M3 MCQ ON LAPLACE TRANSFORM

 

 

Laplace transform

 

1. If f(t) = 1, then its Laplace Transform is given by?
a)s
b) ¹⁄_s
c)1
d)Does not exist

2. If f(t) = tⁿ where, ‘n’ is an integer greater than zero, then its Laplace Transform is given by?
a) n!
b) tⁿ⁺¹
c) n! ⁄ sⁿ⁺¹
d) Does not exist

3. If f(t)=√t, then its Laplace Transform is given by?
a) ¹⁄₂
b) ¹⁄_s
c) √π ⁄ 2√s
d) Does not exist

4. If f(t) = sin(at), then its Laplace Transform is given by?
a) cos(at)
b) 1 ⁄ a^sin(at)
c) Indeterminate
d) a ⁄ s²+a²

5. If f(t) = tsin(at) then its Laplace Transform is given by?
a) 2as ⁄ (s²+a²)²
b) a ⁄ s²+a²
c) Indeterminate
d) √π ⁄ 2√s

6. If f(t) = e^at, its Laplace Transform is given by?
a) a ⁄ s²+a²
b) √π ⁄ 2√s
c) 1 ⁄ s-a
d) Does not exist

7. If f(t) = t^p where p > – 1, its Laplace Transform is given by?
a) √π ⁄ 2√s
b) f(t) = tsin(at)
c) γ(p+1) ⁄ s^p+1
d) Does not exist

8. If f(t) = cos(at), its Laplace transform is given by?
a) s ⁄ s²+a²
b) a ⁄ s²+a²
c) √π ⁄ 2√s
d) Does not exist

9. If f(t) = tcos(at), its Laplace transform is given by?
a) 1 ⁄ s-a
b) s² – a² ⁄ (s²+a²)²
c) Indeterminate
d) s²at

10. If f(t) = sin(at) – atcos(at), then its Laplace transform is given by?
a) Indeterminate form is encountered
b) a³ ⁄ (s² + a²)²
c) 2a³ ⁄ (s² – a²)²
d) 2a³ ⁄ (s² + a²)²

11. If f(t) = sin(at) – atcos(at), then its Laplace transform is given by?
a) s(s2−a2)(s2+a2)2
b) s(s2−3a2)(s2+a2)2
c) Indeterminate
d) 2as2 / (s2+a2)2

 

12. If f(t) = cos(at) – atsin(at), then its Laplace transform is given by?
a) sinat²
b) s(s2−a2)/(s2+a2)2
c) Γ(p+1)sp+1
d) Does not exist

13. If f(t) = cos(at) + atsin(at), its Laplace transform is given by?
a) s+as−a
b) a3(s2+a2)2
c) s(s2+3a2) / (s2+a2)2
d) Does not exist

14. If f(t) = sin(at + b), its Laplace transform is given by?
a) Indeterminate
b) (s)sin(b)+acos(b) / s2+a2
c) s2−a2(s−a)2
d) 2a3(s2+a2)

15. If f(t) = cos(at + b), its Laplace transform is given by?
a) as2+a2
b) 2as(s2+a2)2
c) scos(b)−asin(b) / s2+a2
d) Does not exist

.

 

1. If f(t) = sinhat, then its Laplace transform is?
a) e^at
b) s ⁄ s²-a²
c) a ⁄ s²-a²
d) Exists only if ‘t’ is complex

2. If f(t) = coshat, its Laplace transform is given by?
a) s ⁄ s²-a²
b) s+a ⁄ s-a
c) Indeterminate
d) (sinh(at))²

3. If f(t) = e^at sin(bt), then its Laplace transform is given by?
a) s²-a² ⁄ (s – a)²
b) b ⁄ (s + a)² + b²
c) b ⁄ (s – a)² + b²
d) Indeterminate

4. If f(t) = e^at cos(bt), then its Laplace transform is?
a) 2a³ ⁄ (s² + a²)
b) s+a ⁄ s-a
c) Indeterminate
d) s-a ⁄ (s – a)² + b²

5. If f(t) = e^at sinh(bt) then its Laplace transform is?
a) e^-as ⁄ s
b) s+a ⁄ (s – a)² + b²
c) b ⁄ (s – a)² – b²
d) Does not exist

6. If f(t) = ¹⁄_a sinh(at), then its Laplace transform is?
a) 1⁄s²-a²
b) 2a ⁄ (s – b)² + b²
c) n! ⁄ (s – a)^n-1
d) Does not exist

7. If f(t) = tⁿ ⁄ n, then its Laplace transform is?
a) s+a(s−a)(s−a)2+b2
b) b2(s−a)(s−a)2+b2
c) 2a3(s2+a2)
d) (n−1)! / sn+1

8. If f(t) = ¹ ⁄ _√Πt, then its Laplace transform is?
a) s2−a2 /(s−a)2
b) S^-1/2
c) n! /(s−a)^n−1
d) n! /(s−a)^n−1

.

