Sets(12th Grade > Mathematics ) Questions and answers for exam Preparation

12th Grade > Mathematics

SETS MCQs

Sets(11th And 12th Grade)

Total Questions : 60 | Page 2 of 6 pages

A = {x : x \in R, x^{2} = 16 and 2 x = 6}

can be represented in the roster form as _________ .

A = {}
A = { 14, 3, 4 }
A = { 3 }
A = { 4 }

Discuss Question

Answer: Option A. -> A = {}
:
A

x^{2} = 16 \Rightarrow x = \pm 4

2 x = 6 \Rightarrow x = 3

There is no value of

x

which satisfies both the givenequations. The set A is an empty set or a null set.
Thus, A = {}.

Question 12. In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then the percentage of population travelling by car or bus is

80 percent
40 percent
60 percent
70 percent

Discuss Question

Answer: Option C. -> 60 percent
:
C
n(C) = 20, n(B) = 50, n(C∩ B) = 10
Now n(C∪ B) = n(C) + n(B) - n(C∩ B)
= 20 + 50 - 10 = 60.

Question 13. The number of proper subsets of the set

{1, 2, 3}

is ___.

Discuss Question

Answer: Option B. -> 7
:
B
A set of

n

elements has

2^{n}

subsets.
Every set is a subset of itself.
Thus, the number of proper subsets of a set is

2^{n} - 1

subsets.
The set

{1, 2, 3}

has 3 elements and hence,

2^{3} - 1 = 7

proper subsets.

Question 14. If the sets A and B are defined as A = {(x, y) : y =

e^{x}

, x ∈ R};
B = {(x, y) : y = x, x ∈ R}, then

B ⊆ A
A ⊆ B
A ∩ B = ∅
A ∪ B = A

Discuss Question

Answer: Option C. -> A ∩ B = ∅
:
C
Since, y =

e^{x}

and y = x do not meet for any x∈ R

∴

A∩ B =∅ .

Question 15. In a town of 10,000 families it was found that 40% family buy newspaper A, 20% buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then number of families which buy A only is

3100
3300
2900
1400

Discuss Question

Answer: Option B. -> 3300
:
B
n(A) = 40% of 10,000 = 4,000
n(B) = 20% of 10,000 = 2,000
n(C) = 10% of 10,000 = 1,000
n(A∩ B) = 5% of 10,000 = 500
n(B∩ C) = 3% of 10,000 = 300
n(C∩ A) = 4% of 10,000 = 400
n(A∩ B∩ C) = 2% of 10,000 = 200
We want to find the number of families which buy only A= n(A) - [n(A ∩ B) + n(A ∩ C) - n(A ∩ B∩ C)]
=4000 - [500 + 400 - 200] = 4000 - 700 = 3300

Question 16. If A and B are two given sets, then A ∩

(A \cap B)^{c}

is equal to

A
B
∅
A ∩ (Bc).

Discuss Question

Answer: Option D. -> A ∩ (Bc).
:
D
A∩

(A \cap B)^{c}

) = A∩ (

A^{c}

∪

B^{c}

)
= (A∩(

A^{c}

)∪ (A∩(

B^{c}

)
=∅∪ (A∩(

B^{c}

) = A∩(

B^{c}

Question 17. If A and B are any two sets, then

A \cup (A \cap B)

= ___.

Discuss Question

Answer: Option A. -> A
:
A
If A and B are any two sets, then

A \cap B \subseteq A .

Also,

A \subseteq A \cup (A \cap B)

\Rightarrow A \subseteq A \cup (A \cap B) \subseteq A

\Rightarrow A \cup (A \cap B) = A

Question 18. Let A = { x : x ∈ R, |x| < 1}; B = {x : x ∈ R, |x-1| ≥ 1} and
A ∪ B = R - D, then the set D is

[x : 1
[x : 1 ≤ x < 2]
[x : 1 ≤ x ≤ 2]
None of these

Discuss Question

Answer: Option B. -> [x : 1 ≤ x < 2]
:
B
A = {x:x∈ R, -1 < x < 1}
B = {x:x∈ R:x-1≤ -1 or x-1≥ 1}
= {x : x∈ R:x≤ 0 or x≥ 2}
∴ A∪ B = R - D, where D = {x : x∈ R, 1≤ x < 2}.

Question 19. Let n(U) = 700, n(A) = 200, n(B) = 300 and n(A ∩ B) = 100,
Then n