11th Maths Weekly Test-3 ( Sets, Relations and Functions )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test-3 ( Sets, Relations and Functions )-Aug 2020

Time : 1.00 Hours

Part - A

Multiple Choice Question - Answer All Question

For non-empty sets A and B, if A ⊂ B then (A x B) ⋂ (B x A) is equal to

A ⋂ B
A x A
B x B
none of these.

Which one of the following is false?

(A')' = A
AUA' = A
A⋂A'=Ø
AUA' = U

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

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

The number of reflective relations one set containing n elements is:

2¹²
2⁴
2¹⁶
2⁸

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}

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}

Let R be the relation over the set of all straight lines in a plane such that l₁Rl₂ ⇔ l₁丄l₂ . Then R is

symmetric
reflexive
transitive
an equivalent relation

The inverse of f(x)=\(\begin{cases} x\quad if\quad x<1 \\ { x }^{ 2 }\quad if\quad 1\le x\le 4 \\ 8\sqrt { x } \quad if\quad x>4 \end{cases}\) is

\({ f }^{ -1 }(x)=\begin{cases} x\quad if\quad x<1 \\ \sqrt { x } \quad if\quad 1\le x\le 16 \\ \frac { { x }^{ 2 } }{ 64 } \quad if\quad x>1 \end{cases}\)
\({ f }^{ -1 }(x)=\begin{cases} -x\quad if\quad x<1 \\ \sqrt { x } \quad if\quad 1\le x\le 16 \\ \frac { { x }^{ 2 } }{ 64 } \quad if\quad x>16 \end{cases}\)
\({ f }^{ -1 }(x)=\begin{cases} { x }^{ 2 }\quad if\quad x<1 \\ \sqrt { x } \quad if\quad 1\le x\le 16 \\ \frac { { x }^{ 2 } }{ 64 } \quad if\quad x>16 \end{cases}\)
\({ f }^{ -1 }(x)=\begin{cases} { 2x }\quad if\quad x<1 \\ \sqrt { x } \quad if\quad 1\le x\le 16 \\ \frac { { x }^{ 2 } }{ 8 } \quad if\quad x>16 \end{cases}\)

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

Let A and B be subsets of the universal set N, the set of natural numbers. Then A^'∪[[(A⋂B)∪B^'] is

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

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

The natural domain of the function \(y=\sqrt{9-x^2}\) is:

\(-3\le x \le 3\)
-3 <x < 3
0 <x < 3
\((-\infty, -3)\cup(3,\infty)\)

Let R be the set of all real numbers. Consider the following subsets of the plane R x R: S = {(x, y) : y =x + 1 and 0 < x < 2} and T = {(x,y) : x - y is an integer} Then which of the following is true?

T is an equivalence relation but S is not an equivalence relation
Neither S nor T is an equivalence relation
Both S and T are equivalence relation
S is an equivalence relation but T is not an equivalence relation.

If n((A x B) ∩(A x C)) = 8 and n(B ∩ C) = 2, then n(A) is

n[P[P[p(Ø)]]] =

If f(x) = |x - 2| + |x + 2|, x ∈ R, then

\(f(x)=\begin{cases}-2x\ if\ x∈(-∞,-2] \\4\ if \ x∈(-2,2]\\ 2x\ if\ x∈(2,∞)\end{cases}\)
\(f(x)=\begin{cases}-2x\ if\ x∈(-∞,-2] \\4x\ if \ x∈(-2,2]\\ - 2x\ if\ x∈(2,∞)\end{cases}\)
\(f(x)=\begin{cases}-2x\ if\ x∈(-∞,-2] \\-4x\ if \ x∈(-2,2]\\ 2x\ if\ x∈(2,∞)\end{cases}\)
\(f(x)=\begin{cases}-2x\ if\ x∈(-∞,-2] \\2x\ if \ x∈(-2,2]\\ 2x\ if\ x∈(2,∞)\end{cases}\)

The function f(x) = log (x + \(\sqrt{x^2+1}\)) is

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

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 shaded region in the adjoining diagram represents.