9. If f(t) = ^t⁄₂ a sinat, then its Laplace transform is?
a) b ⁄ (s + a)² + b²
b) 2a ⁄ (s – b)² + b²

c) Indeterminate
d) s ⁄ (s² + a²)²

10. If f(t) = δ(t), then its Laplace transform is?
a) s + a ⁄ (s – a)² + b²
b) a³ ⁄ (s² + a²)²
c) 1
d) Does not exist

11. If f(t) = te^-at, then its Laplace transform is?
a) 1 /(s+a)2
b) 2a /(s−b)2+b2
c) a3 / s2+a2)2
d) Indeterminate

12. If f(t) = u(t), then its Laplace transform is?
a) scos(b)−asin(b)s2+a2
b) 1/2
c) s/s2−a2
d) b /(s−a)2+b2

13. f(t) = t, then its Laplace transform is?
a) (s)sin(b)+acos(b)s2+a2
b) 2as2(s2+a2)2
c) Γ(p+1) / sp+1
d) 1/s²

14. If f(t)=1beatsinh(bt), then its Laplace transform is?
a) 1/s

b) Indeterminate
c) b(s−a)2−b2
d) f(t)=1 / (s−a)2−b2

15. If L { f(t) } = F(s), then L {kf(t)} = ?
a) F(s)
b) k F(s)
c) Does not exist
d) F(^s⁄_k)

 

1. Laplace of function f(t) is given by?
a) F(s)=∫∞−∞f(t)e−stdt
b) F(t)=∫∞−∞f(t)e−tdt
c) f(s)=∫∞−∞f(t)e−stdt
d) f(t)=∫∞−∞f(t)e−tdt

2. Laplace transform any function changes it domain to s-domain.
a) True
b) False

3. Laplace transform if sin⁡(at)u(t) is?
a) s ⁄ a²+s²
b) a ⁄ a²+s²
c) s² ⁄ a²+s²
d) a² ⁄ a²+s²

4. Laplace transform if cos⁡(at)u(t) is?
a) s ⁄ a²+s²
b) a ⁄ a²+s²
c) s² ⁄ a²+s²
d) a² ⁄ a²+s²

5. Find the laplace transform of e^t Sin(t).
a) a / a2+(s+1)2
b) a / a2+(s−1)2
c) s+1 / a2+(s+1)2
d) s+1 / a2+(s+1)2

6. Laplace transform of t² sin⁡(2t).
a) [12s2−16 / (s2+4)4]
b) [3s2−4 / (s2+4)3]
c) [12s2−16 / (s2+4)6]
d) [12s2−16 / (s2+4)3]

7. Find the laplace transform of t⁵⁄₂.
a) 158√πs5/2
b) 15/8   /  √πs7/2
c) 94√πs7/2
d) 154√πs7/2

8. Value of ∫∞−∞etSin(t)Cos(t)dt = ?
a) 0.5
b) 0.75
c) 0.2
d) 0.71

 

 

 

9. Value of ∫∞−∞etSin(t)dt = ?
a) 0.50
b) 0.25
c) 0.17
d) 0.12

 

 

10. Value of ∫∞−∞etlog(1+t)dt = ?
a) Sum of infinite integers
b) Sum of infinite factorials
c) Sum of squares of Integers
d) Sum of square of factorials

.

