Let A = θ ∈ R : 1 3 sin θ + 2 3 cos θ 2 = 1 3 sin 2 θ + 2 3 cos 2 θ . Then

A ∩ 0 , π has exactly one point

A ∩ 0 , π has exactly two points

A ∩ 0 , π has more than two points

EASY

Earn 100

Verify the commutative property of union of sets for the following.

$A = \{1, 2, 3\}$ and $B = \{2, 3, 4, 5\}$

Important Questions on Sets

MEDIUM

Mathematics>Algebra>Sets>Operations on Sets

In a certain town,

25 %

of the families own a phone and

15 %

own a car;

65 %

families own neither a phone nor a car and

2000

families own both a car and a phone. Consider the following three statements:

(i)

5 %

families own both a car and a phone.

(i i)

35 %

families own either a car or a phone.

(i i i)

40000

families live in the town.

Then,

EASY

Mathematics>Algebra>Sets>Operations on Sets

Let

X = \{n \in N : 1 \leq n \leq 50\}

. If

A = \{n \in X : n is a multiple of 2\}

and

B = \{n \in X : n is a multiple of 7\}

, then the number of elements in the smallest subset of

X

, containing both

A

and

B

, is.

MEDIUM

Mathematics>Algebra>Sets>Operations on Sets

A = \{x \in R : |x| < 2\}

and

B = \{x \in R : |x - 2| \geq 3\};

then

EASY

Mathematics>Algebra>Sets>Operations on Sets

A survey shows that

73 %

of the persons working in an office like coffee, whereas

65 %

like tea. If

x

denotes the percentage of them, who like both coffee and tea, then

x

cannot be:

MEDIUM

Mathematics>Algebra>Sets>Operations on Sets

Which of the following is not correct?

MEDIUM

Mathematics>Algebra>Sets>Operations on Sets

A survey shows that

63 %

of the people in a city read newspaper

A

whereas

76 %

read news paper

B

. If

x %

of the people read both the newspapers, then a possible value of

x

can be:

EASY

Mathematics>Algebra>Sets>Operations on Sets

A = {x | x \in N, x

is a prime number less than

12}

and

B = {x |

x \in N

x

is factor of

10}

, then

A \cap B

=

…

HARD

Mathematics>Algebra>Sets>Operations on Sets

Let

A = \{θ \in R : {(\frac{1}{3} \sin θ + \frac{2}{3} \cos θ)}^{2} = \frac{1}{3} \sin^{2} θ + \frac{2}{3} \cos^{2} θ\}

. Then

EASY

Mathematics>Algebra>Sets>Operations on Sets

Transpose of a row matrix is __________

MEDIUM

Mathematics>Algebra>Sets>Operations on Sets

In a class of

140

students numbered

1

140

, all even numbered students opted Mathematics course, those whose number is divisible by

3

opted Physics course and those whose number is divisible by

5

opted Chemistry course. Then the number of students who did not opt for any of the three courses is:

HARD

Mathematics>Algebra>Sets>Operations on Sets

Let $\cup_{i = 1}^{50} X_{i} = \cup_{i = 1}^{n} Y_{i} = T$ , where each $X_{i}$ contains $10$ elements and each $Y_{i}$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of sets $X_{i}$ 's and exactly $6$ of sets $Y_{i}$ 's then $n$ is equal to :

HARD

Mathematics>Algebra>Sets>Operations on Sets

In a certain town,

25 %

families own a phone,

15 %

families own a car,

65 %

families own neither a phone nor a car and

2000

families own both a car and a phone. Consider the following Statements

(S) :

(S_{1}) :

35 %

families own at least one of a car or a phone.

(S_{2}) :

40, 000

families live in the town.
Then:

MEDIUM

Mathematics>Algebra>Sets>Operations on Sets

Consider the two sets:

A = {m \in R :

both the roots of

x^{2} - (m + 1) x + m + 4 = 0

are real

}

and

B = [- 3, 5)

Which of the following is not true?

EASY

Mathematics>Algebra>Sets>Operations on Sets

A \subset B,

then

A Δ B

is equal to

EASY

Mathematics>Algebra>Sets>Operations on Sets

Let

A

and

B

be two sets such that

A \cap X = B \cap X = ϕ

and

A \cup X = B \cup X

for same set

X

. Then,

MEDIUM

Mathematics>Algebra>Sets>Operations on Sets

Let

A = {n \in N : n

is a

3 -

digit number

}

B = \{9 k + 2 : k \in N\}

and

C = \{9 k + l : k \in N\}

for some

l (0 < l < 9)

. If the sum of all the elements of the set

A \cap (B \cup C)

274 \times 400,

then

l

is equal to

EASY

Mathematics>Algebra>Sets>Operations on Sets

A

and

B

are disjoint sets, then

B \cap A^{'}

, where

A^{'}

is complement of

A

, is equal to

MEDIUM

Mathematics>Algebra>Sets>Operations on Sets

Two newspapers

A

and

B

are published in a city. It is known that

25 %

of the city population reads

A

and

20 %

reads

B

while

8 %

reads both

A

and

B .

Further,

30 %

of those who read

A

but not

B

look into advertisements and

40 %

of those who read

B

but not

A

also look into advertisements, while

50 %

of those who read both

A

and

B

look into advertisements. Then the percentage of the population who look into advertisements is:

HARD

Mathematics>Algebra>Sets>Operations on Sets

For any three sets

A, B

and

C

the set

(A \cup B \cup C) \cap {(A \cap B^{'} \cap C^{'})}^{'} \cap C^{'}

is equal to

HARD

Mathematics>Algebra>Sets>Operations on Sets

In a group of

100

persons,

80

people can speak Malayalam and

60

can speak English. Then the number of people who speak English only is

Verify the commutative property of union of sets for the following. A=1,2,3 and B=2,3,4,5

Important Questions on Sets

Learn and Prepare for any exam you want !

Verify the commutative property of union of sets for the following.

$A = \{1, 2, 3\}$ and $B = \{2, 3, 4, 5\}$