Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech ECE (Electronics And Communications Engineering) 2020 March 3rd Sem BTAM 303 18 Mathematics Iii Previous Question Paper
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech.(ECE) (2018 Batch) (Sem.?3)
MATHEMATICS III
Subject Code : BTAM-303-18
M.Code : 76448
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION-A
1. Write briefly :
a) In Poisson frequency distribution, frequency corresponding to 3 successes is 2/3 times
frequency corresponding to 4 successes. Find the standard deviation of the
distribution.
b) Find the Z-transform of e
t
sin 2t
c) Find the Laplace transform of t
2
sin t
d) Define Binomial and Poisson distribution functions.
e) Define Rank correlation.
f) Define the Laplace and Fourier transforms.
g) Define unit-step and dirac delta functions.
h) Define discrete and continuous random variables.
i) State convolution theorem of Fourier transform.
j) Given that
1
( )
2
x
f x k
? ?
?
? ?
? ?
, is a probability distribution for a random variable which can
take on its values x = 0, 1, 2, 3, 4, 5, 6. Find k.
FirstRanker.com - FirstRanker's Choice
1 | M-76448 (S2)- 1505
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech.(ECE) (2018 Batch) (Sem.?3)
MATHEMATICS III
Subject Code : BTAM-303-18
M.Code : 76448
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION-A
1. Write briefly :
a) In Poisson frequency distribution, frequency corresponding to 3 successes is 2/3 times
frequency corresponding to 4 successes. Find the standard deviation of the
distribution.
b) Find the Z-transform of e
t
sin 2t
c) Find the Laplace transform of t
2
sin t
d) Define Binomial and Poisson distribution functions.
e) Define Rank correlation.
f) Define the Laplace and Fourier transforms.
g) Define unit-step and dirac delta functions.
h) Define discrete and continuous random variables.
i) State convolution theorem of Fourier transform.
j) Given that
1
( )
2
x
f x k
? ?
?
? ?
? ?
, is a probability distribution for a random variable which can
take on its values x = 0, 1, 2, 3, 4, 5, 6. Find k.
2 | M-76448 (S2)- 1505
SECTION-B
2. Use Laplace transform method to solve
2
2
2
t
d x dx
x e
dt dt
? ? ?
with x = 2, 1
dx
dt
? ? at t = 0.
3. Find the Fourier sine transform of e
?| x |
. Hence show that :
2
0
sin
, 0
1 2
m
x mx e
dx m
x
?
?
?
? ?
?
?
4. If
2
4
2 5 14
U ( )
( 1)
z z
z
z
? ?
?
?
Evaluate u
2
and u
3
.
5. The theory predicts the proportion of beans, in the four groups A, B, C and D should be
9:3:3:1. In an experiment among 1600 beans, the numbers in the four groups were 882,
313, 287 and 118. Does the experimental result support the theory?
(The table value of ?
2
for 3 d.f. at 5% level of significance is 7.81).
6. The two regression equations of the variables x and y are x = 19.13 ? 0.87y and
y = 11.64 ? 0.50 x. Find
(i) mean of x and y
(ii) the correlation co-efficient between x and y.
SECTION-C
7. Find the Fourier cosine series of the function f (x) = ? ? x in 0 < x < ?. Hence show that
2
2
0
1
(2 1) 8
r
r
?
?
?
?
?
?
FirstRanker.com - FirstRanker's Choice
1 | M-76448 (S2)- 1505
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech.(ECE) (2018 Batch) (Sem.?3)
MATHEMATICS III
Subject Code : BTAM-303-18
M.Code : 76448
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION-A
1. Write briefly :
a) In Poisson frequency distribution, frequency corresponding to 3 successes is 2/3 times
frequency corresponding to 4 successes. Find the standard deviation of the
distribution.
b) Find the Z-transform of e
t
sin 2t
c) Find the Laplace transform of t
2
sin t
d) Define Binomial and Poisson distribution functions.
e) Define Rank correlation.
f) Define the Laplace and Fourier transforms.
g) Define unit-step and dirac delta functions.
h) Define discrete and continuous random variables.
i) State convolution theorem of Fourier transform.
j) Given that
1
( )
2
x
f x k
? ?
?
? ?
? ?
, is a probability distribution for a random variable which can
take on its values x = 0, 1, 2, 3, 4, 5, 6. Find k.
2 | M-76448 (S2)- 1505
SECTION-B
2. Use Laplace transform method to solve
2
2
2
t
d x dx
x e
dt dt
? ? ?
with x = 2, 1
dx
dt
? ? at t = 0.
3. Find the Fourier sine transform of e
?| x |
. Hence show that :
2
0
sin
, 0
1 2
m
x mx e
dx m
x
?
?
?
? ?
?
?
4. If
2
4
2 5 14
U ( )
( 1)
z z
z
z
? ?
?
?
Evaluate u
2
and u
3
.
5. The theory predicts the proportion of beans, in the four groups A, B, C and D should be
9:3:3:1. In an experiment among 1600 beans, the numbers in the four groups were 882,
313, 287 and 118. Does the experimental result support the theory?
(The table value of ?
2
for 3 d.f. at 5% level of significance is 7.81).
6. The two regression equations of the variables x and y are x = 19.13 ? 0.87y and
y = 11.64 ? 0.50 x. Find
(i) mean of x and y
(ii) the correlation co-efficient between x and y.
SECTION-C
7. Find the Fourier cosine series of the function f (x) = ? ? x in 0 < x < ?. Hence show that
2
2
0
1
(2 1) 8
r
r
?
?
?
?
?
?
3 | M-76448 (S2)- 1505
8. a) Marks obtained by a number of students are assumed to be normal distributed with
mean 50 and variance 36. If 4 students are taken at random, what is the probability
that exactly two of them will have marks over 65?
Given that
2
0
( ) 0.4772 z dz ? ?
?
where Z is N (0, 1).
b) Fit the second degree parabola to the following data :
X 0 1 2 3 4
Y 1 1.8 1.3 2.5 6.3
9. From the given data, find (i) the two regression equations, (ii) the coefficient of
correlation between the marks in Mathematics & Statistics, and (iii) the most likely marks
in Statistics when the marks in Mathematics are 30.
Marks in Mathematics 25 38 35 32 31 36 29 38 34 32
Marks in Statistics 43 46 49 41 36 32 31 30 33 39
NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
FirstRanker.com - FirstRanker's Choice
This post was last modified on 21 March 2020