The inverse lapluce transform of the fumation $Y(s)=\frac{s+3}{(s+4{)}^2}$ will be$.$

$($a$)$ texp$(-4t)$

$($b$)$ tex$(-4t)-$exp$(-4t)$

$($c$)$ exp$(-4t)$

$($d$)$ exp$(-4t)-$texp$(-4t)$

What is the laslure transform of $t$ raised to fower $n($where $n$ is a Positive integar$)?$

$($a$)\frac{n!}{s^{n+1}}$

$($b$)\frac{n}{s^n}$

$($c$)*\frac{s^{n+1}}{n}!$

$($d$)\frac{s^n}{n}!$

$(4).U(t)$ B a unit step function and initial condition of yarable $y$ is $y(0)=0.$ The lapluce transform of the following ODE model will be given as : $2d\frac{y}{d}t+4y-6=4(t).$

$(4)\frac{7}{s(2s-4)}$

$($b$)\frac{7}{s}(2s+4)$

$($a$)7s(2s+4)$

$($d$)\frac{14}{s(s+4)}$

$(6)$ Chat is the laplace transform of the derivative of a functian $F(t),$ given $F(0)=0?$

$($a$)B(s)-F(0)$

$($b$)fF(s)+F(0)$

$($c$)F(s)$

$($d$)sF(s)$