Functions Mock Test for JEE

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Subtopics in Sets, Relations and Functions

Sets and their representation
Union, intersection and complement of sets and their algebraic properties
Power set
Relations, type of relations, equivalence relations
Functions
One-one, into and onto functions
The composition of functions

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Q1MathsUnit 1: Sets, Relations and Functions

\mathbf{f}:[\mathbf{0}, \infty) \rightarrow[\mathbf{0}, \infty),

and

\mathbf{f}(\mathbf{x})=\frac{\mathbf{x}}{\mathbf{1}+\mathbf{x}}

then

\boldsymbol{f}

Q2MathsUnit 1: Sets, Relations and Functions

Which of the following is NOT equivalent to

\boldsymbol{p} \rightarrow \boldsymbol{q} ?

Q3MathsUnit 1: Sets, Relations and Functions

The price of 357 mangoes is Rs.1517.25. What will be the approximate price of 49 dozens of such mangoes?

Q4MathsUnit 1: Sets, Relations and Functions

Indian cricket team won 4 more matches than it lost with New Zealand. If it won

\frac{3}{5}

of its matches, how many matches did India play?

Q5MathsUnit 1: Sets, Relations and Functions

Assertion The relation

\boldsymbol{R}

given by

\boldsymbol{R}=\{(\mathbf{1}, \mathbf{3}),(\mathbf{4}, \mathbf{2}),(\mathbf{2}, \mathbf{4}),(\mathbf{2}, \mathbf{3}),(\mathbf{3}, \mathbf{1})\}

on a set

A=\{1,2,3,4\}

is not symmetric. Reason For symmetric relation

\boldsymbol{R}=\boldsymbol{R}^{-1}

Q6MathsUnit 1: Sets, Relations and Functions

9 / 16

of a number is 51 greater than

50 \%

of the number. Then, that number is

Q7MathsUnit 1: Sets, Relations and Functions

Let

\boldsymbol{f}(\boldsymbol{x})=\mathbf{2}^{100} \boldsymbol{x}+\mathbf{1}

\boldsymbol{g}(\boldsymbol{x})=\boldsymbol{3}^{100} \boldsymbol{x}+\mathbf{1}

Then the set of real numbers x such that

\boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x}))=\boldsymbol{x}

Q8MathsUnit 1: Sets, Relations and Functions

Let

f

be a function such that

f(3)=1

and

f(3 x)=x+f(3 x-3)

for all

x

Then find the value of

\boldsymbol{f}(\boldsymbol{3 0 0})

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