36
MCQ (Single Correct Answer)
If $A=\{1,2,3, \ldots, n\}$ and $B=\{a, b\}$. Then, the number of surjections from $A$ into $B$ is
A
${ }^n P_2$
B
$2^n-2$
C
$2^n-1$
D
None of these
37
MCQ (Single Correct Answer)
If $f: R \rightarrow R$ be defined by $f(x)=\frac{1}{x}, \forall x \in R$. Then, $f$ is
A
one-one
B
onto
C
bijective
D
$f$ is not defined
38
MCQ (Single Correct Answer)
If $f: R \rightarrow R$ be defined by $f(x)=3 x^2-5$ and $g: R \rightarrow R$ by $g(x)=\frac{x}{x^2+1}$. Then, $g \circ f$ is
A
$\frac{3 x^2-5}{9 x^4-30 x^2+26}$
B
$\frac{3 x^2-5}{9 x^4-6 x^2+26}$
C
$\frac{3 x^2}{x^4+2 x^2-4}$
D
$\frac{3 x^2}{9 x^4+30 x^2-2}$
39
MCQ (Single Correct Answer)
Which of the following functions from $Z$ into $Z$ are bijections?
A
$f(x)=x^3$
B
$f(x)=x+2$
C
$f(x)=2 x+1$
D
$f(x)=x^2+1$
40
MCQ (Single Correct Answer)
If $f: R \rightarrow R$ be the functions defined by $f(x)=x^3+5$, then $f^{-1}(x)$ is
A
$(x+5)^{\frac{1}{3}}$
B
$(x-5)^{\frac{1}{3}}$
C
$(5-x)^{\frac{1}{3}}$
D
$5-x$