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

The transmitted force through a mass spring damper system will be greater than that transmitted through rigid supports for all values of damping factors, if the frequency ratio (Ï/Ïn) is

50% studentsanswered this correctly

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

=

…

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

Which of the following statements is false?

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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

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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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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 =

The transmitted force through a mass spring damper system will be greater than that transmitted through rigid supports for all values of damping factors, if the frequency ratio (Ï/Ïn) is

Important Questions on Sets, Relations and Functions

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The transmitted force through a mass spring damper system will be greater than that transmitted through rigid supports for all values of damping factors, if the frequency ratio (Ï/Ïn) is