1
###
If S is the set of distinct values of 'b' for which

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:

- an empty set
- an infinite set
- a finite set containing two or more elements
- a singleton

2
###
If X = {4^n - 3n -1 : n ∈ N} and Y = {9(n - 1) : n ∈ N}

If X = {4^{n} - 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

- Y
- Y - X
- X
- N

3
###
Let A and B be two sets containing four and two elements respectively

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

- 510
- 256
- 275
- 219

4
###
If A, B and C are three sets such that

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

- B = C
- A = C
- A ∩ B = φ
- A = B