For real numbers x and y, define xRy if x-y+√2 is an irrational number. Then the relation R is

reflexive
symmetric
transitive
none of these

If \(f(x)={1-x\over 1+x},(x\neq0)\) then f^-1(x) =

f(x)
\(1\over f(x)\)
-f(x)
-\(1\over f(x)\)

Let f:Z➝Z be given by f(x)=\(\begin{cases} \frac { x }{ 2 } \quad if\quad x\quad is\quad even \\ 0\quad if\quad x\quad is\quad odd \end{cases}\) . Then f is

one-one but not onto
onto but not one-one
one-one and onto
neither one-one nor onto

Which of the following functions is an even function?

\(f(x)={2^x+2^{-n}\over 2^x-2^{-x}}\)
\(f(x)={3^x+1\over 3^x-1}\)
\(f(x)={x.3^x-1\over 3^x+1}\)
\(f(x) = log (x +\sqrt{x^2 + 1})\)

Choose the correct statement.

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

\(n(A\cap B)=4\) and \((A\cup B)=11\) then \(n(p(A\triangle B))\) is:

The domain and range of the function \(f(x)={|x-4|\over x-4}\)

R, [-1, 1]
R \ {4};{-1,1}
R \ {4};{-1,l}
R, (-1,1)

If f(x)=2x-3 and g(x)=x²+x-2 then gof(x) is

2(2x²-5x+2)
(2x²-5x-2)
2(2x²+5x+2)
2x²+5x-2

Let X={1,2,3,4}, Y={a,b,c,d} and f={f(1,a),(4,b);(2,c);(3,d);(2,d)}. Then f is

an one-to-one function
an onto function
a function which is not one-to-one
not a function

Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4),(4, 1)}. Then R is

reflexive
symmetric
transitive
equivalence

Let f: R ->R to given by f(x)=(3-x3)^{\(\frac{1}{3}\)}. then fof (x) is

x^{\(\frac{1}{a}\)}
x^a
x
3-x^a

Match List - I with List II

List I List II

i {(1, 1), (2,2), (3,3)(1,2)} a equivalence

ii {(1,2), (2,1), (2,3), (3,2)} b transitive

iii {(1,2), (2,3), (1,3)} c Symmetric

iv {(1,1), (2,2), (3,3), (1,2),(2,1), (2,3), (1,3)} d reflexive

The Correct match is

	List I		List II
i	{(1, 1), (2,2), (3,3)(1,2)}	a	equivalence
ii	{(1,2), (2,1), (2,3), (3,2)}	b	transitive
iii	{(1,2), (2,3), (1,3)}	c	Symmetric
iv	{(1,1), (2,2), (3,3), (1,2),(2,1), (2,3), (1,3)}	d	reflexive

i ii iii iv
i ii iii iv

c d b a
i ii iii iv

d c b a
i ii iii iv

b a b c

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

For any four sets A, B, C and D, which of the following is not true?

A x C ⊂ B x D
(A x B) ∩ (C x D) = (A ∩ C) x (B ∩ D)
A x (B U,C) = (A x B) U (A x C)
A x (B ∩ C) = (A x B) ∩ (A x C)

The domain of the function \(f(x)=\sqrt{log_{10}{3-x\over x}}\)is

\((0,{3\over2})\)
(0, 3)
\((-\infty, {3\over2}]\)
\((0, {3\over2}]\)

Let f: R➝R be given by f(x)=x+\(\sqrt { { x }^{ 2 } } \) is

injective
Surjective
bijective
none of these

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11th Maths Weekly Test-3 ( Sets, Relations and Functions )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test-3 ( Sets, Relations and Functions )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

For non-empty sets A and B, if A ⊂ B then (A x B) ⋂ (B x A) is equal to

Which one of the following is false?

