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Test Details

Chapter 1

Relations and functions

Starts

Nov 19, 7:00 PM

Duration

80 minutes

Deadline

Nov 19, 8:20 PM

Maximum marks

30.0 marks

Question type

MCQ

Total questions

30 questions

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Question Text

Question 1 :

Let N denote the set of all natural numbers and R a relation on $$N\times N$$. Which of the following is an equivalence relation?

Let N denote the set of all natural numbers and R a relation on $$N\times N$$. Which of the following is an equivalence relation?

Question 2 :

$$N$$ is the set of positive integers. The relation $$R$$ is defined on N x N as follows: $$(a,b) R (c,d)\Longleftrightarrow ad=bc$$ Prove that

$$N$$ is the set of positive integers. The relation $$R$$ is defined on N x N as follows: $$(a,b) R (c,d)\Longleftrightarrow ad=bc$$ Prove that

Question 3 :

If $$f:\mathbb{N} \rightarrow \mathbb{N}$$ and $$f(x) = x^{2}$$ then the function is<br/>

If $$f:\mathbb{N} \rightarrow \mathbb{N}$$ and $$f(x) = x^{2}$$ then the function is<br/>

Question 4 :

The true set of real value of $$x$$ for which the function, $$f(x)=x\ \mathrm{ln}\ x-x+1$$ is positive is

The true set of real value of $$x$$ for which the function, $$f(x)=x\ \mathrm{ln}\ x-x+1$$ is positive is

Question 5 :

Let $$f:R\rightarrow R$$ be defined as $$f(x)=x^{3}+2x^{2}+4x+\sin \left(\dfrac{\pi}{2}\right)$$ and $$g(x)$$ be the inverse function of $$f(x)$$, then $$g'(8)$$ is equal to

Let $$f:R\rightarrow R$$ be defined as $$f(x)=x^{3}+2x^{2}+4x+\sin \left(\dfrac{\pi}{2}\right)$$ and $$g(x)$$ be the inverse function of $$f(x)$$, then $$g'(8)$$ is equal to

Question 7 :

Let $$f: N\rightarrow R$$ such that $$f(x)=\dfrac{2x-1}{2}$$ and $$g: Q\rightarrow R$$such that $$g(x)=x+2$$ be two function. Then $$(gof)\left(\dfrac{3}{2}\right)$$ is equal to

Let $$f: N\rightarrow R$$ such that $$f(x)=\dfrac{2x-1}{2}$$ and $$g: Q\rightarrow R$$such that $$g(x)=x+2$$ be two function. Then $$(gof)\left(\dfrac{3}{2}\right)$$ is equal to

Question 8 :

Which one of the following relations on R (set of real numbers) is an equivalence relation

Which one of the following relations on R (set of real numbers) is an equivalence relation

Question 9 :

The number of reflexive relation in set A = {a, b, c} is equal to

The number of reflexive relation in set A = {a, b, c} is equal to

Question 10 :

Let $$T$$ be the set of all triangles in the Euclidean plane, and let a relation $$R$$ on $$T$$ be defined as $$aRb$$, if $$a$$ is congruent to $$b$$ for all $$a,b\in T$$. Then, $$R$$ is

Let $$T$$ be the set of all triangles in the Euclidean plane, and let a relation $$R$$ on $$T$$ be defined as $$aRb$$, if $$a$$ is congruent to $$b$$ for all $$a,b\in T$$. Then, $$R$$ is

Question 11 :

Let $$A=\left\{ 2,3,4,5,....,17,18 \right\} $$. Let $$\simeq $$ be the equivalence relation on $$A\times A$$, cartesian product of $$A$$ with itself, defined by $$(a,b)\simeq (c,d)$$, iff $$ad=bc$$. The the number of ordered pairs of the equivalence class of $$(3,2)$$ is

Let $$A=\left\{ 2,3,4,5,....,17,18 \right\} $$. Let $$\simeq $$ be the equivalence relation on $$A\times A$$, cartesian product of $$A$$ with itself, defined by $$(a,b)\simeq (c,d)$$, iff $$ad=bc$$. The the number of ordered pairs of the equivalence class of $$(3,2)$$ is

Question 12 :

If $$A=\left\{ 1,2,3 \right\} $$, then a relation $$R=\left\{ \left( 2,3 \right) \right\} $$ on $$A$$ is

If $$A=\left\{ 1,2,3 \right\} $$, then a relation $$R=\left\{ \left( 2,3 \right) \right\} $$ on $$A$$ is

Question 14 :

Find number of all such functions $$y = f(x)$$ which are one-one?

Find number of all such functions $$y = f(x)$$ which are one-one?

