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

12th Grade > Mathematics

SETS MCQs

Sets(11th And 12th Grade)

Total Questions : 60 | Page 6 of 6 pages

Question 51. If a set A has n elements, then the total number of subsets of A is

Discuss Question

Answer: Option C. -> 2n
:
C
Number of subsets of A =

^{n} C_{0}

^{n} C_{1}

+ .............+

^{n} C_{n}

2^{n}

Question 52. 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 53.

If n (\cup) = 700, n (A) = 200, n (B) = 300

and

n (A \cap B) = 100,

then

n (A^{^{'}} \cap B^{^{'}}) =

___.

Discuss Question

Answer: Option C. -> 300
:
C
From de-Morgan's law of complementation, we have

A^{'} \cap B^{'} = (A \cup B)^{'} .

\Rightarrow n (A^{'} \cap B^{'}) = n ((A \cup B)^{'})

But,

n ((A \cup B)^{'}) = n (U) - n (A \cup B)

by definition of complement of a set.

∴ n (A^{'} \cap B^{'}) = n (U) - n (A \cup B)

= n (U) - [n (A) + n (B) - n (A \cap B)]

= 700 - (200 + 300 - 100)

= 300

Question 54. In a survey of 200 students from 7 different schools, 50 people do not play NFS, 40 people do not play Dota and 10 people do not play any online game. Find the number of people who do not play both the games.

Discuss Question

Answer: Option A. -> 80
:
A
Let the numberof people who do not play NFS be n(N') = 50. (Given)
Similarly, the number of people who do not play Dota be n(D') = 40. (Given)
And, thenumberof people who do not play any game be n((N ∪ D)')=n(N'∩ D') = 10. (Given) (de-Morgan's law)
We have to find the numberof people who do not play both the games = n(N∩ D)'.
We know from de-Morgan's law that for sets A and B,

(A \cap B)^{'} = A^{'} \cup B^{'} .

So,

n ((N \cap D)^{'}) = n (N^{'} \cup D^{'}) = n (N^{'}) + n (D^{'}) - n (N^{'} \cap D^{'})

= 50 + 40 - 10

= 80

Question 55. 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 56. In a random survey 250 people participated. Out of 250 people who took part in the survey, 40 people have listened to Pink Floyd. 30 people have listened to metallica and 20 people have listened to John Denver. If 10 people have listened to all three then find the no. of people who have listened only Pink Floyd.

Discuss Question

Answer: Option C. -> 30
:
C

In A Random Survey 250 People Participated. Out Of 250 Peopl...

Let the no. of people who have listened to Pink Floyd be n(P) = 40
Similarly, the no. of people who have listened to Metallica be n(M) = 30
and the no. of people who have listened to John Denver be= n(J) = 20
Also given that the no. of people who listen to all three i.e.