11th Maths Monthly Test-2 ( Sets, Relations and Functions )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test-2 ( Sets, Relations and Functions )-Aug 2020

Time : 2.00 Hours

Part - A

Multiple Choice Question - Answer All Question

The number of relations on a set containing 3 elements is

9
81
512
1024

\(n(p(A))=512,n(p(B))=32,n(A\cup B)=16,\) find \(n(A\cap B):\)

If two sets A and B have 17 elements in common, then the number of elements common to the set A x B and B x A is

2¹⁷
17²
34
insufficient data

If n(A) = 1024 then n[P(A)] =

2¹⁰
\(2^{2^{10}}\)
cannot be determined
4¹⁰

If \(f(x)={1-x\over 1+x}, x≠0\) then \(f[f(x)]+f\left[f\left(1\over x\right)\right]\)

<2
> 2
> 2
None

Choose the correct statement.

One-to-one function have inverse
Onto function have inverse
bijection function have inverse
many - to - one function hae inverse

If \(f:[-2,2]\rightarrow A\) is given by f(x)=3³ then f is onto, if A is:

[3, 3]
(3, 3)
[-24,24]
(-24, 24)

The function f:R➝R be defined by f(x)=sinx+cosx is

an odd function
neither an odd function nor an even function
an even function
both odd function and even function

Let R be a relation on the set N given by R={(a,b):a=b-2, b>6}. Then

(2,4)∈R
(3,8)∈R
(6,8)∈R
(8,7)∈R

If A={1,2,3}, B={1,4,6,9} and R is a relation from A to B defined by "x is greater than y". The range of R is

{1,4,6,9}
{4,6,9}
{1}
None of these

The shaded region in the adjoining diagram represents.

Which one of the following is a finite set?

{x:x∈Z, x<5}
{x:x∈W, x≥5}
{x:x∈N, x>10}
{x:x is an even prime number}

Domain of the function \(y={x-1\over x+1}\) is:

1R
Q
R-(-1)
R-1

If the function f:[-3,3]➝S defined by f(x)=x² is onto, then S is

[-9,9]
R
[-3,3]
[0,9]

n[P[P[p(Ø)]]] =

Part - B

Generic 2 - Answer All Question

If A⊂B then find A⋂B and A\B (using venn diagram)

For n, m\(\in \)N, n/m means that n is a factor of n & m. Then find whether the given relation is an equivalence relation.

Find the domain and range of \({1 \over 1-cos\ x}.\)

On the set of natural number let R be the relation defined by aRb if a + b \(\le\) 6. Write down the relation by listing all the pairs. Check whether it is reflexive

Check whether the following sets are disjoint where p={x:x is a prime<15} and Q={x:x is a multiple of 2 and x<16}

If f(x)=\(\frac { x-1 }{ x+1 } \), then show that, f\(\left( \frac { -1 }{ x } \right) =\frac { -1 }{ f(x) } \).

State whether the following sets are finite or infinite.
{x \(\in \) N:x is an even prime number}

In the set Z of integers, define mRn if m-n is divisible by 7.Prove that R is an equivalence relation.

If f: R ⟶ R is an bijection given by f(x)= x³+3, then find f^-1(x)

On a set of natural numbers let R be the relation defined by aRb if a + 2b = 15. Write down the relation by listing all the pairs. Check whether it is reflexive, symmetric, transitive, equivalence.

Part - C

Generic 3 - Answer All Question

Write the values of f at -4, 1, -2, 7, 0 if \(f(x)=\begin{cases}-x+4\quad if\ -\infty <x\le -3 \\ x^2+4\quad if-3<x<-2 \\ x^2-x\quad if-2\le x<1\\x-x^2\quad if\ 1\le x <7\\0\quad \quad \quad otherwise \end{cases}\)

Let A = {0,1, 2, 3}. Construct relations on A of the following types:
(i) not reflexive, not symmetric, not transitive.
(ii) not reflexive, not symmetric, transitive.
(iii) not reflexive, symmetric, not transitive.
(iv) not reflexive, symmetric, transitive.
(v) reflexive, not symmetric, not transitive.

If \(f:R\longrightarrow R\) is defined by f(x)=3x-5,prove that f is a bijection and find its invesre.

Find the quotient of the identity function by the modulus function

Show that the function f: N ⟶ N given by f(x) = 2x is one-one but not onto

Part - D

Generic 5 - Answer All Question

Let f= {(1, 2), (3,4), (2, 2)} and s = {(2, 1), (3, 1), (4, 2)}. Find gof and fog.

For A = {0,1,2,3, 4}, B = {1,-2, 3, 4, 5, 6} and C = {2,4, 6, 7} verify A\(B ∩ C) = (A\B) U(A\C) Using venn diagram.

