Download PTU B-Tech ECE 2020 Dec 3rd Sem 76448 Mathematics Iii Question Paper

Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) (ECE)-Electronics And Communications Engineering 2020 December 3rd Sem 76448 Mathematics Iii Previous Question Paper

Roll No.
Total No. of Pages : 02
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.
Find Laplace of (cos t) u1 (t)
2.
Find L (et t2)
3.
Find an if f (x) = x3, where x (?2, 2).
4.
Discuss behavior of Fourier series near a point of discontinuity of
1
,

x 0
f (x) =
.
1,
0 x
5.
Find Z {sin (n + 1) }
6.
Find relationship between Laplace and Fourier Transform.
7.
Two cards are drawn one after the other from a well shuffled deck of 52 cards. Find the
probability that both are spade, if the first card is not replaced.
8.
If X is Poisson variate satisfies P (X = 1) = 0.5 P (X = 2), find mean and variance.
9.
Define F-test
10. Discuss method to fit Parabola.
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SECTION-B
6s
11. State convolution theorem and find
1
L
2
2
(s 16)
12. Find the Fourier sine series of the function f (x) = sin 3x, 0 x .
13. Solve difference equation yn + 2 ? 2yn+1 + yn = n, y0 = 1, y1 = 1.
14. In a distribution, 12% of the item are under 30 and 85% are under 60. Find the mean and
standard deviation of the distribution.
15. Two independent sample have 28 and 19 pair of observations with correlation co-
efficient 0.55 and 0.75 respectively. Are these values consistent with the hypothesis that
both the samples are drawn from the same population?
SECTION-C
16. Using Laplace transform to solve the initial value problem utt = uxx, 0 < x < 1, t > 0,
subject to u (x, 0) = 0, ut (x, 0) = sin 3x, u (0, t) = sin t, u (1, t) = 0.
1
17. Using convolution 1
F
.
2
6 5i
18. Find correlation coefficient of the following bivariate frequency distribution data :
59-62
63-66
67-70
71-74
75-78
90-109
2
1
110-129
7
8
4
2
130-149
5
15
22
7
1
150-169
2
122
63
19
5
170-189
7
28
32
12
190-209
2
10
20
7
210-229
1
4
2
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.
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