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

MEDIUM

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The number of elements in set $A$ is $30$ , the number of elements in the intersection of the sets $A, B$ is $25$ . Find the cardinal number of the difference of the two sets $A, B$ .

50% studentsanswered this correctly

Important Questions on Sets

EASY

Mathematics>Algebra>Sets>Cardinal Properties of 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

=

…

MEDIUM

Mathematics>Algebra>Sets>Cardinal Properties of 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:

EASY

Mathematics>Algebra>Sets>Cardinal Properties of 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.

EASY

Mathematics>Algebra>Sets>Cardinal Properties of 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:

EASY

Mathematics>Algebra>Sets>Cardinal Properties of Sets

The shaded region in the given figure shows _____

Question Image

MEDIUM

Mathematics>Algebra>Sets>Cardinal Properties of 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:

MEDIUM

Mathematics>Algebra>Sets>Cardinal Properties of 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>Cardinal Properties of 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

MEDIUM

Mathematics>Algebra>Sets>Cardinal Properties of Sets

In a class of

60

students,

25

students play cricket,

20

students play tennis and

10

students play both the games. Then the number of students who play tennis only is

MEDIUM

Mathematics>Algebra>Sets>Cardinal Properties of Sets

Let

S = \{4, 6, 9\}

and

T = \{9, 10, 11, \dots, 1000\}

. If

A = \{a_{1} + a_{2} + \dots + a_{k} : k \in N, a_{1}, a_{2}, a_{3}, \dots, a_{k} \in S\}

then the sum of all the elements in the set

T - A

is equal to _______.

HARD

Mathematics>Algebra>Sets>Cardinal Properties of 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 :

MEDIUM

Mathematics>Algebra>Sets>Cardinal Properties of Sets

If $A = {1, 2, 3, 4, 5}$ and $B = {2, 4, 6}$ , then $A - B =$

MEDIUM

Mathematics>Algebra>Sets>Cardinal Properties of 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?

MEDIUM

Mathematics>Algebra>Sets>Cardinal Properties of Sets

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

and

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

then

EASY

Mathematics>Algebra>Sets>Cardinal Properties of 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,

EASY

Mathematics>Algebra>Sets>Cardinal Properties of Sets

A

and

B

are disjoint sets, then

B \cap A^{'}

, where

A^{'}

is complement of

A

, is equal to

HARD

Mathematics>Algebra>Sets>Cardinal Properties of 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

EASY

Mathematics>Algebra>Sets>Cardinal Properties of Sets

n (A \cup B) = 97, n (A \cap B) = 23

and

n (A - B) = 39

, then

n (B)

is equal to

MEDIUM

Mathematics>Algebra>Sets>Cardinal Properties of Sets

A

and

B

are two non-empty sets, then

(B - A) \cap {(A \cap B)}^{'}

is equal to

EASY

Mathematics>Algebra>Sets>Cardinal Properties of Sets

A \subset B,

then

A Δ B

is equal to

The number of elements in set A is 30, the number of elements in the intersection of the sets A,B is 25. Find the cardinal number of the difference of the two sets A,B.

Important Questions on Sets

Learn and Prepare for any exam you want !

The number of elements in set $A$ is $30$ , the number of elements in the intersection of the sets $A, B$ is $25$ . Find the cardinal number of the difference of the two sets $A, B$ .