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

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

S is an infinite proper subset of R - 0

EASY

Earn 100

Mach Number is related with -

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Important Questions on Sets, Relations and Functions

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Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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, Relations and Functions>Sets and Relations

Which of the following statements is false?

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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, Relations and Functions>Sets and Relations

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, Relations and Functions>Sets and Relations

A \subset B,

then

A Δ B

is equal to

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

In the given Venn diagram $n (A)$ is

Question Image

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

If a set

A

has

4

elements, then the total number of proper subsets of set

A

, is

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Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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

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Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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:

HARD

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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, Relations and Functions>Sets and Relations

n (A) = 3, n (B) = 6

and

A \subseteq B,

then the number of elements in

(A \cup B)

is equal to

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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, Relations and Functions>Sets and Relations

In a class of

175

students the following data shows the number of students opting one or more subjects. Mathematics

100

, Physics

70

, Chemistry

40

, Mathematics and Physics

30,

Mathematics and Chemistry

28

, Physics and Chemistry

23

, Mathematics, physics and Chemistry

18

. The number of students who have opted Mathematics alone is

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

In an examination,

54 %

of the candidates passed in science and

42 %

failed in mathematics. If

32 %

failed in both subjects, what percentage passed in both subjects ?

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

In an examination,

53 %

of the candidates failed in science and

48 %

failed in mathematics. If

40 %

failed in both subjects, what percentage passed in both subjects ?

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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 ?

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Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

Let

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

then

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Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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

and

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

, then

X \cap Y =

Mach Number is related with -

Important Questions on Sets, Relations and Functions

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