Question 15 :

Let $$A = \left\{ {1,2,3} \right\}$$ and $$R = \left\{ {\left( {1,1} \right),\left( {1,3} \right),\left( {3,1} \right),\left( {2,2} \right),\left( {2,1} \right),\left( {3,3} \right)} \right\}$$, then the relation $$R$$ and $$A$$ is

Let $$A = \left\{ {1,2,3} \right\}$$ and $$R = \left\{ {\left( {1,1} \right),\left( {1,3} \right),\left( {3,1} \right),\left( {2,2} \right),\left( {2,1} \right),\left( {3,3} \right)} \right\}$$, then the relation $$R$$ and $$A$$ is

Question 16 :

If $$A=\left\{ a,b,c \right\} $$, then the relation $$R=\left\{ \left( b,c \right) \right\} $$ on $$A$$ is

If $$A=\left\{ a,b,c \right\} $$, then the relation $$R=\left\{ \left( b,c \right) \right\} $$ on $$A$$ is

Question 17 :

The relation $$R=\left\{ \left( 1,1 \right) ,\left( 2,2 \right) \left( 3,3 \right)  \right\} $$ on the set $$A=\left\{ 1,2,3 \right\} $$ is

The relation $$R=\left\{ \left( 1,1 \right) ,\left( 2,2 \right) \left( 3,3 \right)  \right\} $$ on the set $$A=\left\{ 1,2,3 \right\} $$ is

Question 18 :

If the relation is defined on $$R-\left\{ 0 \right\} $$ by $$\left( x,y \right) \in S\Leftrightarrow xy>0$$, then $$S$$ is ________

If the relation is defined on $$R-\left\{ 0 \right\} $$ by $$\left( x,y \right) \in S\Leftrightarrow xy>0$$, then $$S$$ is ________

Question 19 :

Let $$A=\left\{ 1,2,3 \right\} $$. Then, the number of equivalence relations containing $$(1,2)$$ over set A is

Let $$A=\left\{ 1,2,3 \right\} $$. Then, the number of equivalence relations containing $$(1,2)$$ over set A is

Question 20 :

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

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

Question 22 :

Let $$f(x,y)=xy^{2}$$ if $$x$$ and $$y$$ satisfy $$x^{2}+y^{2}=9$$ then the minimum value of $$f(x,y)$$ is

Let $$f(x,y)=xy^{2}$$ if $$x$$ and $$y$$ satisfy $$x^{2}+y^{2}=9$$ then the minimum value of $$f(x,y)$$ is

Question 23 :

If $$A=\left\{ a,b,c,d \right\} $$, then a relation $$R=\left\{ \left( a,b \right) ,\left( b,a \right) ,\left( a,a \right) \right\} $$ on $$A$$ is

If $$A=\left\{ a,b,c,d \right\} $$, then a relation $$R=\left\{ \left( a,b \right) ,\left( b,a \right) ,\left( a,a \right) \right\} $$ on $$A$$ is

Question 24 :

Let E = {1, 2, 3, 4} and F {1, 2}. Then the number of onto functions from E to F is

Let E = {1, 2, 3, 4} and F {1, 2}. Then the number of onto functions from E to F is

Question 25 :

Let A={ 1, 2, 3, 4} and R= {( 2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. Then R is

Let A={ 1, 2, 3, 4} and R= {( 2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. Then R is

Question 26 :

Let $$L$$ denote the set of all straight lines in a plane, Let a relation $$R$$ be defined by $$lRm$$, iff $$l$$ is perpendicular to $$m$$ for all $$l \in L$$. Then, $$R$$ is

Let $$L$$ denote the set of all straight lines in a plane, Let a relation $$R$$ be defined by $$lRm$$, iff $$l$$ is perpendicular to $$m$$ for all $$l \in L$$. Then, $$R$$ is

Question 27 :

On the set $$N$$ of all natural numbers define the relation $$R$$ by $$a R b$$ if and only if the G.C.D. of $$a$$ and $$b$$ is $$2$$. Then $$R$$ is:

On the set $$N$$ of all natural numbers define the relation $$R$$ by $$a R b$$ if and only if the G.C.D. of $$a$$ and $$b$$ is $$2$$. Then $$R$$ is:

Question 28 :

Which of the following is not an equivalence relation on $$Z$$?

Which of the following is not an equivalence relation on $$Z$$?

Question 29 :

For real number $$x$$ and $$y$$, define $$xRy$$ iff $$x-y+\sqrt{2}$$ is an irrational number. Then the relation $$R$$ is

For real number $$x$$ and $$y$$, define $$xRy$$ iff $$x-y+\sqrt{2}$$ is an irrational number. Then the relation $$R$$ is

Question 30 :

Assertion: Domain of $$f(x)$$ is singleton. Reason: Range of $$f(x)$$ is singleton.

Assertion: Domain of $$f(x)$$ is singleton. Reason: Range of $$f(x)$$ is singleton.

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