Discrete Mathematics MCQ Set 1
1. Leibniz rule gives the
a) Nth derivative of addition of two function
b) Nth derivative of division of two functions
c) Nth derivative of multiplication of two functions
d) Nth derivative of subtraction of two function
Answer
Answer: c [Reason:]
Leibniz rule is
Hence Leibniz theorem gives nth derivative of multiplication of two functions u and v.
2. Leibniz theorem is applicable if n is a
a) Rational Number
b) Negative Integer
c) Positive Integer
d) Decimal Number
Answer
Answer: c [Reason:] Leibniz rule is
For all n > 0, i.e n should be positive
Hence Leibniz theorem gives nth derivative of multiplication of two functions u and v if n is a positive integer.
3. If nth derivative of xy3 + x2y2 + x3y0 = 0 then order of its nth differential equation is,
a) n
b) n+1
c) n+2
d) n+3
Answer
Answer: d [Reason:]
1. If we differentiae this equation n times then terms comes in nth order differential equation is yn+3 , yn+2, yn+1, yn, yn-1, yn-2, yn-3. Hence order of differential equation becomes n+3.
2. By Leibniz rule differentiating it n times, we get
Xyn+3 + nyn+2 + x2yn+2 + 2nxyn+1 + 2n(n-1)yn + x3yn + 3nx2yn-1 + 6n(n-1)xyn-2 + 6n(n-1)(n-2)yn-3 = 0
Hence order of differential equlation becomes n+3.
4. Find nth derivative of x2y2 + xy1 + y = 0
a) x2yn+2 + (2n+1)xyn+1 + (n2+1)yn = 0
b) x2yn+2 + nxyn+1 + (n2+1)yn = 0
c) x2yn+2 + (2n+1)xyn+1 + n2yn = 0
d) x2yn+2 + 2nxyn+1 + n2yn = 0
Answer
Answer: a [Reason:] x2y2 + xy1 + y = 0
By Leibniz theorem
x2yn+2 + n(2x)(yn+1) + n(n-1)(2)(yn) + xyn+1 + nyn + yn= 0
x2yn+2 + xyn+1(2n+1) + yn(n2+1) = 0.
5. The nth derivative of x2y2 + (1-x2)y1 + xy = 0 is,
a) x2yn+2 + yn(2n2-2n-2nx+x) – yn-1(2n2-3n)=0
b) x2yn+2 + yn+1(2nx-x2) + yn(2n2-2n-2nx+x) – yn-1(2n2-3n)=0
c) x2yn+2 + yn+1(2nx+1-x2) + yn(2n2-2n-2nx+x)-yn – 1(2n2-3n)=0
d) x2yn+2 + yn+1(2nx+1-x2) + xyn2n2-yn – 1(2n2-3n)=0
Answer
Answer: c
Explanation: x2y2 + (1-x2)y1 + xy = 0
Differenetiating n times by Leibniz Rule
x2yn+2 + 2nxyn+1 + 2n(n-1)yn + (1-x2)yn+1 – 2nxyn – 2n(n-1)yn-1 + xyn + nyn-1 = 0
x2yn+2 + yn+1(2nx+1-x2) + yn(2n2-2n-2nx+x) – yn-1(2n2-3n)=0.
6. Find nth derivative of xnSin(nx)
Answer
Answer: a [Reason:] Y = xnSin(nx)
By Leibniz Rule , put u = xn and v = Sin(nx), we get
7. If y(x) = tan-1x then
a) (yn+1)(0) = (n-1)(yn-1)0
b) (yn+1)(0) = n(n-1)(yn-1)0
c) (yn+1)(0) = -(n-1)(yn-1)0
d) (yn+1)(0) = -n(n-1)(yn-1)0
Answer
Answer: d [Reason:]
Y = tan-1x
Y1 = 1/(1+x2)
(1+x2)y1 = 1
By Leibniz Rule,
(1+x2)yn+1 + 2nxyn + n(n-1)yn-1 = 0
Put x=0, gives
→ (yn+1)(0) = -n(n-1)(yn-1)(0).
8. If y = sin-1x, then
a) (1-x2)yn+2 – xyn+1(2n-1) = nyn(2n-1)
b) x2yn+2 – xyn+1(2n-1) = nyn(2n-1)
c) (1-x2)yn+2 – 2nxyn+1 = nyn(2n-1)
d) (1-x2)yn+2 – xyn+1(2n-1) +nyn(2n-1)=0
Answer
Answer: a [Reason:] Y = sin-1x
Differentiating it
Y1 = 1/√(1-x2 )
(1-x2)(y1)2= 1
Again Differentiating we get
(1-x2)2y1y2 – 2x(y1)2 = 0
(1-x2)y2 = xy1
By Leibniz Rule, Diff it n times,
(1-x2)yn+2 – 2xnyn+1 – 2n(n-1)yn = xyn+1 + nyn
(1-x2) yn+2 – xyn+1(2n-1) = nyn(2(n-1)+1)
(1-x2) yn+2 – xyn+1(2n-1) = nyn(2n-1).
