If the set A has m elements, B has n elements then the number of elements in A x B is ______.

1

(a)

m + n

(b)

m + n + 1

(c)

mn

(d)

n²

Let R be a relation from a set A to B, then ______.

1

(a)

R=A\(\cup\)B

(b)

R =A\(\cap\)B

(c)

R\(\subset\)A x B

(d)

R \(\subset\) B x A

If R is a relation from a finite set A having m elements to a finite set B having n elemen.ts, then the number of relations from A to B is ______.

1

(a)

2^mn

(b)

2^mn-1

(c)

2mn

(d)

mⁿ

Which one of the following is not a function

1

(a)

{(x, y) (:) x, y \(\in\) R, x² = y}

(b)

{(x, y) (:) x, y \(\in\) R, y² = x}

(c)

{(x, y) (:) x, y \(\in\) R, x = y³}

(d)

{(x, y) (:) x, y \(\in\) R, y = x³}

Let f(x) = Ix-1I then ______.

1

(a)

f(x²) = [f(x)]²

(b)

f(x +y) = f(x) f(y)

(c)

f(IxI) = I f(x) I

(d)

none of these

If f(x) = log\({1+x\over 1-x}\) and g(x) = \({3x+x^3\over 1+3x^2}\) then f(g(x)) is equal to ______.

1

(a)

f(2x)

(b)

\([f(x)]^2\)

(c)

3f(x)

(d)

- f(3x)

If \(f(x)={2^x+2^{-x}\over 2}\) then f(x+y) f(x-y)is equal to ______.

1

(a)

\({1\over2}[f(2x)+f(2y)]\)

(b)

\({1\over2}[f(2x)-f(2y)]\)

(c)

\({1\over3}[f(2x)+f(2y)]\)

(d)

\({1\over3}[f(2x)-f(2y)]\)

If f(x) =\({x+1\over x-1}\) is a real function,\(\neq\) 1, then \(f[f\{f(2)\}]\) is ______.

1

(a)

-1

(b)

-3

(c)

3

(d)

4

If f: R\(\rightarrow\) R be given by f(x) =\({4^x\over 4^x+2}\) for all x \(\in\) R, then ______.

1

(a)

f(x) = f(1 + x)

(b)

f(x) + f(1 + x) = 0

(c)

f(x) + f(1 - x) = 1

(d)

none of these

The domain of the function \(f(x)=\sqrt{x-1}+\sqrt{3-x}\) is ______.

1

(a)

(1,\(\infty\))

(b)

(\(\infty\),5)

(c)

(1, 3)

(d)

[1, 3]