If n(A x B) = 6 and A = {1,3} then n(B) is

(a)

1

(b)

2

(c)

3

(d)

6

A = {a,b,p}, B = {2,3}, C = {p,q,r,s} then n[(A U C) x B] is

(a)

8

(b)

20

(c)

12

(d)

16

If A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} then state which of the following statement is true..

(a)

(A x C) ⊂ (B x D)

(b)

(B x D) ⊂ (A x C)

(c)

(A x B) ⊂ (A x D)

(d)

(D x A) ⊂ (B x A)

If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

(a)

3

(b)

2

(c)

4

(d)

8

The range of the relation R = {(x, x²) |x is a prime number less than 13} is

(a)

{2,3,5,7}

(b)

{2,3,5,7,11}

(c)

{4,9,25,49,121}

(d)

{1,4,9,25,49,121}

If the ordered pairs (a + 2, 4) and (5, 2a + b) are equal then (a,b) is

(a)

(2,-2)

(b)

(5,1)

(c)

(2,3)

(d)

(3,-2)

Let n(A) = m and n(B) = n then the total number of non-empty relations that can be defined from A to B is

(a)

mⁿ

(b)

n^m

(c)

2^mn-1

(d)

2^mn

If {(a, 8 ),(6, b)}represents an identity function, then the value of a and b are respectively

(a)

(8,6)

(b)

(8,8)

(c)

(6,8)

(d)

(6,6)

Let A = {1, 2, 3, 4} and B = {4, 8, 9, 10}. A function f: A ⟶ B given by f = {(1, 4), (2, 8), (3, 9), (4,10)} is a

(a)

Many-one function

(b)

Identity function

(c)

One-to-one function

(d)

Into function

If f(x) = 2x² and g(x) = \(\frac{1}{3x}\), then f o g is

(a)

\(\\ \frac { 3 }{ 2x^{ 2 } } \)

(b)

\(\\ \frac { 2 }{ 3x^{ 2 } } \)

(c)

\(\\ \frac { 2 }{ 9x^{ 2 } } \)

(d)

\(\\ \frac { 1 }{ 6x^{ 2 } } \)

If f: A ⟶ B is a bijective function and if n(B) = 7, then n(A) is equal to

(a)

7

(b)

49

(c)

1

(d)

14

Let f and g be two functions given by
f = {(0,1), (2,0), (3,-4), (4,2), (5,7)}
g = {(0,2), (1,0), (2,4), (-4,2), (7,0)} then the  range of f o g is

(a)

{0,2,3,4,5}

(b)

{–4,1,0,2,7}

(c)

{1,2,3,4,5}

(d)

{0,1,2}

Let f(x) = \(\sqrt { 1+x^{ 2 } } \) then

(a)

f(xy) = f(x).f(y)

(b)

f(xy) ≥ f(x).f(y)

(c)

f(xy) ≤ f(x).f(y)

(d)

None of these

If g = {(1,1), (2,3), (3,5), (4,7)} is a function given by g(x) = αx + β then the values of α and β are

(a)

(-1,2)

(b)

(2,-1)

(c)

(-1,-2)

(d)

(1,2)

f(x) = (x + 1)³ - (x - 1)³ represents a function which is

(a)

linear

(b)

cubic

(c)

reciprocal

(d)

quadratic