Sets, Relations and Functions Test

Result

Sets, Relations and Functions Test - 16

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Weekly Quiz Competition

Question 1
4 / -1

If R and C denote the set of real numbers and complex numbers, respectively.Then, the function f : C →R defined by f(z)= |z| is

A
one-one

B
onto

C
bijective

D
neither one-one nor onto

Solution
Question 2
4 / -1

If f : N —> N defined by f(x) = X²+ x + 1,x ∈ N, then f is

A
one-one and onto

B
many-one and onto

C
one-one but not onto

D
None of the above

Solution
Question 3
4 / -1

A
surjective but not injective

B
injective but not surjective

C
bijective

D
neither injective or not surjective

Solution
Question 4
4 / -1

The mapping f : N → N given by f(n) = 1 +n², n ∈ N, where N is the set of natural numbers, is

A
one-one and onto

B
onto but not one-one

C
one-one but not onto

D
neither one-one nor onto

Solution
Question 5
4 / -1

A function f : A → B, where A = {x : -1 ≤ X ≤ 1} and B = {y : 1 ≤ y ≤ 2} is defined by the rule y= f (x)= 1+ x². Which of the following statement is correct?

A
f is injective but not surjective

B
f is surjective but not injective

C
f is both injective and surjective

D
f is neither injective nor surjective

Solution
Question 6
4 / -1

The function f : R → R given by f(x)= x³-1is

A
a one-one function

B
an onto function

C
a bijection

D
neither one-one nor onto

Solution
Question 7
4 / -1

If A = [-1, 1] and f : A → A is defined as f(x) = x|x|,∀ x ∈ A, then f(x) is

A
many-one and into function

B
one-one and into function

C
many-one and onto function

D
one-one and onto function
Question 8
4 / -1

The function f : R → R defined by f(x) = (x -1)(x -2)(x - 3)is

A
one-one but not onto

B
onto but not one-one

C
both one-one and onto

D
neither one-one nor onto

Solution
Question 9
4 / -1

The function f : X → Y defined by f(x) = sin x is one-one but not onto, if X and Y are respectively equal to

A
R and R

B
[0,π] and [0,1]

C

D

Solution
Question 10
4 / -1

If R denotes the set of all real numbers, then the function f : R → R defined by f(x)= lxl is

A
only one-one

B
only onto

C
both one-one and onto

D
neither one-one nor onto

Solution