Let S = x ∈ R : cos x + cos 2 x < 2 , then

S is an infinite proper subset of R - 0

Let A , B and C be sets such that ϕ ≠ A ∩ B ⊆ C . Then which of the following statements is not true?

If ( A - C ) ⊆ B , then A ⊆ B

( C ∪ A ) ∩ ( C ∪ B ) = C

If ( A - B ) ⊆ C , then A ⊆ C

EASY

Earn 100

State whether the following set is a finite or an infinite set.

The set of prime numbers smaller than $99$

Important Questions on Sets

HARD

Mathematics>Algebra>Sets>Types of Sets

Let $A$ be the set of vectors $a = (a_{1}, a_{2}, a_{3})$ satisfying ${(\sum_{i = 1}^{3} \frac{a_{i}}{2^{i}})}^{2} = \sum_{i = 1}^{3} \frac{a_{i}^{2}}{2^{i}}$ . Then,

EASY

Mathematics>Algebra>Sets>Types of Sets

Two finite sets have

m

and

n

elements. The number of subsets of the first set is

112

more than that of the second. The values of

m

and

n

are respectively

MEDIUM

Mathematics>Algebra>Sets>Types of Sets

Let

S = \{x \in R : \cos (x) + \cos (\sqrt{2} x) < 2\},

then

EASY

Mathematics>Algebra>Sets>Types of Sets

A

set

T

is given as

T = \{x \in R ∣ (x - 3) = (x + 4)^{2}, x < 2\} .

Which of these would be TRUE about the set

T ?

EASY

Mathematics>Algebra>Sets>Types of Sets

The following Venn diagram indicates

Question Image

MEDIUM

Mathematics>Algebra>Sets>Types of Sets

A = \{(a_{1}, a_{2}, \dots . a_{10}) : a_{1} \in {1, 2, 3}, a_{1} + a_{i + 1}

is even,

1 \leq i \leq 9\},

then the number of elements in the set

A

HARD

Mathematics>Algebra>Sets>Types of Sets

Let

A, B

and

C

be sets such that

ϕ \neq A \cap B \subseteq C .

Then which of the following statements is not true?

MEDIUM

Mathematics>Algebra>Sets>Types of Sets

Let

A

and

B

be two sets containing

2

elements and

4

elements respectively. The number of subsets of

A \times B

having

3

or more elements is :

EASY

Mathematics>Algebra>Sets>Types of Sets

The set of cubes of natural numbers is

EASY

Mathematics>Algebra>Sets>Types of Sets

Two finite sets respectively have

x

and

y

number of elements. The total number of sub sets of the first is

56

more than the total no. of sub sets of the second. The value of

x, y

are respectively __________

HARD

Mathematics>Algebra>Sets>Types of Sets

Let

A

and

B

be two sets containing four and two elements respectively. Then the number of subsets of the set

A \times B

, each having at least three elements is

EASY

Mathematics>Algebra>Sets>Types of Sets

Which of the following is an empty set?

EASY

Mathematics>Algebra>Sets>Types of Sets

Let

S = \{1, 2, 3, \dots ., 100\}

, then number of non-empty subsets

A

S

such that the product of elements in

A

is even is :

MEDIUM

Mathematics>Algebra>Sets>Types of Sets

An investigator interviewed

100

students to determine the performance of three drinks milk, coffee and tea. The investigator reported that

10

students take all three drinks milk, coffee and tea;

20

students take milk and coffee,

30

students take coffee and tea,

25

students take milk and tea,

12

students take milk only,

5

students take coffee only and

8

students take tea only. Then the number of students who did not take any of the three drinks is

HARD

Mathematics>Algebra>Sets>Types of Sets

Let

Z

be the set of integers. If

A = \{x \in Z : 2^{(x + 2) (x^{2} - 5 x + 6)} = 1\}

and

B = {x \in Z : - 3 < 2 x - 1 < 9}

, then the number of subsets of the set

A \times B

, is :

EASY

Mathematics>Algebra>Sets>Types of Sets

If the total number of

m

-element subsets of the set

A = \{a_{1}, a_{2}, \dots, a_{n}\}

k

times the number of

m

element subsets containing

a_{4}

, then

n

MEDIUM

Mathematics>Algebra>Sets>Types of Sets

Set

A

has

m

elements and set

B

has

n

elements. If the total number of subsets of

A

112

more than the total number of subsets of

B

, then the value of

m \cdot n

is___.

EASY

Mathematics>Algebra>Sets>Types of Sets

A

and

B

are disjoint sets, then

B \cap A^{'}

, where

A^{'}

is complement of

A

, is equal to

EASY

Mathematics>Algebra>Sets>Types of Sets

Let

A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} .

Then the number of subsets of

A

containing two or three elements is

HARD

Mathematics>Algebra>Sets>Types of Sets

Let

a > 0, a \neq 1

. Then, the set

S

of all positive real numbers

b

satisfying

(1 + a^{2}) (1 + b^{2}) = 4 a b

State whether the following set is a finite or an infinite set. The set of prime numbers smaller than 99

Important Questions on Sets

Learn and Prepare for any exam you want !

State whether the following set is a finite or an infinite set.

The set of prime numbers smaller than $99$