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

Define the family of sets with one example.

Important Questions on Sets

HARD

Mathematics>Algebra>Sets>Basics 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

MEDIUM

Mathematics>Algebra>Sets>Basics 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___.

MEDIUM

Mathematics>Algebra>Sets>Basics of Sets

Let

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

then

EASY

Mathematics>Algebra>Sets>Basics 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>Basics 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 :

MEDIUM

Mathematics>Algebra>Sets>Basics 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

EASY

Mathematics>Algebra>Sets>Basics 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>Basics 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

MEDIUM

Mathematics>Algebra>Sets>Basics 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 :

HARD

Mathematics>Algebra>Sets>Basics 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?

EASY

Mathematics>Algebra>Sets>Basics of Sets

If a set

A

has

4

elements, then the total number of proper subsets of set

A

, is

HARD

Mathematics>Algebra>Sets>Basics 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>Basics of Sets

Which of the following is an empty set?

HARD

Mathematics>Algebra>Sets>Basics 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>Basics of Sets

The number of proper subsets of a set having

n + 1

elentents is

HARD

Mathematics>Algebra>Sets>Basics of Sets

A positive integer

k

is said to be good if there exists a partition of

\{1, 2, 3, \dots ., 20\}

into disjoint proper subsets such that the sum of the numbers in each subset of the partition is

k .

How many good numbers are there?

EASY

Mathematics>Algebra>Sets>Basics of Sets

The total number of subsets of the set

{1, 2, \dots \dots, 10}

which do not contain the element

6

EASY

Mathematics>Algebra>Sets>Basics 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

EASY

Mathematics>Algebra>Sets>Basics 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>Basics of Sets

X = (4^{n} - 3 n - 1 : n \in N)

and

Y = \{9 (n - 1) : n \in N\}

, then

X \cap Y =

Define the family of sets with one example.

Important Questions on Sets

Learn and Prepare for any exam you want !