Allied Mathematics ICS: Internal MCQ

Find  $L^{-1}\left(\frac{s}{s^2+25}\right)$  

• cos 25t

• sin 5t

• cos 5t

 $L^{-1}\left(\frac{6}{\left(s\right)}-\frac{4s}{s^2+25}\right)$  What is the property use to find the Inverse Laplace Transform of this equation?

• Second Shifting Property

• First Shifting Property

• Linearity Property

• Convolution theorem

 $L^{-1}\left(\frac{24}{s^5}\right)$ is  $t^4$  . What is  $L^{-1}\left(\frac{1}{s^{\left(5\right)}}\right)$  ?

•  $\frac{24}{s^5}$  

•  $\frac{1}{24}t^4$  

•  $\frac{1}{24}t^5$  

 $L^{-1}\left(\frac{1}{\left(s-3\right)^2}\right)$  

•  $e^{2t}t$  

•  $e^tt^2$  

•  $e^{3t}t$  

Find the partial fraction for  $\frac{\left(2s-8\right)}{\left(s-2\right)\left(s-3\right)}$  

•  $\frac{2}{s-2}-\frac{4}{s-3}$  

•  $\frac{3}{s-2}-\frac{2}{s-3}$  

•  $\frac{4}{s-2}-\frac{2}{s-3}$  

Tags

CCSS.HSA.APR.D.6

Define this property:  $L\left(f\left(t\right)e^{at}\right)=F\left(s-a\right)$  

• Linearity Property

• First Shifting Property

• Convolution Theorem

• Second Shifting Property

Find  $L\left(e^{3t}\left(t^3-3t^2+5t\right)\right)$  

•  $\frac{2}{\left(s-3\right)^4}-\left(\frac{3}{\left(\left(s-3\right)^3\right)}\right)+\frac{5}{\left(s-3\right)^2}$  

•  $\frac{6}{\left(s-3\right)^4}-\left(\frac{6}{\left(s-3\right)^3}\right)+\frac{5}{\left(s-3\right)^2}$  

•  $\frac{2}{\left(s-3\right)^3}-\left(\frac{3}{\left(s-3\right)^{\left(2\right)}}\right)+\frac{5}{s-3}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $L\left(t\ \cos\ 6t\right)$  Which Laplace property is use to solve this?

• Linearity Property

• Derivative of Laplace Transform

• First Shifting Property

• Second Shifting Property

Given  $g\left(t\right)=e^{5t}f\left(t\right)$  , what is G(s)?

•  $G\left(s\right)=F\left(s-5\right)$  

•  $G\left(s\right)=\left(-1\right)^5\frac{\text{d}^5F\left(s\right)}{\text{d}s^5}$  

•  $G\left(s\right)=F\left(s+5\right)$  

•  $G\left(s\right)=\left(-1\right)^4\frac{\text{d}^4F\left(s\right)}{\text{d}s^4}$  

Which one is the correct definition of Laplace Transform?

• $F\left(s\right)=\int_0^{\infty}e^{-st}f\left(t\right)dt$

• $F\left(s\right)=\int_0^tf\left(t\right)g\left(t-u\right)$