Types of Functions - JEE Maths Free MCQ Test with solutions

Test: Types of Functions - Question 1

Let A be the set of all 25 students of Class X in a school. Let f : A → N be function defined by f (x) = roll number of the student x. Then f is:

A.
One-two
B.
Many one
C.
Onto but not one-one
D.
One-one

Detailed Solution: Question 1

f(x) = Roll number of student x
f(x₁) = Roll number of student x₁
f(x₂) = Roll number of student x₂
Putting f(x₁) = f(x₂)
Roll number of student x₁ = Roll number of student x₂
Since no two student of a class have same roll number.
Therefore, x₁ ≠ x₂
So, f is one-one.

Test: Types of Functions - Question 2

A function f: A x B → B x A defined by f (a, b) = (b, a) on two sets A and B. The function is:

A.
Many-one
B.
One-one but not onto
C.
One-one and onto
D.
Neither one-one nor onto

Detailed Solution: Question 2

f:A×B→B×A is defined as f(a,b)=(b,a).
Let (a1,b1),(a2,b2)∈A×B such that f(a1,b1)=f(a2,b2).
⇒(b1,a1)=(b2,a2)
⇒(b1=b2) and (a1=a2)
⇒(a1,b1)=(a2,b2)
∴f is one-one.
Now, let (b,a)∈B×A be any element.
Then, there exists (a,b)∈A×B such that
f(a,b)=(b,a). [By definition of f]
∴ f is onto.

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Test: Types of Functions - Question 3

Let f : N→ R - {0} defined as f(x) = 1/x where x ∈ N is not an onto function. Which one of the following sets should be replaced by N such that the function f will become onto? (where R₀= R - {0})

A.
R₀
B.
W
C.
Z
D.
None of these

Detailed Solution: Question 3

Test: Types of Functions - Question 4

The function f is

A.
One-one
B.
Onto but not one-one
C.
One-one and onto
D.
Many one

Detailed Solution: Question 4

The function is bijective (one-to-one and onto or one-to-one correspondence) if each element of the codomain is mapped to by exactly one element of the domain. (That is, the function is both injective and surjective.) A bijective function is a bijection.

Test: Types of Functions - Question 5

A function f: R → R is defined by f(x) = [x+1], where [x] the greatest integer function, is:

A.
Onto but not one-one
B.
Neither one-one nor onto
C.
One-one but not onto
D.
One-one and onto

Detailed Solution: Question 5

Correct Answer :- b

Explanation : f: R → R is given by,

f(x) = [x+1]

It is seen that f(1.2) = [1.2] = 1, f(1.9) = [1.9] = 1.

∴ f(1.2) = f(1.9), but 1.2 ≠ 1.9.

∴ f is not one-one.

Now, consider 0.7 ∈ R.

It is known that f(x) = [x] is always an integer. Thus, there does not exist any element x ∈ R such that f(x) = 0.7.

∴ f is not onto.

Hence, the greatest integer function is neither one-one nor onto.

Test: Types of Functions - Question 6

How many onto functions from set A to set A can be formed for the set A = {1, 2, 3, 4, 5, ……n}?

A.
n²
B.
n
C.
n!
D.
2n

Detailed Solution: Question 6

Taking set {1,2,3}
Since f is onto,all elements of{1,2,3} have unique pre-image.
Total no. of one-one function = 3×2×1=6
Eg:- Since f is onto,all elements of {1,2,3} have unique pre-image.
total no. of onto functions = n×n−1×n−2×2×1
= n!

Test: Types of Functions - Question 7

Let A = {1, 2, 3}. f: A → A Then complete the function f such that it one-one and onto: f = {(1, 2), (2,1) ______}

A.
The function is already one-one and onto
B.
(3, 2)
C.
(3, 3)
D.
(2, 3)

Test: Types of Functions - Question 8

If a relation f: X → Y is a function, then for g: Y → X to be a function, function f need to be

A.
One-one and onto
B.
One-one
C.
Onto but not one-one
D.
Many one

Test: Types of Functions - Question 9

Find the number of bijective functions from set A to itself when A contains 106 elements.

