If S = {x : x² + 1 = 0, r is real}, then S is

• { - 1}

• {0}

• {1}

• an empty set

If E is the universal set and A = B $\cup$ C, then the set E - (E - (E - (E - (E - A)))) is same as the set :

• $\mathrm{B}\text{'} \cup \mathrm{C}\text{'}$

• $\mathrm{B} \cup \mathrm{C}$

• $\mathrm{B}\text{'} \cap \mathrm{C}\text{'}$

• $\mathrm{B} \cap \mathrm{C}$

If A = {x : x is a multiple of 2}, B = {x : x is a multiple of 5} and C = {x : x is a multiple of 10}, then $\mathrm{A} \cap \left(\mathrm{B} \cap \mathrm{C}\right)$ is equal to :

• A

• B

• C

• {x : x is a multiple of 100}

Let S be a set of all distinct numbers of the form "q' where p. q $\in$ { 1, 2, 3, 4, 5, 6}. What is the cardinality of the set S ?

• 21

• 23

• 32

• 36

What is the domain of the function f (x) = $\frac{1}{\sqrt{\left|\mathrm{x}\right| - \mathrm{x}}} ?$

• $\left( - \infty , 0\right)$

• $\left(0, \infty \right)$

• $0 < \mathrm{x} < 1$

• $\mathrm{x} > 1$

Let S = {2, 4, 6, 8, ..........20}. What is the maximum number of subsets does S have ?

• 10

• 20

• 512

• 1024

If a set A contains 3 elements and another set B contains 6 elements, then what is the minimum number of elements that (A U B) can have ?

• 3

• 6

• 8

• 9

If A, B and C are subsets of a given set, then which one of the following relations is not correct ?

• A U (A ∩ B) = A U B

• A ∩ (A U B) = A

• (A ∩ B) U C = (A U C) ∩ (B U C)

• (A U B) ∩ C = (A ∩ C) U (B ∩ C)

Consider the following Venn diagram, where X, Y and Z are three sets. Let the number of elements in z be denoted by n(Z) which is equal to 90

If the number of elements belonging to neither X, nor Y, nor Z is equal to p, then what is the number of elements in the complement of X ?

• p + b + 60

• p + b + 40

• p + a + 60

• p + a + 40

Consider the following Venn diagram, where X, Y and Z are three sets. Let the number of elements in z be denoted by n(Z) which is equal to 90

What is the value of n(X) + n(Y) + n(Z) – n(X ∩ Y) – n(Y ∩ Z) – n(X ∩ Z) + n(X ∩ Y ∩ Z) ?

• a + b + 43

• a + b + 63

• a + b + 96

• a + b + 106