Download PTU B.Tech 2021 Jan ECE 3rd Sem 76448 Mathematics Iii Question Paper

Download PTU (Punjab Technical University) B.Tech (Bachelor of Technology) / BE (Bachelor of Engineering) 2021 January ECE 3rd Sem 76448 Mathematics Iii Previous Question Paper

Roll No.
Total No. of Pages : 03
Total No. of Questions : 18
B.Tech.(ECE) (2018 Batch) (Sem.?3)
MATHEMATICS III
Subject Code : BTAM-303-18
M.Code : 76448
Time : 3 Hrs. Max. Marks : 60
INST RUCT IONS T O CANDIDAT ES :
1 .
SECT ION-A is COMPULSORY cons is ting of TEN questions carrying TWO marks
each.
2 .
SECT ION-B c ontains F IVE questions c arrying FIVE marks eac h and s tud ents
have to atte mpt any FOUR q ues tions.
3 .
SECT ION-C contains THREE questions carrying T EN marks e ach and s tudents
have to atte mpt any T WO questio ns.
SECTION-A
Write briefly :
1.
If a random variable has a Poisson distribution such that P(l) = P(2). Find the mean of the
distribution.
2.
Find the Laplace transform of t3 e?3t.
3.
Represent f (t) = sin 2t, 2 < t < 4 and 0 otherwise, in terms of unit step function.
4.
State convolution theorem of Fourier transform.
5.
Find the Z-transform of et sin 2t.
6.
Write the relation between Fourier and Laplace transforms.
7.
Define discrete and continuous random variables.
8.
Define Rank correlation.
9.
State initial and final value theorems of Z-transform.
10. Define Binomial and Poisson distribution functions.
1 | M-76448
(S2)- 828

---

SECTION-B
11. Evaluate :
t sin
t
t
L e
dt
0
t
12. Find the Fourier transform of :
2
2 ( x 3 )
e
13. Using the Z-transform, solve :
un+2 + 4un+1 + 3un = 3n
with u0 = 0, u1 = 1.
14. The two regression equations of the variables x and y are x = 19.13 ? 0.87 y and
y = 11.64 ? 0.50 x. Find (i) mean of x and y (ii) the correlation co-efficient between x and
y.
15. The intelligence quotients (IQ) of 16 students from B. Tech. IInd year showed a mean of
107 and a standard deviation of 10, while the IQs of 14 students from B. Tech. 1st year
showed a mean of 112 and a standard deviation of 8. Is there a significant difference
between the IQs of the two groups at significance levels of 0.05? Given that critical value
at 28 degree of freedom with 5% level of significance is 2.05.
SECTION-C
16. a) Apply Convolution theorem to evaluate
1
1
L
2
2
( s 1) ( s 9)
b) Find the inverse Laplace transform of
s/2
s
se
e
2
2
s
2 | M-76448
(S2)- 828

---

17. If f (x) = sin x, 0 x and f (x) = 0, ? x 0, Prove that
sin x
cos 2
1
2
nx
f ( x )
2
2
1 4 n
1
n
Hence show that :
1
1
1
2
...
1.3
3.5
5.7
4
18. Find the coefficient of correlation and obtain the lines of regression from the given data
X
62
64
65
69
70
71
72
74
Y
126 125 139
145
165
152
180
208
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.
3 | M-76448
(S2)- 828

---