The CAT QA section requires speed and accuracy, along with a thorough understanding of the Set Theory. This article provides a set of MCQs on Set Theory to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT 2025 exam preparation
Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.
The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.
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CAT MCQs on Set Theory
1. Let a,b,c be non-zero real numbers such that b2<4ac, and f(x)=ax2+bx+c. If the set S consists of all integers m such that f(m)<0, then the set S must necessarily be
A
the set of all integers
B
either the empty set or the set of all integers
C
the empty setthe set of all positive integers
D
the set of all positive integers
2. A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, while 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is
A
45
B
38
C
32
D
43
3. Consider two sets A = {2, 3, 5, 7, 11, 13} and B = {1, 8, 27}. Let f be a function from A to B such that for every element b in B, there is at least one element a in A such that f(a) = b. Then, the total number of such functions f is
A
537
B
540
C
667
D
665
4. In a class of 50 students, 23 speak English, 15 speak Hindi, and 18 speak Tamil. 8 speak both English and Hindi, 11 speak both Hindi and Tamil, 6 speak both English and Tamil, and 5 speak all three languages. How many students speak exactly two languages?
A
10
B
12
C
14
D
16
5. In a locality, two-thirds of the people have cable TV, one-fifth have VCR, and one-tenth have both. What is the fraction of people having either cable-TV or VCR?
A
19/30
B
2/3
C
17/30
D
23/30
6. A set \( S = \{1, 2, 3, \ldots, n\} \) is partitioned into \( n \) disjoint subsets \( A_1, A_2, \ldots, A_n \), each containing four elements. It is given that in each subset, one element is the arithmetic mean of the other three. Which of the following statements is true?
A
\( n \neq 1 \) and \( n \neq 2 \)
B
\( n \neq 1 \) but can be equal to 2
C
\( n \neq 2 \) but can be equal to 1
D
It is possible to satisfy for \( n = 1 \) as well as for \( n = 2 \)
7. In a certain zoo, there are 42 animals in one sector, 34 in the second sector and 20 in the third sector. Out of this, 24 graze in sector one and also in sector two. 10 graze in sector two and sector three, 12 graze in sector one and sector three. These figures also include four animals grazing in all the three sectors are now transported to another zoo. Find the total number of animals.
A
38
B
36
C
54
D
None of the above
8. A survey of 100 people was conducted to find out whether they had read recent issues of Golmal magazine in July, August, and September. Data:
- Only September: 18
- September but not August: 23
- September and July: 8
- September: 28
- July: 48
- July and August: 10
- None: 24
A
7
B
9
C
12
D
14
9. A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options — air conditioning, radio and power windows were already installed. Following were the observation of the survey:
I. 15 had air conditioning
II. 2 had air conditioning and power windows but no radios
III. 12 had radio
IV. 6 had air conditioning and radio but no power windows
V. 11 had power windows
VI. 4 had radio and power windows
VII. 3 had all three options
What is the number of cars that had none of the options?
I. 15 had air conditioning
II. 2 had air conditioning and power windows but no radios
III. 12 had radio
IV. 6 had air conditioning and radio but no power windows
V. 11 had power windows
VI. 4 had radio and power windows
VII. 3 had all three options
What is the number of cars that had none of the options?
A
4
B
3
C
1
D
2
10. In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals I, II and III. If 50% favoured the first proposal, 30% the second and 20% the third, 5% favoured all the three, what is the percentage of those asked favoured more than one of the three proposals?
A
10
B
12
C
17
D
22
11. Which of the following is true?
A
\(7^{3} = (7^{3})^{2}\)
B
\(7^{3}>(7^{3})^{2}\)
C
\(7^{3}<(7^{3})^{2}\)
D
None of these
12. In a locality of 100 families: 45 have radios, 75 have TVs, 25 have VCRs. 10 have all three. Every VCR owner has TV. 25 have radio only. How many families have only TV?
A
30
B
35
C
40
D
45
13. Fifty college teachers are surveyed as to their possession of colour TV, VCR and tape recorder. Of them, 22 own colour TV, 15 own VCR and 14 own tape recorders. Nine of these college teachers own exactly two items out of colour TV, VCR and tape recorder; and, one college teacher owns all three. How many of the 50 teachers own none of the three, colour TV, VCR or tape recorder?
A
4
B
9
C
10
D
11
14. There are 3 clubs A, B \& C in a town with 40, 50 \& 60 members respectively. While 10 people are members of all 3 clubs, 70 are members in only one club. How many belong to exactly two clubs?
A
20
B
25
C
50
D
70
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