Sets

1

If S is the set of distinct values of 'b' for which the following system of linear equations
x + y + z = 1
x + ay + z = 1
ax + by + z = 0
has no solution, then S is:

  1. an empty set
  2. an infinite set
  3. a finite set containing two or more elements
  4. a singleton
2

If X = {4n - 3n -1 : n ∈ N} and Y = {9(n - 1) : n ∈ N}, where N is the set of natural numbers, then X ∪ Y is equal to

  1. Y
  2. Y - X
  3. X
  4. N
3

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is

  1. 510
  2. 256
  3. 275
  4. 219
4

If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C, then

  1. B = C
  2. A = C
  3. A ∩ B = φ
  4. A = B