9. If y = cos-1x, then
a) (yn+2)(0) = -n(2n-1) yn(0)
b) (yn+2)(0) = n(2n-1) yn(0)
c) (yn+2)(0) = n(n-2) yn(0)
d) (yn+2)(0) = n(n-3) yn(0)
Answer
Answer: b [Reason:] y = cos-1x
Differentiating it
Y1 = 1/√(1-x2 )
(1-x2)(y1)2= 1
Again Differentiating we get
(1-x2)2y1y2 – 2x(y1)2 = 0
(1-x2)y2 = xy1
By Leibniz Rule, Diff it n times,
(1-x2)yn+2 – 2xnyn+1 – 2n(n-1)yn = xyn+1 + nyn
(1-x2) yn+2 – xyn+1(2n-1) = nyn(2(n-1)+1)
(1-x2) yn+2 – xyn+1(2n-1) = nyn(2n-1)
At x=0, we get
(yn+2)(0) = n(2n-1) yn(0).
Discrete Mathematics MCQ Set 2
1. If f(t) = sinhat, then its Laplace transform is
a) eat
b) s ⁄ s2-a2
c) a ⁄ s2-a2
d) Exists only if ‘t’ is complex
Answer
Answer: c [Reason:] The Laplace transform of a function is given by
put f(t) = sinhat
On solving, a ⁄ s2-a2 is obtained.
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
Answer
Answer: a [Reason:] The Laplace transform of a function is given by
put f(t) = coshat
On solving, s ⁄ s2-a2 is obtained.
3. 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
Answer: c [Reason:] The Laplace transform of a function is given by
put f(t) = eatsin(bt)
On solving, we get the b ⁄ (s – a)2 + b2.
4. 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
Answer: d [Reason:] The Laplace transform of a function is given by
put f(t) = eatcos(bt)
Solve the above integral, to obtain s-a ⁄ (s – a)2 + b2.
5. 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
Answer: c [Reason:] The Laplace transform of a function is given by
put f(t) = eatsinh(bt)
On solving, we get the b ⁄ (s – a)2 – b2.
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
Answer
Answer: a [Reason:] The Laplace transform of a function is given by
put f(t) = f(t) = 1⁄a sinh(at)
On solving the above integral, we get the 1⁄s2-a2.
7. If f(t) = tn ⁄ n, then its Laplace transform is
Answer
Answer: d [Reason:] The Laplace transform of a function is given by
put f(t) = tn ⁄ n
On solving, we obtain the Laplace transform of the required function.
8. If f(t) = 1 ⁄ √Πt, then its Laplace transform is
Answer
Answer: b [Reason:] The Laplace transform of a function is given by
put f(t) = 1 ⁄ √Πt
The solution for the above question is obtained by solving the above integral.
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
Answer
Answer: d [Reason:] The Laplace transform of a function is given by
put f(t) = t⁄2a sinat
Integrate to obtain, the required transform 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
Answer
Answer: c [Reason:] The Laplace transform of a function is given by
put f(t) = δ(t)
Solve the above integral to obtain 1 as RHS.
11. If f(t) = te-at, then its Laplace transform is
Answer
Answer: a [Reason:] The Laplace transform of a function is given by
put f(t) = te-at
On solving, the required answer is obtained.
12. If f(t) = u(t), then its Laplace transform is
Answer
Answer: b [Reason:] The Laplace transform of a function is given by
put f(t) = u(t) to solve the problem.
13. f(t) = t, then its Laplace transform is
Answer
Answer: d [Reason:] The Laplace transform of a function is given by
put f(t) = t to solve the problem.
Answer
Answer: d [Reason:]The Laplace transform of a function is given by
put f(t) = 1⁄b eatsinh(bt) to solve the problem.
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)
Answer
Answer: b [Reason:] This is the Linearity property of Laplace transform.
Discrete Mathematics MCQ Set 3
1. In a Binomial Distribution, if ‘n’ is the number of trials and ‘p’ is the probability of success, then the mean value is given by
a) np
b) n
c) p
d) np(1-p)
Answer
Answer: a [Reason:] For a discrete probability function, the mean value or the expected value is given by
For Binomial Distribution P(x)= nCx px q(n-x), substitute in above equation and solve to get
µ = np.