A.
106
B.
106²
C.
2¹⁰⁶
D.
106!

Detailed Solution: Question 9

For a finite set S, there is a bijection between the set of possible total orderings of the elements and the set of bijections from S to S. That is to say, the number of permutations of elements of S is the same as the number of total orderings of that set, i.e. n!
We have set A that contains 106 elements, so the number of bijective functions from set A to itself is 106!

Test: Types of Functions - Question 10

Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = 3x + 4. Then the composition of f and g is ____________

A.
6x + 9
B.
6x + 7
C.
6x + 6
D.
6x + 8

Detailed Solution: Question 10

The composition of f and g is given by f (g(x)) which is equal to 2 (3x + 4) + 1.

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Types of Functions - Free MCQ Practice Test with solutions, JEE Maths

MCQ Practice Test & Solutions: Test: Types of Functions (10 Questions)

Let A be the set of all 25 students of Class X in a school. Let f : A → N be function defined by f (x) = roll number of the student x. Then f is:

A function f: A x B → B x A defined by f (a, b) = (b, a) on two sets A and B. The function is:

Let f : N→ R - {0} defined as f(x) = 1/x where x ∈ N is not an onto function. Which one of the following sets should be replaced by N such that the function f will become onto? (where R₀= R - {0})

The function f is

A function f: R → R is defined by f(x) = [x+1], where [x] the greatest integer function, is:

How many onto functions from set A to set A can be formed for the set A = {1, 2, 3, 4, 5, ……n}?

Let A = {1, 2, 3}. f: A → A Then complete the function f such that it one-one and onto: f = {(1, 2), (2,1) ______}

If a relation f: X → Y is a function, then for g: Y → X to be a function, function f need to be

Find the number of bijective functions from set A to itself when A contains 106 elements.

Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = 3x + 4. Then the composition of f and g is ____________

Mathematics (Maths) for JEE Main & Advanced

Mathematics (Maths) for JEE Main & Advanced

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Types of Functions - Free MCQ Practice Test with solutions, JEE Maths

MCQ Practice Test & Solutions: Test: Types of Functions (10 Questions)

Let A be the set of all 25 students of Class X in a school. Let f : A → N be function defined by f (x) = roll number of the student x. Then f is:​

A function f: A x B → B x A defined by f (a, b) = (b, a) on two sets A and B. The function is:​

Let f : N→ R - {0} defined as f(x) = 1/x where x ∈ N is not an onto function. Which one of the following sets should be replaced by N such that the function f will become onto?​ (where R0 = R - {0})

The function f is

A function f: R → R is defined by f(x) = [x+1], where [x] the greatest integer function, is:​

How many onto functions from set A to set A can be formed for the set A = {1, 2, 3, 4, 5, ……n}?​

Let A = {1, 2, 3}. f: A → A Then complete the function f such that it one-one and onto: f = {(1, 2), (2,1) ______}

If a relation f: X → Y is a function, then for g: Y → X to be a function, function f need to be​

Find the number of bijective functions from set A to itself when A contains 106 elements.

Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = 3x + 4. Then the composition of f and g is ____________

Mathematics (Maths) for JEE Main & Advanced

Mathematics (Maths) for JEE Main & Advanced

Top Courses for JEE

About this JEE Practice Test

Explore more JEE Study Resources

Let A be the set of all 25 students of Class X in a school. Let f : A → N be function defined by f (x) = roll number of the student x. Then f is:

A function f: A x B → B x A defined by f (a, b) = (b, a) on two sets A and B. The function is:

Let f : N→ R - {0} defined as f(x) = 1/x where x ∈ N is not an onto function. Which one of the following sets should be replaced by N such that the function f will become onto? (where R₀= R - {0})

A function f: R → R is defined by f(x) = [x+1], where [x] the greatest integer function, is:

How many onto functions from set A to set A can be formed for the set A = {1, 2, 3, 4, 5, ……n}?

If a relation f: X → Y is a function, then for g: Y → X to be a function, function f need to be