AMITY UNIVERSITY UTTAR PRADESH
B.Tech. (2nd Semester)
APPLIED MATHEMATICS - II
(Laplace transform) Quiz-1
1. If f(t) = 1, then its Laplace Transform is given by
a) s
b) 1⁄s
c) 1
d) Does not exist
Ans b
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
Ans c
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
Ans c
4. If f(t) = sinh at, then its Laplace transform is given by
a) eat
b) s ⁄ s2-a2
c) a ⁄ s2-a2
d) Exists only if ‘t’ is complex
Answer: c
AMITY UNIVERSITY UTTAR PRADESH
B.Tech. (2nd Semester)
APPLIED MATHEMATICS - II
(Laplace transform) Quiz-2
1. If f(t) = cosh at, its Laplace transform is given by
a) s ⁄ (s2-a2)
b) ( s+a ) ⁄ (s-a)
c) Indeterminate
d) {(Sinh (at)}2
Answer: a
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
Ans c
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
Ans c
4. If f(t) = Sin (at), then its Laplace Transform is given by
a) Cos (at)
b) 1 ⁄ asin(at)
c) Indeterminate
d) a ⁄ (s2+a2)
Ans a
AMITY UNIVERSITY UTTAR PRADESH
B.Tech. (2nd Semester)
APPLIED MATHEMATICS - II
(Laplace transform) Quiz-3
1. If f(t) = eat 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
Answer: c
2. If f(t) = eat 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}
Answer: d
3. If f(t) = eat 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
Answer: c
4. 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
Answer: a
AMITY UNIVERSITY UTTAR PRADESH
B.Tech. (2nd Semester)
APPLIED MATHEMATICS - II
(Laplace transform) Quiz-4
1. If f(t) = (t/2)a sin at, then its Laplace transform is
a) b ⁄ {(s + a)2 + b2 }
b) 2a ⁄ { (s – b)2 + b2 }
c) Indeterminate
d) s ⁄ (s2 + a2)2
Answer: d
2. f(t) = t, then its Laplace transform is given by
a) Γ(n) / sn+1
b) 2as / (s2+a2)2
c) Γ(p+1) / sn+1
d) 1/s2
Answer: d
3. If L { f(t) } = F(s), then L {k f(t)} is given by
a) F(s)
b) k F(s)
c) Does not exist
d) F(s⁄k)
Answer: b
4. If f(t) = Sin (at), then its Laplace Transform is given by
a) Cos (at)
b) 1 ⁄ asin(at)
c) Indeterminate
d) a ⁄ (s2+a2)
Ans a
AMITY UNIVERSITY UTTAR PRADESH
B.Tech. (2nd Semester)
APPLIED MATHEMATICS - II
(Laplace transform) Quiz-5
1. If f(t) = t sin (at) then its Laplace Transform is given by
a) 2as ⁄ (s2+a2)2
b) a ⁄ ( s2+a2)
c) Indeterminate
d) √π ⁄ 2√s
Ans a
2. If f(t) = eat, its Laplace Transform is given by
a) a ⁄ (s2+a2)
b) √π ⁄ 2√s
c) 1 ⁄ (s-a)
d) Does not exist
Ans c
3. If f(t) = t cos (at), its Laplace transform is given by
a) 1 ⁄ (s-a)
b) (s2 – a2 ) ⁄ (s2+a2)2
c) Indeterminate
d) (s2 + a2 ) ⁄ (s2-a2)2
Ans d
4. The laplace transformation is one of the important tool for solving
a) Linear differential equations
b) Constant coefficient ordinary differential equations
c) Partial differential equations
d) All of these
Ans d
AMITY UNIVERSITY UTTAR PRADESH
B.Tech. (2nd Semester)
APPLIED MATHEMATICS - II
(Laplace transform) Quiz-6
1. Laplace transform of sin (at).u(t) is given by
a) s ⁄ (a2+s2)
b) a ⁄ (a2+s2)
c) s2 ⁄ (a2+s2)
d) a2 ⁄ (a2+s2)
Answer: b
2. If f(t) = 1, then its Laplace Transform is given by
a) s
b) 1⁄s
c) 1
d) Does not exist
Ans b
3. If f(t) = t sin(at) then its Laplace Transform is given by
a) 2as ⁄ (s2+a2)2
b) a ⁄ (s2+a2)
c) Indeterminate
d) √π ⁄ 2√s
Ans a
4. If f(t) = eat, its Laplace Transform is given by
a) a ⁄ s2+a2
b) √π ⁄ 2√s
c) 1 ⁄ s-a
d) Does not exist
Ans c
AMITY UNIVERSITY UTTAR PRADESH
B.Tech. (2nd Semester)
APPLIED MATHEMATICS - II
(Laplace transform) Quiz-7
1. If f(t) = t Cos (at), its Laplace transform is given by
a) 1 ⁄ ( s-a)