11. Find the laplace transform of y(t)=e^t.t.Sin(t)Cos(t).
a) 4(s−1)  / [(s−1)2+4]2
b) 2(s+1)  /  [(s+1)2+4]2
c) 4(s+1) / [(s+1)2+4]2
d) 2(s−1) /  [(s−1)2+4]2

12. Find the value of ∫∞0tsin(t)cos(t).
a) s ⁄ s²+2²
b) a ⁄ a²+s⁴
c) 1
d) 0

13. Find the laplace transform of y(t)=e^|t-1| u(t).
a) 2s / 1−s2es
b) 2s / 1+s2e−s
c) 2s / 1+s2es
d) 2s / 1−s2e−s

 

 

1. Transfer function may be defined as ____________
a) Ratio of out to input
b) Ratio of laplace transform of output to input
c) Ratio of laplace transform of output to input with zero initial conditions
d) None of the mentioned

2. Poles of any transfer function is define as the roots of equation of denominator of transfer function.
a) True
b) False

3. Zeros of any transfer function is define as the roots of equation of numerator of transfer function.
a) True
b) False

4. Find the poles of transfer function which is defined by input x(t)=5Sin(t)-u(t) and output y(t)=Cos(t)-u(t).
a) 4.79, 0.208
b) 5.73, 0.31
c) 5.89, 0.208
d) 5.49, 0.308

5. Find the equation of transfer function which is defined by y(t)-∫₀^t y(t)dt + ^d⁄_dt x(t) – 5Sin(t) = 0.
a) s(e−as−1) / s−1
b) (e−as−s) / s−1
c) s(e−as−s) / s−1
d) s(e−as−s2) / s−1

6. Find the poles of transfer function given by system ^d2⁄_dt² y(t) – ^d⁄_dt y(t) + y(t) – ∫₀^t x(t)dt = x(t).
a) 0, 0.7 ± 0.466
b) 0, 2.5 ± 0.866
c) 0, 0 .5 ± 0.866
d) 0, 1.5 ± 0.876

7. Find the transfer function of a system given by equation ^d2⁄_dt² y(t-a) + x(t) + 5 ^d⁄_dt y(t) = x(t-a).
a) (e^-as-s)/(1+e^-as s²)
b) (e^-as-5s)/(e^-as s²)
c) (e^-as-s)/(2+e^-as s²)
d) (e^-as-5s)/(1+e^-as s²)

8. Any system is said to be stable if and only if ____________
a) It poles lies at the left of imaginary axis
b) It zeros lies at the left of imaginary axis
c) It poles lies at the right of imaginary axis
d) It zeros lies at the right of imaginary axis

 

9. The system given by equation 5 ^d3⁄_dt³ y(t) + 10 ^d⁄_dt y(t) – 5y(t) = x(t) + ∫₀^t x(t)dt, is?
a) Stable
b) Unstable
c) Has poles 0, 0.455, -0.236±1.567
d) Has zeros 0, 0.455, -0.226±1.467

10. Find the laplace transform of input x(t) if the system given by ^d3⁄_dt³ y(t) – 2 ^d2⁄_dt² y(t) –^d⁄_dt y(t) + 2y(t) = x(t), is stable.
a) s + 1
b) s – 1
c) s + 2
d) s – 2

11. The system given by equation y(t – 2a) – 3y(t – a) + 2y(t) = x(t – a) is?
a) Stable
b) Unstable
c) Marginally stable
d) 0

 

 

1. Time domain function of sa2+s2 is given by?
a) Cos(at)
b) Sin(at)
c) Cos(at)Sin(at)
d) Sin(t)

2. Inverse Laplace transform of 1(s+1)(s−1)(s+2) is?
a) –¹⁄₂ e^t + ¹⁄₆ e^-t + ¹⁄₃ e^2t
b) –¹⁄₂ e^-t + ¹⁄₆ e^t + ¹⁄₃ e^-2t
c) ¹⁄₂ e^-t – ¹⁄₆ e^t – ¹⁄₃ e^-2
d) –¹⁄₂ e^-t + ¹⁄₆ e^-t + ¹⁄₃ e^-2

3. Inverse laplace transform of 1(s−1)2(s+5) is?
a) ¹⁄₆ e ^{– t} – ¹⁄₃₆ e^t + ¹⁄₃₆ e^-5t
b) ¹⁄₆ e^tt – ¹⁄₃₆ e^t + ¹⁄₃₆ e^-5t
c) ¹⁄₆ e^-tt² – ¹⁄₃₆ e^-t + ¹⁄₃₆ e^5t
d) ¹⁄₆ e^-t t-¹⁄₃₆ e^-t + ¹⁄₃₆ e^5t