2. In a Binomial Distribution, if p, q and n are probability of success, failure and number of trials respectively then variance is given by
a) np
b) npq
c) np2q
d) npq2
Answer
Answer: b [Reason:] For a discrete probability function, the variance is given by
Where µ is the mean, substitute P(x)=nCx px q(n-x) in the above equation and put µ = np to obtain
V = npq.
3. If ‘X’ is a random variable, taking values ‘x’, probability of success and failure being ‘p’ and ‘q’ respectively and ‘n’ trials being conducted, then what is the probability that ‘X’ takes values ‘x’? Use Binomial Distribution
a) P(X = x) = nCx px qx
b) P(X = x) = nCx px q(n-x)
c) P(X = x) = xCn qx p(n-x)
d) P(x = x) = xCn pn qx
Answer
Answer: b [Reason:] It is the formula for Binomial Distribution that is asked here which is given by P(X = x) = nCx px q(n-x).
4. If ‘p’, ‘q’ and ‘n’ are probability pf success, failure and number of trials respectively in a Binomial Distribution, what is its Standard Deviation ?
a) (np)1⁄2
b) (pq)1⁄2
c) (np)2
d) (npq)1⁄2
Answer
Answer: d [Reason:] The variance (V) for a Binomial Distribution is given by V = npq
Standard Deviation = (variance)1⁄2 = (npq)1⁄2.
5. In a Binomial Distribution, the mean and variance are equal
a) True
b) False
Answer
Answer: b [Reason:] Mean = np
Variance = npq
∴ Mean and Variance are not equal.
6. It is suitable to use Binomial Distribution only for
a) Large values of ‘n’
b) Fractional values of ‘n’
c) Small values of ‘n’
d) Any value of ‘n’
Answer
Answer: c [Reason:] As the value of ‘n’ increases, it becomes difficult and tedious to calculate the value of nCx.
7. For larger values of ‘n’, Binomial Distribution
a) loses its discreteness
b) tends to Poisson Distribution
c) stays as it is
d) gives oscillatory values
Answer
Answer: b [Reason:] 
Where m = np is the mean of Poisson Distribution.
8. In a Binomial Distribution, if p = q, then P(X = x) is given by
a) nCx (0.5)n
b) nCn (0.5)n
c) nCx p(n-x)
d) nCn p(n-x)
Answer
Answer: a [Reason:] If p = q, then p = 0.5
Substituting in P(x)=nCx px q(n-x) we get nCn (0.5)n.
9. Binomial Distribution is a
a) Continuous distribution
b) Discrete distribution
c) Irregular distribution
d) Not a Probability distribution
Answer
Answer: b [Reason:] It is applied to a discrete Random variable, hence it is a discrete distribution.
Discrete Mathematics MCQ Set 4
1. Error is the Uncertainty in measurement
a) True
b) False
Answer
Answer: a [Reason:] In the term of mathematics, “Error tells the person how much correct or certain its measurement is.”
2. Relative error in x is
a) δx
b) δx⁄x
c) δx⁄x * 100
d) 0
Answer
Answer: b [Reason:]
Option ‘a’ is called absolute error.
Option ‘b’ is called relative error.
Option ‘c’ is called Percentage error.
3. Find the percentage change power in the circuit if error in value of resistor is 1% and that of voltage source is .99%
a) z should be homogeneous and of order n
b) z should not be homogeneous but of order n
c) z should be implicit
d) z should be the function of x and y only
Answer
Answer: a [Reason:]
Power is given by P = V2⁄R
Taking log on both sides,
log(P) = 2log(V) – log(r)
Differentiating it ,
δp⁄p = 2δV⁄V – δr⁄r
Multiplying by 100 we get,
%P = 2%V – %r = (2*.99) – 1 = 0.98%.
4. Magnitude of error can be negative or positive
a) True
b) False
Answer
Answer: b [Reason:] Magnitude of error can not be negative.Negative or positive sign only shows the increase or decrease in the quatity.
5. Given the kinetic energy of body is T = 1⁄2 mv2 . If the mass of body changes from 100 kg to 100 kg and 500 gm and velocity of a body changes from 1600 mt/sec to 1590 mt/sec. Then find the approximate change in T.
a) 960000 J decrease in value
b) 960000 J increase in value
c) 450000 J decrease in value
d) 450000 J increase in value
Answer
Answer: a [Reason:]
Given T = 1⁄2 mv2
Now taking log and differentiating,
δT = 0.5[v2 δm + 2mvδv]
Now, v = 1600 mt/sec m = 100kg δv = -10 δm = 0.5
Then,
δT = -960000 J => decrese in value of T by 960000 J.