b) (s2 – a2) ⁄ (s2+a2)2
c) Indeterminate
d) (s2 + a2) ⁄ (s2-a2)2
2. Laplace transform of sin (at).u(t) is?
a) s ⁄ a2+s2
b) a ⁄ a2+s2
c) s2 ⁄ a2+s2
d) a2 ⁄ a2+s2
Answer: b
3. Laplace of function f(t) is given by
∞
a) F(s) = ∫0 f(t)e−st dt
∞
b) F(t) = ∫0 f(t)e−st dt
∞
c) F(s) = ∫0 f(t)e−t dt
∞
d) F(t) = ∫0 f(t)e−st dt
Answer: a
4. The laplace transformation of 𝑓(𝑡) = 𝑡 sin 𝑎𝑡 is given by
2𝑎𝑠 𝑎𝑠
a) (𝑠2+𝑎2)2 b) (𝑠2 −𝑎2 )2
𝑎𝑠 2𝑎𝑠
c) (𝑠2+𝑎2)2 d) (𝑠2 −𝑎 2 )2
Ans a
AMITY UNIVERSITY UTTAR PRADESH
B.Tech. (2nd Semester)
APPLIED MATHEMATICS - II
(Laplace transform) Quiz-8
1. Find the laplace transform of et Sin (t).
a) (s-1) /{a2+(s−1)2}
b) a/{a2+(s−1)2}
c) s/{a2+(s−1)2}
d) a/{a2+(s+1)2}
Answer: b
2.The laplace transform of t2 sin (2t) is given by
a) (12s2−18) / (s2+4)3
b) (12s2−16) / (s2-4)3
c) (2s2−16) / (s2+8)3
d) (12s2−16) / (s2+4)3
Answer: d
3. The laplace transform of y(t) = et t. Sin (t).Cos (t) is given by
a) (s−1)/ [(s−1)2+4]2
b) 2(s+1)/ [(s−1)2+4]2
c) 2(s−1)/ [(s+1)2+4]2
d) 2(s−1)/ [(s−1)2+4]2
Answer: d
∞
4. The value of ∫0 𝑡 sin 𝑡 𝑐𝑜𝑠𝑡 𝑑𝑡 is given by
a) s ⁄ ( s2+4)
b) a ⁄ ( s2+4)
c) 1
d) 0 Answer: d
AMITY UNIVERSITY UTTAR PRADESH
B.Tech. (2nd Semester)
APPLIED MATHEMATICS - II
(Laplace transform) Quiz-9
1. If f(t) = δ(t), then its Laplace transform is given by
a)( s + a ) ⁄ {(s – a)2 + b2 }
b) a3 ⁄ (s2 + a2)2
c) 1
d) Does not exist
Ans c
2. Laplace transform if cos (at).u(t) is given by
a) s ⁄ a2+s2
b) a ⁄ a2+s2
c) s2 ⁄ a2+s2
d) a2 ⁄ a2+s2
Answer: a
3. The laplace transformation of 𝑓(𝑡) = t 2 e t sin 4t is given by
8(2s 2 − 6s − 13)
a) b)
8(3s 2 − 6s − 13) ( s 2 − 2s + 17) 3
( s 2 − 2s + 18) 3
8(3s 2 − 6s − 13)
c) d)
8(3s 2 − s − 13) ( s 2 − 2s + 17)3
( s 2 − 2s + 17) 3
Ans d
4. The laplace transformation of unit step function 𝑓(𝑡) = 𝑢(𝑡 − 𝑎) is given by
𝑒 −𝑠 𝑒 −𝑎𝑠
a) 𝑠
b) 𝑠
𝑒 𝑎𝑠 𝑒𝑠
c)− 𝑠
d) − 𝑠
Ans b
AMITY UNIVERSITY UTTAR PRADESH
B.Tech. (2nd Semester)
APPLIED MATHEMATICS - II
(Laplace transform) Quiz-10
1. The inverse Laplace transform for 1 / (s+1)2 is given by
a) t et u(t)
b) t e-t u(t)
c) t u(t)
d) et u(t)
Answer: b
s+3
2. Inverse laplace transform of
4s 2 + 9
a) 1/4cos(3t/2)+1/2sin(3t/2)
b) 1/4sin(3t/2)+1/2cos(3t/2)
c) 1/4cos(t/2)+1/2cos(3t/2)
d) 1/4cos(3t/2)+1/2cos(t/2)
Ans d
1
3. The value of L−1 is given by
( s + 2) 4
t3 t3
a) e −t . b) e −2t .
6 9
t3 t2
c) e − 2t . d) e − 2t .
