Relations And Functions Test

Relations And Functions

This is Relations and functions Test-06 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

A function \(f{\text{ }}:{\text{ }}X{\text{ }} \to {\text{ }}Y\) is defined to be one – one (or injective), if

A
the images of distinct elements of X under f are identical
B
the images of distinct elements of X under f are not distinct
C
the images of distinct elements of X under f are not defined
D
the images of distinct elements of X under f are distinct
Correct

Function \(f{\text{ }}:{\text{ }}X{\text{ }} \to {\text{ }}Y\) is called many – one if

A
f is many – many
B
f is not one – one
Correct
C
f is not well defined
D
f has many elements

A function \(f{\text{ }}:{\text{ }}X{\text{ }} \to {\text{ }}Y\) is said to be onto if

A
Every elementof Y is the image of some element of X under f
Correct
B
every elementof Y is the image of same element of X under f
C
No elementof Y is the image of some element of X under f
D
Some elements of Y are the images of some element of X under f

A function \(f{\text{ }}:{\text{ }}X{\text{ }} \to {\text{ }}Y\) is said to be surjective if

A
No elementof Y is the image of some element of X under f
B
every elementof Y is the image of same element of X under f
C
Some elements of Y are the images of some element of X under f
D
Every elementof Y is the image of some element of X under f
Correct

A function \(f{\text{ }}:{\text{ }}X{\text{ }} \to {\text{ }}Y\) is said to be bijective, if f is

A
Injective
B
Both one – one and onto.
Correct
C
Surjective
D
Projective

Let A be the set of all 50 students of Class X in a school. Let \(f{\text{ }}:{\text{ A }} \to {\text{ N}}\) be function defined by f (x) = roll number of the student. f is

A
one – one and not onto
B
one – onebut not onto
Correct
C
Onto
D
Odd

If N is the set of integers \(f{\text{ }}:{\text{ N }} \to {\text{ N}}\), given by f(x) = 2x is

A
one – one and not onto
B
one – onebut not onto
Correct
C
Odd
D
Onto

If R is the set of real numbers, \(f{\text{ }}:{\text{ }}R{\text{ }} \to R\) , given by f (x) = 2x is

A
Onto
B
one – onebut not onto
C
Odd
D
one – one and onto
Correct

If R is the set of real numbers, defined as\(f{\text{ }}\left( x \right){\text{ }} = {\text{ }}{x^2}\) , is

A
Odd
B
one – one and onto
C
neither one – one nor onto
Correct
D
one – onebut not onto

If R is the set of real numbers,f: R → R be defined as\(f\left( x \right){\text{ }} = {\text{ }}{x^4}\) .

A
f is many – one onto
Correct
B
neither one – one nor onto
C
f is neither one – one nor onto
D
f is one – one but not onto

If R is the set of real numbers, \(Let\;\;\;f{\text{ }}:{\text{ }}R{\text{ }} \to {\text{ }}R\) be defined as f (x) = 3x then f is

A
neither one – one nor onto
B
f is one – one onto
Correct
C
f is one – one but not onto
D
f is neither one – one nor onto

\(f{\text{ }}:{\text{ }}\left[ {--1,{\text{ }}1} \right]{\text{ }} \to R\) , given by \(f\left( x \right) = \frac{x}{{\left( {x + 2} \right)}}\) is

A
many – one
B
Even
C
one – one
Correct
D
one – many

Let \(f{\text{ }}:{\text{ }}R{\text{ }} \to {\text{ }}R\) be defined by f (x) = \(\;\frac{1}{x}\) \(x \in R\) . Then f is

A
Onto
B
f is not defined
Correct
C
one – one
D
Bijective

Which of the following functions from Z into Z is a bijection?

A
f (x) = x + 2
Correct
B
f (x) = 2x + 1
C
\(f{\text{ }}\left( x \right){\text{ }} = {\text{ }}{x^3}\)
D
\(\begin{array}{*{20}{l}} {f{\text{ }}\left( x \right){\text{ }} = {\text{ }}{x^2} + {\text{ }}1} \end{array}\)

Let \(f{\text{ }}:{\text{ }}R{\text{ }} \to {\text{ }}R\) be the functions defined by\(f{\text{ }}\left( x \right){\text{ }} = {\text{ }}{x^3} + {\text{ }}5\) . Then \({f^{--1}}\left( x \right)\) is

A
\({(5 - x)^{\frac{1}{3}}}\)
B
\({(x - 5)^{\frac{1}{3}}}\)
Correct
C
5 – x
D
\({(x + 5)^{\frac{1}{3}}}\)