6. The speed of a boat is given by, v = k(1⁄t – at), where k is the constant and l us the distance travel by boat in time t and a is the acceleration of water. If there is an change in ‘l’ from 2cm to 1cm in time 2sec to 1sec. If the acceleration of water changes from 0.95 mt/sec2 to 2 mt/sec2 find the motion of boat.
a) -2
b) 2
c) 0.5
d) -0.5
Answer
Answer: a [Reason:]
Given, v = k(1⁄t – at)
Differentiating it we get
Put, l = 2cm , t = 2sec , a = 0.95 mt/sec2
and δl = 1cm ,δt = 1 secand δa = -1.05 mt/sec2
we get,
δv⁄v = 2.
7. The relative error in the volume of figure having hemispherical ends and a body of right circular cylinder is, if error in radius(r) is 0 and in height(h) is 1.
a) 1/(h + 4⁄3 r)
b) 1/(h + 2⁄3 r)
c) h/(h + 4⁄3 r)
d) r/(h + 4⁄3 r)
Answer
Answer: a [Reason:]
Given V = πr2 h + 4⁄3 πr3
Now since error in radius is zero , it should be treated as constant, Hence,
8. If n resistors of unequal resistances are connected in parallel,and the percenrage error in all
resistors are k then,total error in parallel combination is
Answer
Answer: b [Reason:] Given 1⁄r = 1⁄a + 1⁄b + 1⁄c +⋯.. + 1⁄n
Differentiating all,
– 1⁄r2 dr = – 1⁄a2 da – 1⁄b2 db – ….- 1⁄n2 dn
Now,
1⁄r2 dr = + 1⁄a2 da + 1⁄b2 db + ….+ 1⁄n2 dn
Multiplying by 100 and putting da = db = ……. = dn =k.
9. The approximate value of function f(x + δx, y + δy) is
a) f + ∂f⁄∂x dx + ∂f⁄∂y dy
b) ∂f⁄∂x dx + ∂f⁄∂y dy
c) f – ∂f⁄∂x dx + ∂f⁄∂y dy
d) ∂f⁄∂x dx – ∂f⁄∂y dy
Answer
Answer: a [Reason:] f(x + δx, y + δy) = f(x,y) + df = f + ∂f⁄∂x dx + ∂f⁄∂y dy.
10. At a distance of 120ft from the foot of a tower the elevation of its top is 60o. If the possible error in measuring the distance and elevation are 1 inch and 1 minute, find approximate error in calculated height.
a) 0.342
b) 0.284
c) 0.154
d) 0.986
Answer
Answer: b [Reason:] Tan(z) = h⁄x
h = x Tan(z)
Taking log and then differentiate we get,
∂h⁄h = ∂x⁄x + 1⁄Tan(z) Sec2 (z)δz
Now h = 120 tan(60o) = 120√3
Putting, δx = 1⁄12 ft ,δz = π⁄(60*180)
Putting the values we get,
δh = 0.284.
11. Find the approximate value of (1.04)3.01
a) 1.14
b) 1.13
c) 1.11
d) 1.12
Answer
Answer: d [Reason:] Let, f(x,y) = xy
Now,
∂f⁄∂x = yx(y-1) and ∂f⁄∂y = xy log(x)
Putting, x = 1, y = 3 δx = 0.04, δy = 0.01
Now, df = δx ∂f⁄∂x + δy∂f⁄∂y =0.12
Hence, f(x + δx,y + δy) = (1.04)3.01 = 1.12.
12. Find the approximate value of [0.982+2.012+1.942 ](1⁄2)
a) 1.96
b) 2.96
c) 0.04
d)-0.04
Answer
Answer: b [Reason:] Let f(x,y,z) = (x2+y2+z2 )(1⁄2) ……………..(1)
Hence, x = 1, y = 2, z = 2 so that, dx = -0.02, dy = 0.01, dz = -0.06
From (1),
∂f⁄∂x = x⁄f
∂f⁄∂y = y⁄f
∂f⁄∂z = z⁄f
And df= ∂f⁄∂x dx + ∂f⁄∂y dy + ∂f⁄∂z dz = ((xdx + ydy + zdz))/f = (-0.02 + 0.02 – 0.12)/3 = -0.04
Hence,
[0.982+2.012+1.942 ](1⁄2) = f(1, 2, 2) + df = 3-0.04 = 2.96.
