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

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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

50% studentsanswered this correctly

Important Questions on Sets

EASY

Mathematics>Algebra>Sets>Difference of Sets

A \subset B,

then

A Δ B

is equal to

EASY

Mathematics>Algebra>Sets>Difference 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.

MEDIUM

Mathematics>Algebra>Sets>Difference of Sets

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

and

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

then

HARD

Mathematics>Algebra>Sets>Difference 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 :

EASY

Mathematics>Algebra>Sets>Difference of Sets

The shaded region in the given figure shows _____

Question Image

EASY

Mathematics>Algebra>Sets>Difference 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>Difference 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

=

…

HARD

Mathematics>Algebra>Sets>Difference 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

MEDIUM

Mathematics>Algebra>Sets>Difference 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 _______.

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Mathematics>Algebra>Sets>Difference 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:

MEDIUM

Mathematics>Algebra>Sets>Difference 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?

EASY

Mathematics>Algebra>Sets>Difference of Sets

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

and

n (A - B) = 39

, then

n (B)

is equal to

EASY

Mathematics>Algebra>Sets>Difference 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,

MEDIUM

Mathematics>Algebra>Sets>Difference 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:

HARD

Mathematics>Algebra>Sets>Difference 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>Difference of 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>Difference of Sets

A

and

B

are disjoint sets, then

B \cap A^{'}

, where

A^{'}

is complement of

A

, is equal to

MEDIUM

Mathematics>Algebra>Sets>Difference 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:

MEDIUM

Mathematics>Algebra>Sets>Difference of Sets

A

and

B

are two non-empty sets, then

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

is equal to

MEDIUM

Mathematics>Algebra>Sets>Difference of Sets

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

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

Important Questions on Sets

Learn and Prepare for any exam you want !

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