4. Find the inverse laplace transform of 1(s2+1)(s–1)(s+5).
a) ¹⁄₁₂ e^t – ¹⁄₁₃ Cos(-t) – ¹⁄₁₂ Sin(-t) – ¹⁄₁₅₆ e^-5t
b) ¹⁄₁₂ e^-t – ¹⁄₁₃ Cos(t) – ¹⁄₁₂ Sin(t) – ¹⁄₁₅₆ e^5t
c) ¹⁄₁₂ e^t – ¹⁄₁₃ Cos(t) – ¹⁄₁₂ Sin(t) – ¹⁄₁₅₆ e^-5t
d) ¹⁄₁₂ e^t + ¹⁄₁₃ Cos(t) + ¹⁄₁₂ Sin(t) + ¹⁄₁₅₆ e^-5t

5. Find the inverse laplace transform of s(s2+4)2.
a) ¹⁄₄ sin(2t)
b) ^t2⁄₄ sin(2t)
c) ^t⁄₄ sin(2t)
d) ^t⁄₄ sin(2t²)

6. Final value theorem states that _________
a) x(0)=limx→∞sX(s)
b) x(∞)=limx→∞sX(s)
c) x(0)=limx→0sX(s)
d) x(∞)=limx→0sX(s)

7. Initial value theorem states that ___________
a) x(0)=limx→∞sX(s)
b) x(∞)=limx→∞sX(s)
c) x(0)=limx→0sX(s)
d) x(∞)=limx→0sX(s)

8. Find the value of x(∞) if X(s)=2s2+5s+12/ss3+4s2+14s+20.
a) 5
b) 4
c) ¹²⁄₂₀
d) 2

9. Find the value of x(0) if X(s)=2s2+5s+12/ss3+4s2+14s+20.
a) 5
b) 4
c) 12
d) 2

10. Find the inverse lapace of (s+1)[(s+1)2+4][(s+1)2+1].
a) ¹⁄₃ e^t [Cos(t) – Cos(2t)].
b) ¹⁄₃ e^-t [Cos(t) + Cos(2t)].
c) ¹⁄₃ e^t [Cos(t) + Cos(2t)].
d) ¹⁄₃ e^-t [Cos(t) – Cos(2t)].

11. Find the inverse laplace transform of Y(s)=\frac{2s}{1-s^2}e^{-s}.
a) -e^{-t + 1} + e^{t – 1}
b) -e^{-t + 1} – e^{t + 1}
c) -e^{-t + 1} + e^{t + 1}
d) -e^{-t + 1} – e^{t – 1}

12. Find the inverse laplace transform of \frac{1}{s(s-1)(s^2+1)}.
a) ¹⁄₂ e^-t + ¹⁄₂ Sin(-t) – ¹⁄₂ Cos(-t)
b) ¹⁄₂ e^t + ¹⁄₂ Sin(t) – ¹⁄₂ Cos(t)
c) ¹⁄₂ e^t + ¹⁄₂ Sin(t) + ¹⁄₂ Cos(t)
d) ¹⁄₂ e^t – ¹⁄₂ Sin(t) – ¹⁄₂ Cos(t)

 

 

 

 

 

1. Find the laplace transform of f(t), where
f(t) = 1 for 0 < t < a
-1 for a < t < 2a
a) 1scoth(as2)
b) 1ssinh(as2)
c) 1se−as
d) 1/stanh(as / 2)

2. Find the laplace transform of f(t), where f(t) = |sin(pt)| and t>0.
a) ps2+p2×cosh(sπ2p)
b) ps2+p2×sinh(sπ2p)
c) p /s2+p2×coth(sπ / 2p)
d) ps2+p2×tanh(sπ2p)

 

                             Inverse laplace transform

1. Find the L−1(s+34s2+9).
a) 14cos(3t2)+12cos(3t2)
b) 14cos(3t4)+12sin(3t2)
c) 12cos(3t2)+12sin(3t2)
d) 14cos(3t / 2)+12sin(3t /2)

2. Find the L−1(1(s+2)4).
a) e−2t×3
b) e−2t×t3 /3
c) e−2t×t^3/6
d) e−2t×t2 / 6

3. Find the L−1(s(s−1)7).
a) e−t(t65!+t56!)
b) et(t65!+t56!)
c) et(t66!+t55!)
d) e−t(t66!+t55!)

4. Find the L−1(s2s+9+s2).
a) e^−t{cos(2√2t)−sin(2t−−√2t)}
b) e^−t{cos(2√2t)−sin(22t−−√2t)}
c) e^−t{cos(2√2t)−cos(2t−−√2t)}
d) e^−2t{cos(2√2t)−sin(22t−−√2t)}