Check the following functions for one-to-oneness and ontoness.
\(f:R\rightarrow R\) defined by f(n) = n².

Let A = {2, 3, 5} and relation R = {(2, 5)} write down the minimum number of ordered pairs to be included to R to make it an equivalence relation.

Let f, g: \(R \rightarrow R\) be defined as f (x) = 2x -|x| and g(x) = 2x + |x|. find fog.

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11th Maths Monthly Test-2 ( Sets, Relations and Functions )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test-2 ( Sets, Relations and Functions )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

The number of relations on a set containing 3 elements is

\(n(p(A))=512,n(p(B))=32,n(A\cup B)=16,\) find \(n(A\cap B):\)

If two sets A and B have 17 elements in common, then the number of elements common to the set A x B and B x A is

If n(A) = 1024 then n[P(A)] =

If \(f(x)={1-x\over 1+x}, x≠0\) then \(f[f(x)]+f\left[f\left(1\over x\right)\right]\)

Choose the correct statement.

If \(f:[-2,2]\rightarrow A\) is given by f(x)=33 then f is onto, if A is:

The function f:R➝R be defined by f(x)=sinx+cosx is

Let R be a relation on the set N given by R={(a,b):a=b-2, b>6}. Then

If A={1,2,3}, B={1,4,6,9} and R is a relation from A to B defined by "x is greater than y". The range of R is

The shaded region in the adjoining diagram represents.

Which one of the following is a finite set?

Domain of the function \(y={x-1\over x+1}\) is:

If the function f:[-3,3]➝S defined by f(x)=x2 is onto, then S is

n[P[P[p(Ø)]]] =

Part - B

Generic 2 - Answer All Question

If A⊂B then find A⋂B and A\B (using venn diagram)

For n, m\(\in \)N, n/m means that n is a factor of n & m. Then find whether the given relation is an equivalence relation.

Find the domain and range of \({1 \over 1-cos\ x}.\)

On the set of natural number let R be the relation defined by aRb if a + b \(\le\) 6. Write down the relation by listing all the pairs. Check whether it is reflexive

Check whether the following sets are disjoint where p={x:x is a prime<15} and Q={x:x is a multiple of 2 and x<16}

If f(x)=\(\frac { x-1 }{ x+1 } \), then show that, f\(\left( \frac { -1 }{ x } \right) =\frac { -1 }{ f(x) } \).

State whether the following sets are finite or infinite. {x \(\in \) N:x is an even prime number}

In the set Z of integers, define mRn if m-n is divisible by 7.Prove that R is an equivalence relation.

If f: R ⟶ R is an bijection given by f(x)= x3+3, then find f-1(x)

On a set of natural numbers let R be the relation defined by aRb if a + 2b = 15. Write down the relation by listing all the pairs. Check whether it is reflexive, symmetric, transitive, equivalence.

Part - C

Generic 3 - Answer All Question

Write the values of f at -4, 1, -2, 7, 0 if \(f(x)=\begin{cases}-x+4\quad if\ -\infty <x\le -3 \\ x^2+4\quad if-3<x<-2 \\ x^2-x\quad if-2\le x<1\\x-x^2\quad if\ 1\le x <7\\0\quad \quad \quad otherwise \end{cases}\)

If \(f:R\longrightarrow R\) is defined by f(x)=3x-5,prove that f is a bijection and find its invesre.

Find the quotient of the identity function by the modulus function

Show that the function f: N ⟶ N given by f(x) = 2x is one-one but not onto

Part - D

Generic 5 - Answer All Question

Let f= {(1, 2), (3,4), (2, 2)} and s = {(2, 1), (3, 1), (4, 2)}. Find gof and fog.

For A = {0,1,2,3, 4}, B = {1,-2, 3, 4, 5, 6} and C = {2,4, 6, 7} verify A\(B ∩ C) = (A\B) U(A\C) Using venn diagram.

Check the following functions for one-to-oneness and ontoness. \(f:R\rightarrow R\) defined by f(n) = n2.

Let A = {2, 3, 5} and relation R = {(2, 5)} write down the minimum number of ordered pairs to be included to R to make it an equivalence relation.

Let f, g: \(R \rightarrow R\) be defined as f (x) = 2x -|x| and g(x) = 2x + |x|. find fog.

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Tamilnadu Stateboardszs - Class

If \(f:[-2,2]\rightarrow A\) is given by f(x)=3³ then f is onto, if A is:

If the function f:[-3,3]➝S defined by f(x)=x² is onto, then S is

State whether the following sets are finite or infinite.
{x \(\in \) N:x is an even prime number}

If f: R ⟶ R is an bijection given by f(x)= x³+3, then find f^-1(x)

Check the following functions for one-to-oneness and ontoness.
\(f:R\rightarrow R\) defined by f(n) = n².