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11th Maths Monthly Test-1( Sets, Relations and Functions )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test-1( Sets, Relations and Functions )-Aug 2020

Time : 2.00 Hours

Part - A

Multiple Choice Question - Answer All Question

If X and Y are two sets such that n (X) = 17, n (Y) = 23 and n(X U Y) = 38. Then n (X n 1) =

0
cannot determined
6
2

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}

The number of students who take both the subjects Mathematics and Chemistry is 70. This represents 10% of the enrollment in Mathematics and 14% of the enrollment in Chemistry. The number of students take at least one of these two subjects, is

1120
1130
1100
insufficient data

If A and B are any two finite sets having m and n elements respectively then the cardinality of the power set of A x B is

2^m
2ⁿ
mn
2^mn

The number of relations on a set containing 3 elements is

9
81
512
1024

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

Which one of the following is not a singleton set?

A = {x : 3x - 5 = 0, x ∈ Q}
B = {| x | = 1 / x ∈ Z}
{x : x³ - 1 = 0, x ∈ R}
{x : 30x = 60, x ∈ N}

The domain of the function \(f(x)=\sqrt{ x - 5 }+ \sqrt{6 - x}\)is

[5, ∞)
(- ∞, 6)
[5, 6]
(-5, ≠6)

Let S = (1, 2, 3), R be (1, 1) (1, 2) (2, 2) (1, 3) (3, 1), what are the elements to-be included to make R reflexive:

(3, 3)
(2, 3)
(3, 2)
none of these

The range of the function is \(f(x)=\sqrt{3x^2-4x+5}\) is

\(\left( -\infty,\sqrt{11\over 3}\right)\)
\(\left( -\infty,-\sqrt{11\over 3}\right)\)
\(\left( \sqrt{11\over 3},-\infty\right)\)
none

The range of the function \({1\over 1-2sinx}\)is

\((-∞,-1)\cup\left( {2\over 3},\infty\right)\)
\(\left( -1,{2\over 3}\right)\)
\(\left[ -1,{1\over 3}\right]\)
\((-∞,-1)\cup\left[ {1\over 3},\infty\right)\)

Let f and g be two odd functions then the function of f o g is

an even function
an odd function
neither even nor odd
a periodic function

The number of constant functions from a set containing m elements to a set containing n elements is

mn
m
n
m+n

Which one of the following is false?

(A')' = A
AUA' = A
A⋂A'=Ø
AUA' = U

Which of the following functions from z to itself are bijections (one-one and onto)?

f(x)=x³
f(x)=x+2
f(x)=2x+1
f(x)=x²+1

Part - B

Generic 2 - Answer All Question

The weight of the muscles of a man is a function of his body weight x and can be expressed as W(x)=0.35x. Determine the domain of this function.

From the curve y=sin x, draw y=sin|x|. (Hint: sin(-x)=-sin x)

If Ax A has 9 elements, S = {(a, b) ∈ A x A: a> b}; (2, -1) and (2, 1) are two elements, then find the remaining elements of S.

Show that the relation xy=-2 is a function for a suitable domain. Find the domain and the range of the function.

Check whether the following functions are one to one and onto.
\(f:N\cup(2,-1,0)\rightarrow N\) defined by f(x) =x + 3.

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 equivalence.

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.

Let C be the set of all circles in a plane and define a circle C is related to a circle C', if the radius of C is equal to the radius of C'

If A = (1, 2, 3, 4), B = (3, 4, 5, 6), find \(n(A\cup B)\times m(A\cap B)\times m(p(A)).\)

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

Part - C

Generic 3 - Answer All Question

By taking suitable sets A, B, C, verify the following results:
A \(\times\) (B\(\cup \)C)=(A\(\times\)B) \(\cup \) (A\(\times\)C)

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

Find the domain and range of the function f(x)=\(\frac { 1 }{ \sqrt { x-5 } } \).

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

Find the range of the following functions given by \( f(x) = \frac { 1 }{ 2-sin\ 3x } .\)

Find the quotient of the identity function by the modulus function

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 and B be two sets. Using properties of sets prove that A ∩ B' = Φ ⇒ A ⊂ B.

Draw venn diagram of three sets A, B and C which illustrates the following:
A and B disjoint but both are subsets of C.

Consider the functions:(i) y = e^x; (ii) y = log_eX.

Part - D

Generic 5 - Answer All Question

Let f and g be real functions defined by \(f(x)=\sqrt{x+2}\)and \(g(x)=\sqrt{4-x^2}\). Find f-g

From the curve y=sin x, graph the functions.
(i) y=sin(-x)
(ii) y=-sin(-x)
(iii) \(y=sin\left( {\pi\over 2}+x\right)\)
(iv) \(y=sin\left({\pi\over 2}-x \right)\)

Let f and g be real functions defined by \(f(x)=\sqrt{x+2}\) and \(g(x)=\sqrt{4-x^2}\). Find fg

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.

Find the domain of \(f(x)={1\over 1-2\cos\ x}.\)

Let f: R ⟶ R be the signum function defined as \(f(x)=\begin{cases} 1,\ x>0\\0, x=0 \\-1, x<0 \end{cases}\)and g: R ⟶ R to the greatest integer function given by g(x) = [x]. Then prove that fog and gof coincide in [-1,0).

From the curve y=x, draw
(i) y=- x
(ii) y=2x
(iii) y=x+1
(iv) \(y={1\over 2}x+1\)
(v) 2x+y+3=0

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