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Published on: 24/07/2019
Sets
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Questions + Answers key
Take MCQ Mathematics Test
1.
Draw the Venn diagram of the following:
A' \(\cap\) (C - B)
2.
Draw the Venn diagram of the following:
A' \(\cap\) (B \(\cup\) C)
3.
Which of the following sets are finite or infinite?
(i) {x: x ∈ N and x is a prime number}
(ii) {x: x is a letter in the word CALCUTTA}
(iii) {x: x is a set of rational numbers between 1 and 2}
(iv) The set of natural numbers greater than 50.
(v) {x: x is a prime divisor of 30}
4.
Which of the following are sets? Justify your answer:
The collection of all odd integers.
5.
Which of the following are sets? Justify your answer:
The collection of beautiful girls in India.
6.
Which of the following are sets? Justify your answer:
The collection of all divisors of 30.
7.
Which of the following are sets? Justify your answer:
The collection of all the months of a year having 31 days
8.
Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Find the values of m and n.
9.
If U={a,b,c,d,e,f}, A={a,b,c}, B={c,d,e,f}, C={c,d,e}, D={d,e,f}, then tabulate the following set A\(\cap \)D
10.
If n(A\(\cup \)B)=25, n(A)=12, n(A-B)=8, then write the number of elements in A\(\cap \)B and B-A
11.
Let F1 be the set of parallelograms, F2 be the set of rectangles, F3 be the set of rhombus and F4 be the set of squares. Then, show that F1 is equal to the union of all sets.
12.
Let n(U) = 700, n(A) = 200, n(B) = 300 and \(n(A\cap B)\) = 100 .Find \(n({ A }^{ ' }\cap { B }^{ ' })\).
13.
In a group of 400 people, 250 can speak Hindi and 200 can speak English.How many can speak both Hindi and English?
14.
Which of the following sets are finite and which are infinite?
(i) \(\{x \in R: 0
15.
Which of the following are sets? Justify your answer.
The collection of all the months of a year beginning with the letter J.
16.
Which of the following sets are finite and which are infinite?
Set of concentric circles in a plane.
17.
In a survey of 400 movie viewers, 150 were listed as liking 'Veer Zaara', 100 were listed as liking 'Aitraaz' and 75 were listed both liking 'Aitraaz' as well as 'Veer zaara'.Find how many people liking neither 'Aitraaz' nor 'Veer Zaara'?
18.
If A={4n-3n-1, n\(\epsilon \)N} and B={9(n-1):n \(\in\) N}, show that A\(\subset \)B.
19.
Draw the Venn diagrams to illustrate the following relationship among sets, E, M and U, where E is the set of students studying English in a school, M is the set of students studying Mathematics in the same school, U is the set of all students in that school.
There is no student who studies both Mathematics and English.
20.
Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why?
(i) {3, 4} ⊂ A
(ii) {3, 4} ∈ A
(iii) {{3, 4}} ⊂ A
(iv) 1 ∈ A
(v) 1⊂ A
(vi) {1, 2, 5} ⊂ A
(vii) {1, 2, 5} ∈ A
(viii) {1, 2, 3} ⊂ A
(ix) ¢ ∈ A
(x) ¢⊂ A
(xi) {¢} ⊂ A.
21.
For any two sets A and B, A \(\cup\) B = A iff _____.
A ⊂ B
B∈A
A=B
A\(\ne\)B
22.
For any two sets A and B, (A - B) \(\cup\) (B - A)=_____.
(A - B) \(\cup\) A
(B - A) \(\cup\) B
(A \(\cup\) B) - (A \(\cap\) B)
(A \(\cup\) B) \(\cap\) (A \(\cap\) B)
23.
If \(A\cap B=B\) then _____.
B⊂A
A=ф
A⊂B
B=ф
24.
For any two sets A and B, \(A\cap(A\cup B)=\)_____.
B
A
ф
none of these
25.
The number of subsets of a set containing n elements is _____.
2n - 2
n2
2n
n
1.
2.
3.
(i) Infinite
(ii) Finite
(iii) Infinite
(iv) Infinite
(v) Finite
4.
Yes, {..........., -5, -3, -1, 1,3,5,............}
5.
No
6.
Yes, {1, 2, 3, 5, 6, 10, 15, 30}
7.
