Free Printable DE & LT CAT I -MCQ

1.

What is the Laplace Transform for $f\left(t\right)=t^3$ ?

a)

$\frac{1}{s^3}$

b)

$\frac{2}{s^3}$

c)

$\frac{6}{s^4}$

d)

$\frac{3}{s^3}$

2.

Laplace\ transform\ of\ e^{3t}-\frac{1}{2}

a)

$\frac{1}{s+3}-\frac{1}{2s}$

b)

$\frac{1}{s-3}-\frac{2}{s}$

c)

$\frac{1}{s-3}-\frac{1}{2s}$

d)

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

3.

f\left(t\right)=te^{-2t}

a)

b)

c)

d)

4.

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

a)

Linearity Property

b)

Derivative of Laplace Transform

c)

First Shifting Property

d)

Second Shifting Property

5.

Inverse Laplace transform, transform

a)

$f\left(t\right)\ to\ F\left(s\right)$

b)

$F\left(s\right)\ to\ f\left(t\right)$

c)

$f'\left(t\ \right)\ to\ f\left(t\right)$

d)

$f\left(t\right)\ to\ f'\left(t\right)$

6.

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

a)

Second Shifting Property

b)

First Shifting Property

c)

Linearity Property

d)

Convolution theorem

7.

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

a)

$e^{2t}t$

b)

$e^tt^2$

c)

$e^{3t}t$

8.

$L^{-1}\left(\frac{s+2}{s^2-2s-5}\right)$

a)

$f(t)=e^t\left(\cosh\sqrt{6}\ t+\frac{3}{\sqrt{6}}\sinh\sqrt{6\ }t\right)$

b)

$f(t)=e^{-t}\left(\cosh\sqrt{6}\ t+\frac{3}{\sqrt{6}}\sinh\sqrt{6\ }t\right)$

c)

$f(t)=e^t\left(\cosh2\ t+\frac{3}{2}\sinh2t\right)$

9.

$\left(D^2+1\right)x=\sin2t,\ then\$ with initial conditions as zero then,

a)

$L\left(y\left(t\right)\right)=\frac{2}{\left(s^2+1\right)\left(s^2+4\right)}$

b)

$L\left(x\left(t\right)\right)=\frac{2}{\left(s^2+1\right)\left(s^2+4\right)}$

10.

GIVEN

\left(D^2-5D+6\right)y=0,\ \ y\left(0\right)=1,\ \ y'\left(0\right)=-1

a)

$L\left(y\right)=\frac{s+4}{s^2-5s+6}$

b)

$L\left(y\right)=\frac{s-6}{s^2-5s+6}$

c)

$L\left(y\right)=\frac{s+5}{s^2-5s+6}$

d)

$L\left(y\right)=\frac{s-5}{s^2-5s+6}$

DE & LT CAT I -MCQ

Total questions: 10

Worksheet time: 30mins

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