Set Theory & Algebra

Question 91

Let G be a finite group on 84 elements. The size of a largest possible proper subgroup of G is _______ . Note - This was Numerical Type question.

• 42
• 84
• 1
• 28

Question 92

Let N be the set of natural numbers. Consider the following sets, P: Set of Rational numbers (positive and negative) Q: Set of functions from {0, 1} to N R: Set of functions from N to {0, 1} S: Set of finite subsets of N Which of the above sets are countable?

• Q and S only
• P and S only
• P and R only
• P, Q and S only

Question 93

Suppose A is a finite set with n elements. The number of elements and the rank of the largest equivalence relation on A are

• {n,1}
• {n, n}
• {n², 1}
• {1, n²}

Question 94

Consider the set of integers I. Let D denote “divides with an integer quotient” (e.g. 4D8 but 4D7). Then D is

• Reflexive, not symmetric, transitive
• Not reflexive, not antisymmetric, transitive
• Reflexive, antisymmetric, transitive
• Not reflexive, not antisymmetric, not transitive

Question 95

The number of elements in the power set of { {1, 2}, {2, 1, 1}, {2, 1, 1, 2} } is

• 3
• 8
• 4
• 2

Question 96

The function f: [0,3]→[1,29] defined by f(x) = 2x³ - 15x² + 36x + 1 is

• injective and surjective
• surjective but not injective
• injective but not surjective
• neither injective nor surjective

Question 97

The symmetric difference of sets A = {1, 2, 3, 4, 5, 6, 7, 8} and B = {1, 3, 5, 6, 7, 8, 9} is

• {1, 3, 5, 6, 7, 8}
• {2, 4, 9}
• {2, 4}
• {1, 2, 3, 4, 5, 6, 7, 8, 9}

Question 98

Let A be a finite set having x elements and let B be a finite set having y elements. What is the number of distinct functions mapping B into A.

• x^y
• 2^(x+y)
• y^x
• y! / (y-x)!

Question 99

The rank of a matrix A =

• 0
• 1
• 2
• 3

Question 100

How many different equivalence relations with exactly three different equivalence classes are there on a set with five elements?

• 10
• 15
• 25
• 30