Yes, {January, March, May, July, August, October, December}
8.
2m=56+2n\(\Rightarrow \)2m-2n=56
Ans. m-6,n=3
9.
\(\phi \)
10.
n(A-B)=n(A)-n(A\(\cap \)B)
\(\Rightarrow \)n(A\(\cap \)B)=12-8=4
\(\because \)n(B)= n(A\(\cup
\)B)+n(A\(\cap \)B)-n(A)=25+4-12=17
\(\therefore \)(B-A)=n(B)-n(B\(\cap \)A)
Ans. n(A\(\cap \)B)=4, n(B-A)=13
11.
All rectangles, Rhombus and square are parallelograms because its opposite sides are equal and parallel.
Therefore \({ F }_{ 2 }\subset { F }_{ 1 },{ F }_{ 3 }\subset { F }_{ 1 }\) and \({ F }_{ 4 }\subset { F }_{ 1 }\)
\({ F }_{ 1 }={ F }_{ 2 }\cup { F }_{ 3 }\subset { F }_{ 4 }\)
12.
\(n({ A }^{ ' }\cap { B }^{ ' })=n(U)-n(A\cup B)\)
Ans.300
13.
Let H be the set of people speaking Hindi and E be the set of people speaking English.
\(\therefore\) n(H) = 250, n(E) = 200 and n(H \(\cup\) E) = 400
We have to find n(H \(\cap\) E).
We know that
n(H \(\cup\) E) = n(H) + n(E) - n(H \(\cap\) E)
\(\therefore\) 400 = 250 + 200 - n(H \(\cap\) E)
\(\therefore\) n(H \(\cap\) E) = 450 - 400 = 50.
14.
Given, \(\{x \in R: 0
\(\therefore \)
15.
We are sure that members of this collection are January, June, and July. So, this collection is well-defined. Hence, it is a set.
16.
We can draw infinite circles having same centre.
\(\therefore \) It is an infinite set.
17.
The number of people who were liking neither (A) 'Aitraaz' nor 'Veer Zaara' (V) is given by
\(n({ V }^{ ' }\cap { A }^{ , }) ={ n(V\cup A) }^{ ' }\)
=\(n(\cup )-n(V\cup A)\)
=\(n(\cup )-n(V)-n(A)+n(V\cap A)\)
18.
Now, 4n-3n-1=(3+1)n-3n-1
\(=1+3n+\frac { n(n-1) }{ 2 } .{ (3) }^{ 2 }+....-3n-1\\ =9(\frac { n(n-1) }{ 2 } +.......)\)
and B={9(n-1):n \(\in\) N}
19.
20.
(i) {3, 4} is a member of set A.
\(\therefore\) {3, 4} ∈ A
Hence {3, 4}⊂ A is incorrect.
(ii) {3, 4} is a member of set A.
\(\therefore\){3, 4} ∈ A is correct.
(iii) Here {3, 4} is a member of set A.
\(\therefore\) {{3,4}} is a set
\(\therefore\) {{3,4}} ⊂ A is correct.
(iv) 1 is a member of set A.
\(\therefore\) 1 ∈ A is correct.
(v) 1 is not a set, it is a member of set A.
\(\therefore\) 1⊂ A is incorrect.
(vi) 1, 2, 5 are members of set A.
\(\therefore\) {1, 2, 5} is a subset of set A.
\(\therefore\) {1, 2, 5} ⊂ A is correct.
(vii) 1, 2, 5 are members of set A.
\(\therefore\) {1, 2, 5} is a subset of set A.
\(\therefore\) {1, 2, 5} ∈ A is incorrect.
(viii) 3 is not a member of set A.
\(\therefore\) {1, 2, 3} is not a subset of set A.
\(\therefore\) {1, 2, 3} ⊂ A is incorrect.
(ix) ф is not a member of set A.
\(\therefore\) ф ∈ A is incorrect.
(x) Since ф is subset of every set,
\(\therefore\)ф ⊂ A is correct.
(xi)ф is not a member of set A.
\(\therefore\) {ф} ⊂ A is incorrect.
21.
(b)
B∈A
22.
(c)
(A \(\cup\) B) - (A \(\cap\) B)
23.
(a)
B⊂A
24.
(b)
A
25.
(c)
2n
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