If n((A \(\times\) B) ∩(A \(\times\) C)) = 8 and n(B ∩ C) = 2, then n(A) is

(a)

6

(b)

4

(c)

8

(d)

16

If n(A) = 2 and n(B ∪ C) = 3, then n[(A \(\times\) B) ∪ (A \(\times\) C)] is

(a)

2³

(b)

3²

(c)

6

(d)

5

If two sets A and B have 17 elements in common, then the number of elements common to the set A \(\times\)B and B \(\times\)A is

(a)

2¹⁷

(b)

17²

(c)

34

(d)

insufficient data

For non-empty sets A and B, if A ⊂ B then (A \(\times\)B) ⋂ (B \(\times\)A) is equal to

(a)

A ⋂ B

(b)

A \(\times\)A

(c)

B \(\times\)B

(d)

none of these.

The number of relations on a set containing 3 elements is

(a)

9

(b)

81

(c)

512

(d)

1024

Let R be the universal relation on a set X with more than one element. Then R is

(a)

not reflexive

(b)

not symmetric

(c)

transitive

(d)

none of the above

Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4),(4, 1)}. Then R is

(a)

reflexive

(b)

symmetric

(c)

transitive

(d)

equivalence

The range of the function \({1\over 1-2sinx}\) is

(a)

\((-∞,-1)\cup\left( {1\over 3},\infty\right)\)

(b)

\(\left( -1,{1\over 3}\right)\)

(c)

\(\left[ -1,{1\over 3}\right]\)

(d)

\((-∞,-1]\cup [\frac { 1 }{ 3 } ,∞)\)

The range of the function \(f(x) = \left| \left\lfloor x \right\rfloor - x \right| ,x \in R\)  is 

(a)

[0, 1]

(b)

[0, ∞)

(c)

[0, 1)

(d)

(0, 1)

The rule f(x) = x² is a bijection if the domain and the co-domain are given by

(a)

R, R

(b)

R, (0, ∞)

(c)

(0, ∞), R

(d)

[0, ∞), [0,∞)