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

The number of reflective relations one set containing n elements is:

Which one of the following is not a singleton set?

Which one of the following is a finite set?

Let R be the relation over the set of all straight lines in a plane such that l1Rl2 ⇔ l1丄l2 . Then R is

The inverse of f(x)=\(\begin{cases} x\quad if\quad x<1 \\ { x }^{ 2 }\quad if\quad 1\le x\le 4 \\ 8\sqrt { x } \quad if\quad x>4 \end{cases}\) is

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

Let A and B be subsets of the universal set N, the set of natural numbers. Then A'∪[[(A⋂B)∪B'] is

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

The natural domain of the function \(y=\sqrt{9-x^2}\) is:

Let R be the set of all real numbers. Consider the following subsets of the plane R x R: S = {(x, y) : y =x + 1 and 0 < x < 2} and T = {(x,y) : x - y is an integer} Then which of the following is true?

If n((A x B) ∩(A x C)) = 8 and n(B ∩ C) = 2, then n(A) is

n[P[P[p(Ø)]]] =

If f(x) = |x - 2| + |x + 2|, x ∈ R, then

The function f(x) = log (x + \(\sqrt{x^2+1}\)) is

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:

The shaded region in the adjoining diagram represents.

For real numbers x and y, define xRy if x-y+√2 is an irrational number. Then the relation R is

If \(f(x)={1-x\over 1+x},(x\neq0)\) then f-1(x) =

Let f:Z➝Z be given by f(x)=\(\begin{cases} \frac { x }{ 2 } \quad if\quad x\quad is\quad even \\ 0\quad if\quad x\quad is\quad odd \end{cases}\) . Then f is

Which of the following functions is an even function?

Choose the correct statement.

\(n(A\cap B)=4\) and \((A\cup B)=11\) then \(n(p(A\triangle B))\) is:

The domain and range of the function \(f(x)={|x-4|\over x-4}\)

If f(x)=2x-3 and g(x)=x2+x-2 then gof(x) is

Let X={1,2,3,4}, Y={a,b,c,d} and f={f(1,a),(4,b);(2,c);(3,d);(2,d)}. Then f is

Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4),(4, 1)}. Then R is

Let f: R ->R to given by f(x)=(3-x3)\(\frac{1}{3}\). then fof (x) is

Match List - I with List II List I List II i {(1, 1), (2,2), (3,3)(1,2)} a equivalence ii {(1,2), (2,1), (2,3), (3,2)} b transitive iii {(1,2), (2,3), (1,3)} c Symmetric iv {(1,1), (2,2), (3,3), (1,2),(2,1), (2,3), (1,3)} d reflexive The Correct match is

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

For any four sets A, B, C and D, which of the following is not true?

The domain of the function \(f(x)=\sqrt{log_{10}{3-x\over x}}\)is

Let f: R➝R be given by f(x)=x+\(\sqrt { { x }^{ 2 } } \) is

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Let R be the relation over the set of all straight lines in a plane such that l₁Rl₂ ⇔ l₁丄l₂ . Then R is

Let A and B be subsets of the universal set N, the set of natural numbers. Then A^'∪[[(A⋂B)∪B^'] is

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

If \(f(x)={1-x\over 1+x},(x\neq0)\) then f^-1(x) =

If f(x)=2x-3 and g(x)=x²+x-2 then gof(x) is

Let f: R ->R to given by f(x)=(3-x3)^{\(\frac{1}{3}\)}. then fof (x) is

Match List - I with List II

List I List II

i {(1, 1), (2,2), (3,3)(1,2)} a equivalence

ii {(1,2), (2,1), (2,3), (3,2)} b transitive

iii {(1,2), (2,3), (1,3)} c Symmetric

iv {(1,1), (2,2), (3,3), (1,2),(2,1), (2,3), (1,3)} d reflexive

The Correct match is