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JEE Advanced

Explore popular questions from Sets, Relations and Functions for JEE Advanced. This collection covers Sets, Relations and Functions previous year JEE Advanced questions hand picked by experienced teachers.

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Physics

Chemistry

Mathematics

Sets, Relations and Functions

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Q 1. The function is

A

An even function

An odd function

C

Periodic function

D

None of these

Explanation

We have,


for all
for all
is an odd function

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Q 2. The domain of the real valued function
is

A

B

and

D

Explanation

For to be defined, and

And

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Q 3. Let and be defined as for all , then is

A

Many-one into function

B

One-one into function

C

Many-one onto function

One-one onto function

Explanation



Since, , therefore
Function is one-one onto.

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Q 4. If and are defined by and for , then is equal to

A

{0, 1}

B

{1, 2}

{-3, -2}

D

{2, 3}

Explanation

Given that, and
For
Now, for ,


Again, for


Hence, required set is .

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Q 5. Let Then,

A

B

C

None of these

Explanation

We have,


And,

Hence, none of the above given option is true

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Q 6. The domain of the function is

A

B

D

Explanation

The given function is defined when and
and
,
Domain of the function is

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Q 7. If a function satisfies the condition

A

for all

for all satisfying

C

for all satisfying

D

None of these

Explanation

We have,

where
Now,
and,
Thus, for all satisfying

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Q 8. The period of the function is

A

B

D

None of these

Explanation

Since is a periodic function with period and

is periodic with period

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Q 9. is a function defined by If then

A

B

D

Explanation

Let Then,

Hence,

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Q 10. If and then

A

B

C

None of these

Explanation

We have,


Clearly,
Thus, option (a) is not correct
Now,




Thus, option (b) is not correct
Also,


Thus, option (c) is not correct
Hence, option (d) is correct

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Q 11. If and are two real functions such that and then

A

is an odd function

B

is an even function

C

and are periodic functions

None of these

Explanation

We have,


Clearly, and for all
Hence, is an even function and is an odd function

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Q 12. If is defined as , then is

A

B

D

Explanation

Given,


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Q 13. If the function given by is a surjection, then

A

B

C

Explanation

The domain of is the complete set of real numbers. Since is a surjection. Therefore, is the range of
Let Then,
Now,




Now,
is real
Therefore, range of is Hence,

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Q 14. If is an odd function, then the curve is symmetric

A

About -axis

B

About -axis

C

About both the axes

In opposite quadrants

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Q 15. Let and be defined by for Then, the range of is

B

C

D

Explanation

We have,

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Q 16. The period of the function is

A

B

D

None of these

Explanation

Since is periodic with period
is periodic with period

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Q 17. The number of reflexive relations of a set with four elements is equal to

A

C

D

Explanation

Number of reflexive relations of a set of 4 elements

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Q 18. If a function defined by is a bijection, then

A

C

D

Explanation

We have,
such that
Since is a bijection. Therefore, Range of
Now,
for all
for all Range of
Hence,

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Q 19. If is a real number, then belongs to

A

C

D

None of these

Explanation

We have,

Clearly, will assume real values, if

Clearly, will assume real values, if




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Q 20. If the function is defined by and .... (repeated times), then is equal to

A

B

C

Explanation





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Q 21. If is a real valued function such that and , then the value of is

A

200

B

300

C

350

500

Explanation

Given,

For we get


Also


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Q 22. In a class of 35 students, 17 have taken Mathematics, 10 have taken Mathematics but not Economics. If each student has taken either Mathematics or Economics or both, then the number of students who have taken Economics but not Mathematics is

A

7

B

25

18

D

32

Explanation

Let and denote the sets of students who have taken Mathematics and Economics respectively. Then, we have

Now,


Now,


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Q 23. Let be a relation defined by Then, is

A

An equivalence relation on

Reflexive, transitive but not symmetric

C

Symmetric, transitive but not reflexive

D

Neither transitive not reflexive but symmetric

Explanation

For any we have
Therefore, the relation is reflexive.
is not symmetric as but The relation is transitive also, because imply that and which in turn imply that

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Q 24. If two sets and are having 99 elements in common, then the number of elements common to each of the sets and are

A

C

100

D

18

Explanation

Number of elements common to each set is .

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Q 25. If and then is equal to

A

C

D

None of these

Explanation

We have,
Set of some multiple of 9
and, Set of all multiple of 9