6 6
Ans c
1
1. Inverse Laplace transform of is given by
(s+1)(s−1)(s+2)
a) –1⁄2 et + 1⁄6 e-t + 1⁄3 e2t
b) –1⁄2 e-t + 1⁄6 et + 1⁄3 e-2t
c) 1⁄2 e-t – 1⁄6 et – 1⁄3 e-2
d) –1⁄2 e-t + 1⁄6 e-t + 1⁄3 e-2
Ans b
AMITY UNIVERSITY UTTAR PRADESH
B.Tech. (2nd Semester)
APPLIED MATHEMATICS - II
(Laplace transform) Quiz-11
1. The inverse Laplace transform for 1 / {(s+1)2+1} is given by
a) t e-t u(t)
b) e-t sin t u(t)
c) e-t cost u(t)
d) e-t u(t)
Answer: b
1
2. Inverse laplace transform of is given by
(s−1)2 (s+5)
a) 1⁄6 e – t – 1⁄36 et + 1⁄36 e-5t
b) 1⁄6 et t – 1⁄36 et + 1⁄36 e-5t
c) 1⁄6 e-t t2 – 1⁄36 e-t + 1⁄36 e5t
d) 1⁄6 e-t t- 1⁄36 e-t + 1⁄36 e5
Ans a
1
3. The inverse laplace transform of . is given by
(s2 +1)(s–1)(s+5).
a) 1⁄12 et – 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 e5t
c) 1⁄12 et – 1⁄13 Cos(t) – 1⁄12 Sin(t) – 1⁄156 e-5t
d) 1⁄12 et + 1⁄13 Cos(t) + 1⁄12 Sin(t) + 1⁄156 e-5t
Ans c
4. The inverse Laplace transform for s / (s+2)2 is given by
a) t e-t u(t)
b) e-t sin t u(t)
c) e-2t (1-2t)u(t)
d) e2t (1-2t)u(t)
Answer: c
AMITY UNIVERSITY UTTAR PRADESH
B.Tech. (2nd Semester)
APPLIED MATHEMATICS - II
(Laplace transform) Quiz-12
1. The inverse Laplace transform for s / {(s+2)2+1} is given by
a) [2e-2t Cos t + e-2t Sin t]u(t)
b) [e-2t Cos t + 2e-2t Sin t]u(t)
c) [2e-2t Cos t – e-2t Sin t]u(t)
d) [e-2t Cos t – 2e-2t Sin t]u(t)
Answer: d
2. The inverse Laplace transform of F(s) = s / (s2 a2 +b2) is given by
a) ( 1 /a2) Cos (1/a)t
b)( 1 /a2) Cos (b/a)t
c) ( 1 /a) Cos (b/a)t
d) ( 1 /a2) Cos (b/a)t2
Answer: b
1
3. The inverse laplace transform of is given by
s(s2 +4)2 .
a) 1⁄4 sin(2t)
b) t⁄8 sin(2t)
c) t⁄4 sin(2t)
d) t⁄4 sin(2t2)
Ans c
𝑠+1
4. The inverse lapace of is given by
[(s+1)2 +4][(s+1)2 +1]
a) 1⁄3 et [Cos(t) – Cos(2t)].
b) 1⁄3 e-t [Cos(t) + Cos(2t)].
c) 1⁄3 et [Cos(t) + Cos(2t)].
d) 1⁄3 e-t [Cos(t) – Cos(2t)].
Ans d
AMITY UNIVERSITY UTTAR PRADESH
B.Tech. (2nd Semester)
APPLIED MATHEMATICS - II
(Laplace transform) Quiz-13
1. The inverse Laplace transform of F(s) = s / (s2+a2)2 is given by
a) (1/2) t sin at b) (1/2a) t sin at
c) (1/a) t sin at d) (1/2a) sin at
Answer: b
2. The value of L-1 [s / {(s2+1)(s2+2)(s2+3)}] is given by
a) (1/2) Cos (t) – Cos (2√t) − Cos (3√t)
b) (1/2) Sin (t) + Cos (2√t) − (1/2) Cos (3√t)
c) (1/2) Cos (t) – Cos (2√t) − (1/2) Cos (3√t)
d) (1/2) Cos (t) – Cos (2√t) − (1/2) Sin (3√t)
Answer: c
3. The inverse Laplace transform for F(s) = s / (2s2−8) is given by
a) (1/2) cosh t
b) (1/2) cosh 2t
c) (1/2) sinh 2t
d) (1/3) cosh 2t
Answer: b
4. The inverse Laplace transform for F(s) = log {(s+a) / (s+b)} is given by
a) (1 /2 t )( e-bt – e-at)
b)(1 / t )( e-bt – e-at)
c) (1 / t )( e-at – e-bt)
d) (1 / t )( e-bt + e-at)
Answer: b
