Set Theory - General Aptitude - General Aptitude (GA) Previous Year Questions

1

2012 · General Aptitude (GA) · General Aptitude · Set Theory

Computer Science & Information Technology (CS) 2012

Given the language \(L = \{ab, aa, baa\}\), which of the following strings are in \(L^*\)?
1) \(abaabaaabaa\)
2) \(aaaabaaaa\)
3) \(baaaaabaaaab\)
4) \(baaaaabaa\)

A

1, 2 and 3

B

2, 3 and 4

C

1, 2 and 4

D

1, 3 and 4

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2

2012 · General Aptitude (GA) · General Aptitude · Set Theory

Computer Science & Information Technology (CS) 2012

How many onto (or surjective) functions are there from an n-element (n ≥ 2) set to a 2-element set?

A

2^n

B

2^n - 1

C

2^n - 2

D

2(2^n - 2)

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3

2015 · General Aptitude (GA) · General Aptitude · Set Theory

Computer Science & Information Technology (CS) 2015 [Session 1]

For a set \( A \), the power set of \( A \) is denoted by \( 2^A \). If \( A = \{5, \{6\}, \{7\}\} \), which of the following options are TRUE? I. \( \emptyset \in 2^A \) II. \( \emptyset \subseteq 2^A \) III. \( \{5, \{6\}\} \in 2^A \) IV. \( \{5, \{6\}\} \subseteq 2^A \)

A

I and III only

B

II and III only

C

I, II and III only

D

I, II and IV only

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4

2015 · General Aptitude (GA) · General Aptitude · Set Theory

Computer Science & Information Technology (CS) 2015 [Session 2]

The cardinality of the power set of { 0, 1, 2, ..., 10 } is ______.

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5

2015 · General Aptitude (GA) · General Aptitude · Set Theory

Computer Science & Information Technology (CS) 2015 [Session 2]

Consider two relations R₁(A,B) with the tuples (1,5), (3,7) and R₂(A,C) = (1,7), (4,9). Assume that R(A,B,C) is the full natural outer join of R₁ and R₂. Consider the following tuples of the form (A,B,C): a = (1,5,null), b = (1,null,7), c = (3, null, 9), d = (4,7,null), e = (1,5,7), f = (3,7,null), g = (4,null,9). Which one of the following statements is correct?

A

R contains a, b, e, f, g but not c, d.

B

R contains all of a, b, c, d, e, f, g.

C

R contains e, f, g but not a, b.

D

R contains e but not f, g.

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6

2015 · General Aptitude (GA) · General Aptitude · Set Theory

Computer Science & Information Technology (CS) 2015 [Session 3]

Suppose U is the power set of the set S = {1,2,3,4,5,6}. For any T ∈ U, let |T| denote the number of elements in T and T' denote the complement of T. For any T, R ∈ U, let T \ R be the set of all elements in T which are not in R. Which one of the following is true?

A

∀X ∈ U (|X| = |X'|)

B

∃X ∈ U ∃Y ∈ U (|X| = 5, |Y| = 5 and X ∩ Y = ∅)

C

∀X ∈ U ∀Y ∈ U (|X| = 2, |Y| = 3 and X \ Y = ∅)

D

∀X ∈ U ∀Y ∈ U (X \ Y = Y' \ X')

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7

2019 · General Aptitude (GA) · General Aptitude · Set Theory

Computer Science & Information Technology (CS) 2019 [Session 2]

In a college, there are three student clubs. Sixty students are only in the Drama club, 80 students are only in the Dance club, 30 students are only in the Maths club, 40 students are in both Drama and Dance clubs, 12 students are in both Dance and Maths clubs, 7 students are in both Drama and Maths clubs, and 2 students are in all the clubs. If 75% of the students in the college are not in any of these clubs, then the total number of students in the college is ____.

A

1000

B

975

C

900

D

225

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8

2024 · General Aptitude (GA) · General Aptitude · Set Theory

Computer Science & Information Technology (CS) 2024 [Session 2]

In an engineering college of 10,000 students, 1,500 like neither their core branches nor other branches. The number of students who like their core branches is 1/4^th of the number of students who like other branches. The number of students who like both their core and other branches is 500. The number of students who like their core branches is

A

1,800

B

3,500

C

1,600

D

1,500

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9

2017 · General Aptitude (GA) · General Aptitude · Set Theory

Computer Science & Information Technology (CS) 2017 [Session 1]

Consider the following languages over the alphabet Σ = {a,b,c}. Let L1 = { a^n b^n c^m | m,n ≥ 0 } and L2 = { a^m b^n c^n | m,n ≥ 0 }.
Which of the following are context-free languages?
I. L1 ∪ L2
II. L1 ∩ L2

A

I only

B

II only

C

I and II

D

Neither I nor II

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10

2017 · General Aptitude (GA) · General Aptitude · Set Theory

Computer Science & Information Technology (CS) 2017 [Session 1]

The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is __________.

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