 

 

5. Find the L−1((s+1)(s+2)(s+3)).
a) 2e^-3t-e^-2t
b) 3e^-3t-e^-2t
c) 2e^-3t-3e^-2t
d) 2e^-2t-e^-t

6. Find the L−1((3s+9)(s+1)(s−1)(s−2)).
a) e^-t+6e^t+5e^2t
b) e^-t-e^t+5e^2t
c) e^-3t-6e^t+5e^2t
d) e^-t-6e^t+5e^2t

7. Find the L−1(1(s2+4)(s2+9)).
a) 15(sin(2t)2−sin(t)3)
b) 15(sin(2t)2+sin(3t)3)
c) 15(sin(t)2−sin(3t)3)
d) 1/5(sin(2t)/2−sin(3t)/3)

8. Find the L−1(s(s2+1)(s2+2)(s2+3)).
a) 12cos(t)−cos(√3t)−12cos(√3t)
b) 12cos(t)+cos(√2t)−12cos(√3t)
c) 1/2cos(t)−cos(√2t))−1/2cos(√3t)
d) 12cos(t)+cos(√2t)+12cos(√3t)

9. Find the L−1(s+1(s−1)(s+2)2).
a) 27et−29e−2t+13e−2t×t
b) 2/9et−2/9e−2t+1/3e^−2t×t
c) 29et−29e−3t+13e−2t×t
d) 29et−29e−2t+13e−2t

10. The L−1(3s+8s2+4s+25) is e−st(3cos(21−−√t+2sin(21√t)21√). What is the value of s?

a) 0
b) 1
c) 2
d) 3

 

Convolution Theorem

1. Find the L−1(1s(s2+4)).
a) 1−sin(t)4
b) 1−cos(t)4
c) 1−sin(2t)4
d) 1−cos(2t) / 4

2. Find the L−1(1s(s+4)12), give the answer in terms of error function.
a) 1/2erf(2t)
b) 1/2erf(√t)
c) 1/2erf(2√t)
d) 1/2erf(4√t)

3. Find the L−1s(s2+4)2.
a) 1/4tcos(2t)
b) 1/4tsin(t)
c) 1/4tsin(2t)
d) 1/2tsin(2t)

 

1. While solving the ordinary differential equation using unilateral laplace transform, we consider the initial conditions of the system.
a) True
b) False

2. With the help of _____________________ Mr.Melin gave inverse laplace transformation formula.
a) Theory of calculus
b) Theory of probability
c) Theory of statistics
d) Theory of residues

3. What is the laplce tranform of the first derivative of a function y(t) with respect to t : y’(t)?
a) sy(0) – Y(s)
b) sY(s) – y(0)
c) s² Y(s)-sy(0)-y'(0)
d) s² Y(s)-sy'(0)-y(0)

4. Solve the Ordinary Differential Equation by Laplace Transformation y’’ – 2y’ – 8y = 0 if y(0) = 3 and y’(0) = 6.
a) 3e^tcos(3t)+tsint(3t)
b) 3e^tcos(3t)+te−tsint(3t)
c) 2e^−tcos(3t)−2t3sint(3t)
d) 2e^−tcos(3t)−2te−t3sint(3t)

5. Solve the Ordinary Differential Equation y’’ + 2y’ + 5y = e^-t sin(t) when y(0) = 0 and y’(0) = 1.(Without solving for the constants we get in the partial fractions).
a) et[Acost+A1sint+Bcos(2t)+(B1)2sin(2t)]
b) e−t[Acost+A1sint+Bcos(2t)+B1sin(2t)]
c) e−t[Acost+A1sint+Bcos(2t)+(B1)2sin(2t)]
d) et[Acost+A1sint+Bcos(2t)+(B1)sin(2t)]

6. Solve the Ordinary Diferential Equation using Laplace Transformation y’’’ – 3y’’ + 3y’ – y = t² e^t when y(0) = 1, y’(0) = 0 and y’’(0) = 2.
a) 2e^tt^5 / 720+2e^tt/6+4e^tt^2 /24
b) ett5720+2e−t+2ett6+4ett224
c) e−tt5720+e−t+2e−tt6+4e−tt224
d) 2e−tt5720+e−t+2e−tt6+4e−tt224

