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Set Theory - Past Year Questions

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Q1:

Let A and B be two finite sets such that n(A−B)n(A - B), n(A∩B)n(A\cap B), n(B−A)n(B - A) are in an arithmetic progression. Here n(X)n(X) denotes the number of elements in a finite set XX. If n(A∪B)=18n(A\cup B) = 18, then n(A)+n(B)n(A) + n(B) is ____
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Q2:

English exam and Math exam were conducted separately for a class of 120 students. The number of students who did not appear for the English exam is twice the number of students who did not appear for the Math exam. The number of students who passed the Math exam is twice the number of students who appeared but failed the English exam. If the number of students who passed the English exam is twice the number of students who appeared but failed the Math exam, then the number of students who appeared but failed the English exam is ________
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Q3:

In a survey of 500 people, it was found that 250 owned a 4-wheeler but not a 2-wheeler, 100 owned a 2-wheeler but not a 4-wheeler, and 100 owned neither a 4-wheeler nor a 2-wheeler. Then the number of people who owned both is
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Q4:

In a group of 150 students, 52 like tea, 48 like juice and 62 like coffee. If each student in the group likes at least one among tea, juice and coffee, then the maximum number of students that like more than one drink is:
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Q5:

In a group of 120 students, 80 students are from the Science stream and the rest are from the Commerce stream. It is known that 70 students support Mumbai Indians in the Indian Premier League; all the other students support Chennai Super Kings. The number of Science students who are supporters of Mumbai Indians is
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Q6:

Let AA and BB be two sets such that the Cartesian product A×BA \times B consists of four elements. If two elements of A×BA \times B are (1,4)(1,4) and (4,1)(4,1), then
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Q7:

Let P(X)P(X) denote power set of a set XX. If AA is the null set, then the number of elements in P(P(P(P(A))))P(P(P(P(A)))) is _________.
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Q8:

In a city, 50% of the population can speak in exactly one language among Hindi, English and Tamil, while 40% of the population can speak in at least two of these three languages. Moreover, the number of people who cannot speak in any of these three languages is twice the number of people who can speak in all these three languages. If 52% of the population can speak in Hindi and 25% of the population can speak exactly in one language among English and Tamil, then the percentage of the population who can speak in Hindi and in exactly one more language among English and Tamil is
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Q9:

In a class, 60% and 68% of students passed their Physics and Mathematics examinations respectively. Then at least ________ percentage of students passed both their Physics and Mathematics examinations.
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Q10:

In a class, students are assigned roll numbers from 1 to 140. All students with even roll numbers opted for cricket, all those whose roll numbers are divisible by 5 opted for football, and all those whose roll numbers are divisible by 3 opted for basketball. The number of students who did not opt for any of the three sports is
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Q11:

Out of 80 students who appeared for the school exams in Mathematics (M), Physics (P) and Chemistry (C), 50 passed M, 30 passed P and 40 passed C. At most 20 students passed M and P, at most 20 students passed P and C, and at most 20 students passed C and M. The maximum number of students who could have passed all three exams is __________.
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Q12:

In a school 70%70\% of the boys like cricket and 50%50\% like football. If x%x\% like both Cricket and Football, then
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Q13:

In a class of 65 students 40 like cricket, 25 like football and 20 like hockey. 10 students like both cricket and football, 8 students like football and hockey and 5 students like all three sports. If all the students like at least one sport, then the number of students who like both cricket and hockey is
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Q14:

Let the set P={2,3,4,...,25}P= \{2,3,4,..., 25\}. For each k∈Pk ∈ P, define Q(k)={x∈PQ(k)= \{x ∈ P such that x>kx > k and kk divides x}x\}. Then the number of elements in the set P−Uk=225Q(k)P - U_{k=2}^{25} Q(k) is
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Q15:

In a survey of 100 students, the number of students studying various languages were found to be:

  1. English only-18
  2. English but not Hindi-23
  3. English and German-8
  4. English-26
  5. German-48
  6. German and Hindi-8
  7. No language-24
Then, which of the following statements are true?

A. Number of students who were studying Hindi is 18.

B. Number of students who were studying English and Hindi is 3.

C. Number of students who were studying English, Hindi and German is 3.

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Set Theory - Past Year Questions (Free PDF Download)

Practice with our comprehensive collection of Set Theory Past Year Questions (PYQs of IPMAT Indore, IPMAT Rohtak & JIPMAT) with detailed solutions. These questions are carefully curated from previous year papers to help you understand the exam pattern and improve your preparation.

Our free resources include handwritten solutions for all questions, making it easier to understand the concepts and approach. Use these PYQs to assess your preparation level and identify areas that need more focus. No login required. Compilation of IPMAT Indore, IPMAT Rohtak & JIPMAT Questions!