Relations And Functions Test

Relations And Functions

This is Relations and functions Test-08 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

Let f : {2, 3, 4, 5} → {3, 4, 5, 9} and g : {3, 4, 5, 9} → {7, 11, 15} befunctions defined as f (2) = 3, f(3) = 4, f (4) = f (5) = 5 and g (3) = g (4) = 7 andg (5) = g (9) = 11. gof. is

A
{7, 7, 11, 11}
Correct
B
{15, 15, 11, 11}
C
{7, 7, 15, 11}
D
{7, 7, 15, 11}

if \(f{\text{ }}:{\text{ }}R{\text{ }} \to {\text{ }}R{\text{ }}and{\text{ }}g{\text{ }}:{\text{ }}R{\text{ }} \to {\text{ }}R\) are given by f (x) = cos x and\(g{\text{ }}\left( x \right){\text{ }} = {\text{ }}3{x^2}\) . Then

A
f is odd
B
g is odd
C
\(gof{\text{ }} \ne {\text{ }}fog\)
Correct
D
\(\begin{array}{*{20}{l}} {gof = fog} \end{array}\)

Let \(f{\text{ }}:{\text{ }}N{\text{ }} \to {\text{ }}Y\) be a function defined as f (x) = 4x + 3, where,\(Y{\text{ }} = {\text{ }}\{ y \in N:{\text{ }}y{\text{ }} = {\text{ }}4x{\text{ }} + {\text{ }}3\) for some \(x \in N \). Then f is

A
Non Invertible
B
Invertible
Correct
C
f is even
D
g is even

Let \(Y{\text{ }} = {\text{ }}\{ {n^2}:{\text{ }}n \in N\} \subset N\) . Consider\(f:{\text{ }}N{\text{ }} \to {\text{ }}Y{\text{ }}as{\text{ }}f{\text{ }}\left( n \right){\text{ }} = {\text{ }}{n^2}\) . Inverse of f is

A
\(\sqrt y \)
Correct
B
\({y^2} + 2\)
C
\({y^2}\)
D
\({y^2} + 1\)

Let \(f{\text{ }}:{\text{ }}X{\text{ }} \to {\text{ }}Y{\text{ }}and{\text{ }}g{\text{ }}:{\text{ }}Y{\text{ }} \to {\text{ }}Z\) be two invertible functions. Then gof is

A
Non invertible
B
invertible with \({\left( {gof} \right)^{--1}} = {\text{ }}{f^{--1}}o{g^{--1}}.\)
Correct
C
\({I_y}\)
D
\({I_N}\)

Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} be given by f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}. Then gof is

A
{(1, 3), (3, 3), (4, 3)}
B
{(1, 3), (3, 3), (4, 1)}
C
{(1, 3), (3, 1), (4, 3)}
Correct
D
{(1, 3), (3, 1), (4, 1)}

Let f, g and h be functions from R to R, then

A
(f + g) oh = h of + goh
B
(f + g) oh = ho(f + g)
C
(f + g) oh = foh + goh
D
(f + g) oh = foh + hog
Correct

Consider \(f{\text{ }}:{\text{ }}{R_ + } \to {\text{ }}\left[ {4,{\text{ }}\infty } \right)\) given by \(f{\text{ }}\left( x \right){\text{ }} = {\text{ }}{x^2} + {\text{ }}4\) .

A
f is many – many
B
f is one – one
C
f is not invertible
D
f is invertible
Correct

If \(f{\text{ }}:{\text{ }}R{\text{ }} \to {\text{ }}R\) be given by \(f\left( x \right){\text{ }} = f \bullet f\;\) is

A
\(\begin{array}{*{20}{l}} {{x^2}} \end{array}\)
B
x
Correct
C
\({x^3}\)
D
\({x^{\frac{1}{3}}}\)

If the set A contains 5 elements and the set B contains 6 elements, then the number of one – one and onto mappings from A to B is

A
120
B
720
C
0
Correct
D
none of these

Let A = {1, 2, 3,… n} and B = {a, b}. Then the number of surjections from A into B is

A
\({2^n}--{\text{ }}1\)
B
\({2^n}--{\text{ }}2\)
Correct
C
\(^n{P_2}\)
D
None of these

Let \(f{\text{ }}:{\text{ }}A{\text{ }} \to {\text{ }}B{\text{ }} \) and \( g{\text{ }}:{\text{ }}B{\text{ }} \to {\text{ }}C\) be the bijective functions. Then (g o f)–1 is

A
\({g^{--1}}o{\text{ }}{f^{--1}}\)
B
g o f
C
\({f^{--1}}o{\text{ }}{g^{--1}}\)
Correct
D
f o g

Let \(f{\text{ }}:{\text{ }}\left[ {2,{\text{ }}\infty } \right){\text{ }} \to {\text{ }}R\) be the function defined by \(f{\text{ }}\left( x \right){\text{ }} = {\text{ }}{x^2}--{\text{ }}4x{\text{ }} + {\text{ }}5\) , then the range of f is

A
\(\left[ {1,{\text{ }}\infty } \right)\)
Correct
B
\(\left[ {5,{\text{ }}\infty } \right)\)
C
R
D
\(\left[ {4,{\text{ }}\infty } \right)\)

Let \(f{\text{ }}:{\text{ }}N{\text{ }} \to {\text{ }}R\) be the function defined by f (x) =\(\frac{{2x - 1}}{2}\) and \(g{\text{ }}:{\text{ }}Q{\text{ }} \to {\text{ }}R\) be another function defined by g (x) = x + 2. Then (g o f)\(\frac{3}{2}\) is

A
1
B
none of these
Correct
C
2
D
\(\frac{7}{2}\)

Let \(f{\text{ }}:{\text{ }}R{\text{ }} \to {\text{ }}R\) be given by f (x) = tan x. Then \({f^{--1}}\left( 1 \right)\) is

A
\({2^3}\pi \)
B
\(\pi \)
C
\(2\pi \)
D
\(\frac{\pi }{4}\)
Correct