Deemed University 2010 B.Tech Electronics and Communications Engineering University: Lingayas University Term: III Title of the : MATH III - Question Paper
Roll No. ..
Lingayas University, Faridabad
Examination May, 2010
Course: B.Tech. Year: IInd
Semester: III Paper Code: MATH-201E
Subject: Math - III
[Time: 3 Hours] [Max. Marks: 100]
Before answering the question, candidate should ensure that they have been supplied the correct and complete question paper. No complaint in this regard, will be entertained after examination.
Note: Attempt Five Question in all. Selecting at least one question from each part.
Part- A
Q.1. (a) If f(x) = |cosx|, expand f(x) as a Fourier series in the internal (-p,p), (10)
(b) Write half range cosine series for the function (10)
f (x) =
Q-2 (a) State and prove convolution theorem for Fourier transforms (10)
(b) Find the Fourier transform of of 
, where a>0. (10)
Part B
Q-3. (a) If coshx = sec
, prove that
tanh2 
= tan2 (/2) (10)
(b) Reduce tan-1 (cos+ isin ) to the form a + ib.
Hence show that
tan-1 (
) = 
(10)
Q-4. (a) if f(z) = 
(10)
Then discuss 
at z = o
(b) Show that the real and imaginary parts of
the function W=logz satisfy the C-R equations when z 
0 (10)
Q-5. (a) State and prove residue theorem and use it to evaluate.
dz, where c is |z| = 2.5
(b) Expand 
for |z| = 3 (10)
Part- C
Q-6. (a) Assuming half the population of a town consumes chocolates and that 100 investigators each take 10 individuals to see. Whether they are consumers, how many investigators would your expect to report that these people or less were consumers? (10)
(b) If 10% of bolts produced by a machine are defective. Determine the probability that out of 10 bolts, chosen at random (i) one (ii) none (iii) at most 2 bolts will be defective. (10)
Q-7. (a) Fit a binomial distribution to the following frequency data. (10)
|
x |
0 |
1 |
3 |
4 |
|
f |
28 |
62 |
10 |
4 |
(b) If the variance of the poisson
distribution is 2, find the probabilities for r = 1, 2, 3, 4 from the
recurrence relation of the poisson distribution also find P (r
4) (10)
Q-8. (a) Using dual simplex method maximize Z= -3x1-x2 (10)
Subject to x1+x21,
2x1
+ 3x2 2,
x1,
x2 0
(b) Solve the following L.P.P graphically MaxZ = x1 + x2 (10)
s.t.
x1 + 2x2
2000
x1+x2
1500
x2 600
x1 x2
0
Roll No. ..
Lingayas University, Faridabad
Examination December, 2009
Course: B.Tech. Year: IInd
Semester: III Paper Code: MATH-201E
Subject: Math - III
[Time: 3 Hours] [Max. Marks: 100]
Before answering the question, candidate should ensure that they have been supplied the correct and complete question paper. No complaint in this regard, will be entertained after examination.
Note: Attempt Five Question in all. Selecting at least one question from each part.
Part- A
Q.1. (a) If f(x) = |cosx|, expand f(x) as a Fourier series in the internal (-p,p), (10)
(b) Write half range cosine series for the function (10)
f (x) =
Q-2 (a) State and prove convolution theorem for Fourier transforms (10)
(b) Find the Fourier transform of of , where a>0. (10)
Part B
Q-3. (a) If coshx = sec, prove that
tanh2 = tan2 (/2) (10)
(b) Reduce tan-1 (cos+ isin ) to the form a + ib.
Hence show that
tan-1 () = (10)
Q-4. (a) if f(z) = (10)
Then discuss at z = o
(b) Show that the real and imaginary parts of
the function W=logz satisfy the C-R equations when z 0 (10)
Q-5. (a) State and prove residue theorem and use it to evaluate.
dz, where c is |z| = 2.5
(b) Expand for |z| = 3 (10)
Part- C
Q-6. (a) Assuming half the population of a town consumes chocolates and that 100 investigators each take 10 individuals to see. Whether they are consumers, how many investigators would your expect to report that these people or less were consumers? (10)
(b) If 10% of bolts produced by a machine are defective. Determine the probability that out of 10 bolts, chosen at random (i) one (ii) none (iii) at most 2 bolts will be defective. (10)
Q-7. (a) Fit a binomial distribution to the following frequency data. (10)
|
x |
0 |
1 |
3 |
4 |
|
f |
28 |
62 |
10 |
4 |
(b) If the variance of the poisson
distribution is 2, find the probabilities for r = 1, 2, 3, 4 from the
recurrence relation of the poisson distribution also find P (r4) (10)
Q-8. (a) Using dual simplex method maximize Z= -3x1-x2 (10)
Subject to x1+x21,
2x1
+ 3x2 2,
x1,
x2 0
(b) Solve the following L.P.P graphically MaxZ = x1 + x2 (10)
s.t.
x1 + 2x2
2000
x1+x2
1500
x2 600
x1 x2
0
| Earning: Approval pending. |