7. Take Laplace Transformation on the Ordinary Differential Equation if y’’’ – 3y’’ + 3y’ – y = t² e^t if y(0) = 1, y’(0) = b and y’’(0) = c.
a) (s3−3s2+3s−1)Y(s)+(−as2+(3a−b)s+(−3a−c))=2(s−1)3
b) (s3−3s2+3s−1)Y(s)+(−as2+(3a−b)+(−3a−c)s)=2(s−1)3
c) (s3−3s2+3s)Y(s)+(−as+(3a−b)s+(−3a−c))=2(s−1)3
d) (s3−3s2+3s−1)Y(s)+(−as2+(3a−b)s+(−3a−c))=2(s−1)3

8. What is the inverse Laplace Transform of a function y(t) if after solving the Ordinary Differential Equation Y(s) comes out to be Y(s)=s2−s+3(s+1)(s+2)(s+3) ?
a) 1/2e−t+9/2e^−3t−3e−2t
b) −1/2e−t+9/2e^−2t−3e−3t
c) 1/2e−t−3/2e^−2t−3e−3t
d) −1/2et+9/2e^2t−3e3t

9. For the Transient analysis of a circuit with capacitors, inductors, resistors, we use bilateral Laplace Transformation to solve the equation obtained from the Kirchoff’s current/voltage law.
a) True
b) False

10. While solving an Ordinary Differential Equation using the unilateral Laplace Transform, it is possible to solve if there is no function in the right hand side of the equation in standard form and if the initial conditions are zero.
a) True
b) False

 

1. Find the L(sin³ t).
a) 3/ 4(s2+1)−1/ 4(s2+9)
b) 3/4(s2+1)−3/4(s2+9)
c) 3/4(s2+1)−9/4(s2+9)
d) 3/4(s2−1)−3/4(s2+9)

2. Find the L(e2t(1+t)2).
a) 1 /s−2+2/(s−2)3+2/(s−2)2
b) 3/s−2+2/(s−2)3+2/(s−2)2
c) 1//s−2+2/(s+2)3+2/(s−2)2
d) 1/s−2+2/(s−2)3

3. Find the Laplace Transform of g(t) which has value (t-1)³ for t>1 and 0 for t<1.
a) e^−2as×6/ s4
b) e^−as×2/s5
c) e^−as×6/s4
d) e^−as×2/4s4

4. Find the L(t e^-2t sinh⁡(4t)).
a) 8s+16 / (s2+2s−12)2
b) 2s+16 / (s2+2s−12)2
c) 8s+16 / (s2+21s−12)2
d) 8s+16 / (s2+s−12)2

5. Find the L(t+sin(2t)).
a) 1/s+2/ (s2+4)
b) 1/s+3/(s2+4)
c) 1/s+2/(s2+2)
d) 2/s+2/(s2+4)

6. The L(te^-3t cos⁡(2t)cos⁡(3t)) is given by k[25−(s+3)2((s+3)2+25)2+(1−(s+3)2)((s+3)2+1)2]. Find the value of k.
a) 0
b) 1
c) 12
d) −1/2

7. Find the L(sinh(at)t).
a) 1/2log(s×a / s−a)
b) 1/2log(s−a / s+a)
c) 1/2log(s+a / s−a)
d) 1/3log(s+a / s−a)

8. Find the L(ddt(sintt)).
a) s×cot^-1 s-1
b) s×tan^-1 s-1
c) s×cot⁡(s)-1
d) s×tan⁡(s)-1

9. Find the L(∫t0sin(u)cos(2u)du).
a) 1/2s[3/s2+9−1/s2+1]
b) 1/2s[9/s2+9−1/s2+1]
c) 1/2s[3/s2+9+1/s2+1]
d) 1/s[3/s2+9−1/s2+1]

 

 

 

 

10. Which of the following is not a term present in the Laplace Transform of e^2t sin⁴ t.
a) 38s
b) 38(s−2)
c) s8((s−2)2+16)
d) s2((s−2)2+4)

11. If (erf(t√))=1ss√, then what is L(erf(2t√))?
a) 2 / √s
b) 1 / s√s
c) 2 / s√s
d) 4  / s√s

12. Find the value of L(3^2t).
a) 1/ s−2log(3)
b) 1 / s+2log(3)
c) 1 / s−3log(2)
d) 1  / s+3log(2)

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