The function f:[0,2π]➝[-1,1] defined by f(x) = sin x is

(a)

one-to-one

(b)

on to

(c)

bijection

(d)

cannot be defined

The shaded region in the adjoining diagram represents.

(a)

A\B

(b)

B\A

(c)

AΔB

(d)

A'

If f(x) = |x - 2| + |x + 2|, x ∈ R, then

(a)

\(f(x)=\left\{\begin{array}{lll} -2 x & \text { if } & x \in(-\infty,-2] \\ 4 & \text { if } & x \in(-2,2] \\ 2 x & \text { if } & x \in(2, \infty) \end{array}\right.\)

(b)

\(f(x)=\begin{cases}2x\ if\ x∈(-∞,-2] \\4x\ if \ x∈(-2,2]\\ - 2x\ if\ x∈(2,∞)\end{cases}\)

(c)

\(f(x)=\begin{cases}-2x\ if\ x∈(-∞,-2] \\-4x\ if \ x∈(-2,2]\\ 2x\ if\ x∈(2,∞)\end{cases}\)

(d)

\(f(x)=\begin{cases}-2x\ if\ x∈(-∞,-2] \\2x\ if \ x∈(-2,2]\\ 2x\ if\ x∈(2,∞)\end{cases}\)

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 f : Z➝Z be given by f(x) = \(\begin{cases} \frac { x }{ 2 } \quad if\quad x\quad is\quad even \\ 0\quad if\quad x\quad is\quad odd \end{cases}\). Then f is __________

(a)

one-one but not onto

(b)

onto but not one-one

(c)

one-one and onto

(d)

neither one-one nor onto

Domain of the function \(y={x-1\over x+1}\) is __________

(a)

1R

(b)

Q

(c)

R-(-1)

(d)

R-1

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

The function f(x) = log (x + \(\sqrt{x^2+1}\)) is ___________

(a)

an even function

(b)

an odd function

(c)

a periodic function

(d)

neither an even nor an odd function

If \(f(x)={1-x\over 1+x},(x\neq0)\) then f^-1(x) =

(a)

f(x)

(b)

\(1\over f(x)\)

(c)

-f(x)

(d)

-\(1\over f(x)\)

If n(A) = 1024 then n[P(A)] =

(a)

2¹⁰

(b)

\(2^{2^{10}}\)

(c)

cannot be determined

(d)

4¹⁰