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

(a)

1

(b)

2

(c)

3

(d)

6

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)

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}

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

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: 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(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

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

(a)

linear

(b)

cubic

(c)

reciprocal

(d)

quadratic

If f : R⟶R is defined by (x) = x² + 2, then the preimage 27 are _________

(a)

0.5

(b)

5, -5

(c)

5, 0

(d)

\(\sqrt { 5 } ,-\sqrt { 5 } \)

Let f(x) = x² - x, then f(x- 1) - (x + 1) is ___________

(a)

4x

(b)

2-2x

(c)

2-4x

(d)

4x-2

If function f : N⟶N, f(x) = 2x then the function is, then the function is ___________

(a)

Not one - one and not onto

(b)

one-one and onto

(c)

Not one -one but not onto

(d)

one - one but not onto

If f(x) = mx + n, when m and n are integers f(-2) = 7, and f(3) = 2 then m and n are equal to ___________

(a)

-1, -5

(b)

1, -9

(c)

-1, 5

(d)

1, 9

If f(x) = ax - 2, g(x) = 2x - 1 and fog = gof, the value of a is ___________

(a)

3

(b)

-3

(c)

\(\frac { 1 }{ 3 } \)

(d)

13

If f(x) = 2 - 3x, then f o f(1 - x) = ?

(a)

5x+9

(b)

9x-5

(c)

5-9x

(d)

5x-9

If f is identify function, then the value of f(1) - 2f(2) + f(3) is: 

(a)

-1

(b)

-3

(c)

1

(d)

0