Onto Function

Q. If $A=\{1,2,3,4\}$ and $B=\{5,7,9\}$, then the number of onto function from $A$ to $B$ is

1. $36$
2. $45$
3. $81$
4. $64$

Q. Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of onto functions from A into B is

1. $nP2$
2. $2^n-1$
3. $2^n-2$
4. $\left(n-1\right)!$

Q. Let E = {1, 2, 3, 4} and F = {1, 2}. Then, the number of onto functions from E to F is

1. 14
2. 16
3. 12
4. 8

Q. The function : $R\to [-\frac{1}{2},\frac{1}{2}]$ defined as $f\left(x\right)=\frac{x}{1+x^2}$ is

1. invertible
2. injective but not surjective
3. surjective but not injective
4. neither injective nor surjective

Q. Let $f:R\to R$ be a differentiable function with $f\left(0\right)=0.$ If $y=f\left(x\right)$ satisfies the differential equation
$\frac{dy}{dx}=(2+5y)(5y-2)$
then the value of $\underset{x\to -\infty }{lim}f\left(x\right)$ is

Q. Let a function f defined from $R\to R$ as $f\left(x\right)=\{\begin{array}{cc}x+p^2,& x\le 2\\ 2px+5,& x>2\end{array}$.
If the function is surjective, then sum of all possible integral value of p in [-100, 100] is

Q. Let a function f defined from $R\to R$ as $f\left(x\right)=\{\begin{array}{cc}2m-x,& x\le 1\\ 4mx+1,& x>1\end{array}$
If function is onto on R, then range of m is

1. $[-1,\infty )$
2. $[-1,0)$
3. {-1}
4. $(0,\infty )$