13. Find the approximate value of log(11.01-log(10.1)), Given log(10) = 2.30 and and log(8.69) = 2.16, all the log are in base ‘e’.
a) 2.1654
b) 2.1632
c)2.1645
d) 2.1623
Answer
Answer: d [Reason:] Let, f(x,y) = log(x-log(y))
Now by differentiating,
Hence, df = 0.0023
Hence, f(x + δx, y + δy) = log(11.01 – log(10.1) )= 2.16 + df = 2.1623.
14. Find approximate value of e10.19.09 ,given e90 = 1.22 * 1039.
a) 2.41 * 1039
b) 2.42 * 1039
c) 2.43 * 1039
d) 2.44 * 1039
Answer
Answer: b [Reason:] Let, f(x,y) = exy = exy
Now by differentiating,
∂f⁄∂x = yexy and ∂f⁄∂y = xexy
Now , putting, x = 10, y = 9, δx = .01 and δy = .09
We get,
∂f⁄∂x = 1.09* 1040 and ∂f⁄∂y = 1.22* 1040
Hence, df = 1.27* 1039
Hence, f(x + δx, y + δy) = e10.19.09 = 2.42 * 1039.
Discrete Mathematics MCQ Set 5
1. If f(t) = 1, then its Laplace Transform is given by
a) s
b) 1⁄s
c) 1
d) Does not exist
Answer
Answer: b [Reason:] The Laplace Transform of a functions is given by
put f(t) = 1
On simplifying, we get 1⁄s.
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
Answer
Answer: c [Reason:]The Laplace Transform of a functions is given by
f(t) = tn
On simplifying, we get n! ⁄ sn+1.
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
Answer
Answer: c [Reason:]The Laplace Transform of a functions is given by
Put f(t)=√t
On Solving, we get √π ⁄ 2√s.
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
Answer
Answer: d [Reason:]The Laplace Transform of a functions is given by
Put f(t) = sin(at)
On solving, we get 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
Answer
Answer: a [Reason:]The Laplace Transform of a functions is given by
Put f(t) = tsin(at)
On Solving, we get 2as ⁄ (s2+a2)2.
6. 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
Answer
Answer: c [Reason:] The Laplace Transform of a functions is given by
Put f(t) = eat
On solving the above integral, we obtain 1 ⁄ s-a.
7. If f(t) = tp where p > – 1, its Laplace Transform is given by
a) √π ⁄ 2√s
b) f(t) = tsin(at)
c) γ(p+1) ⁄ sp+1
d) Does not exist
Answer
Answer: d [Reason:]The Laplace Transform of a functions is given by
Put f(t) = tp
On Solving, we get γ(p+1) ⁄ sp+1.
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
Answer
Answer: a [Reason:]The Laplace Transform of a functions is given by
Put f(t) = cos(at)
On solving the above integral, we get s ⁄ s2+a2.
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
Answer
Answer: b [Reason:]The Laplace Transform of a functions is given by
Put f(t) = tcos(at)
On solving the above integral, using suitable rules of integration we get the answer s2 – a2 ⁄ (s2+a2)2.
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
Answer
Answer: d [Reason:]The Laplace Transform of a functions is given by
Put f(t) = sin(at) – atcos(at)
On solving the above integral, we obtain the answer2 a3 ⁄ (s2 + a2)2.
11. If f(t) = sin(at) – atcos(at), then its Laplace transform is given by
Answer
Answer: d [Reason:]The Laplace Transform of a functions is given by
Put f(t) = sin(at) – atcos(at)
On solving, we obtain 2as2 ⁄ (s2+a2)2
12. If f(t) = cos(at) – atsin(at), then its Laplace transform is given by
Answer
Answer: b [Reason:]The Laplace Transform of a functions is given by
Put f(t) = cos(at) – atsin(at)
On solving, we obtain a3 ⁄ (s2 + a2)2.
13. If f(t) = cos(at) + atsin(at), its Laplace transform is given by
Answer
Answer: c [Reason:]The Laplace Transform of a functions is given by
Put f(t) = cos(at) + atsin(at) to solve the problem.
14. If f(t) = sin(at + b), its Laplace transform is given by
Answer
Answer: b [Reason:]The Laplace Transform of a functions is given by
Put f(t) = sin(at + b) to solve the problem.
15. If f(t) = cos(at + b) , its Laplace transform is given by
Answer
Answer: c [Reason:]The Laplace Transform of a functions is given by
Put f(t) = cos(at + b) to solve the problem.
