The number of constant functions from a set containing m elements to a set containing n elements is

(a)

mn

(b)

m

(c)

n

(d)

m+n

If the function f:[-3,3]➝S defined by f(x) = x² is onto, then S is

(a)

[-9,9]

(b)

R

(c)

[-3,3]

(d)

[0,9]

The function f:R➝R be defined by f(x) = sinx + cosx is

(a)

an odd function

(b)

neither an odd function nor an even function

(c)

an even function

(d)

both odd function and even function

If A⊆B, then A\B is  ________

(a)

B

(b)

A

(c)

Ø

(d)

\(\frac{B}{A}\)

Let R be a relation on the set N given by R = {(a,b) : a = b - 2, b > 6}. Then ____________

(a)

(2,4)∈R

(b)

(3,8)∈R

(c)

(6,8)∈R

(d)

(8,7)∈R

Let R be the relation over the set of all straight lines in a plane such that l₁Rl₂ ⇔ l₁丄l₂ . Then  R is __________

(a)

symmetric

(b)

reflexive

(c)

transitive

(d)

an equivalent relation

Which of the following is not an equivalence relation on z?

(a)

aRb ⇔ a+b is an even integer

(b)

aRb ⇔ a-b is an even integer

(c)

aRb ⇔ a

(d)

aRb ⇔ a=b

If A = {(x,y) : y = e^x, x∈R} and B = {(x,y) : y = e^-x, x ∈ R} then n(A∩B) is

(a)

Infinity

(b)

0

(c)

1

(d)

2

The relation R defined on a set A= {0,-1, 1, 2} by xRy if |x²+y²| ≤ 2, then which one of the following is true?

(a)

R = {(0,0), (0,-1), (0, 1), (-1, 0), (-1, 1), (1, 2), (1, 0)}

(b)

R^-1 = {(0,0), (0,-1), (0, 1), (-1, 0), (1, 0)}

(c)

Domain of R is {0,-1, 1, 2}

(d)

Range of R is {0,-1, 1}

Let A and B be subsets of the universal set N, the set of natural numbers. Then A^'∪[(A⋂B)∪B^'] is

(a)

A

(b)

A'

(c)

B

(d)

N

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 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

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

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 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,∞)

Let X = {a, b,c},y = (1, 2, 3) then \(f:x\rightarrow y\) given by (a, 1) (b, 1) (c, 1) is called ___________

(a)

onto

(b)

constant function

(c)

one one

(d)

bijective

If \(f:[-2,2]\rightarrow A\) is given by f(x) = 3³ then f is onto, if A is ___________

(a)

[3, 3]

(b)

(3, 3)

(c)

[-24,24]

(d)

(-24, 24)

Which one of the following statements is false? The graph of the function \(f(x)={1\over x}\)

(a)

exist is the first and third quadrant only

(b)

is a reciprocal function

(c)

is defined at x = 0

(d)

it is symmetric about y = x and y = - x.

The domain of the function \(f(x)=\sqrt{ x - 5 }+ \sqrt{6 - x}\) is 

(a)

[5, ∞)

(b)

(- ∞, 6)

(c)

[5, 6]

(d)

(-5, ≠6)

If f(x) = 1 - x, x ∈ [- 3, 3] then the domain off is ___________

(a)

[- 2,3]

(b)

(- 2,3)

(c)

(- 3, -2)

(d)

[-2, 3)

If A = {1, 2}, B = {1, 3} then n(A x B) = ___________

(a)

2

(b)

4

(c)

8

(d)

0

Which one of the following is false?

(a)

A⋂(BΔ\C) = (A ⋂ B)Δ(A ∩ C)

(b)

A∩(B - C) = (A ∩B) \ (A∩C)

(c)

(A U B), = A' ∩ B'

(d)

(A \ B) U B = A ⋂ B

Which one of the following is not a singleton set?

(a)

A = {x : 3x - 5 = 0, x ∈ Q}

(b)

B = {| x | = 1 / x ∈ Z}

(c)

{x : x³ - 1 = 0, x ∈ R}

(d)

{x : 30x = 60, x ∈ N}

For any four sets A, B, C and D, which of the following is not true?

(a)

A x C ⊂  B x D

(b)

(A x B) ∩ (C x D) = (A ∩ C) x (B ∩ D)

(c)

A x (B U,C) = (A x B) U (A x C)

(d)

A x (B ∩ C) = (A x B) ∩ (A x C)

If A and B are any two finite sets having m and n elements respectively then the cardinality of the power set of A \(\times\) B is ___________

(a)

2^m

(b)

2ⁿ

(c)

mn

(d)

2^mn