Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) (CSE-IT)- Computer Science Engineering -Information Technology 2020 December 3rd Sem 70808 Mathematics Iii Previous Question Paper
Roll No.
Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (CSE / IT) (2012 to 2017)
(Sem.?3)
MATHEMATICS ? III
Subject Code : BTAM-302
M.Code : 70808
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 each and s tudents
have to atte mpt any T WO questio ns.
SECTION-A
Answer briefly :
1.
State and prove second shifting theorem for Laplace transforms.
2.
Show that | z |2 is not analytic at any other point except z = 0.
3.
Discuss modified Euler's method.
4.
Find the half-range cosine series for the function f (x) = (x ? 1)2 in the interval 0 x 1.
5.
Solve pq = p + q.
6.
Evaluate L (eat sin bt).
7.
Find the inverse Laplace transform of (6 + s) / (s2 + 6s + 13).
8.
Write Cauchy-Riemann equations in polar form.
9.
In a normal distribution, 31% of the items are under 45 and 8% are over 64. Find the
mean and standard deviation of the distribution.
10. State Cayley-Hamilton theorem.
1 | M-70808
(S2)-416
SECTION-B
11. Find Fourier series expansion of f (x) = x + x2 in the interval ? < x < . Hence show that
2
1
1
1
1
....
.
2
2
2
2
1
2
3
4
12
n
d
12. Show that if L (f (t)) = F (s) then L (tn f (t)) = (1)n
F (s) where n = 1, 2, 3, ........
n
ds
Hence evaluate L (t3 e?3t).
13. If f (z) is an analytic function of z, prove that :
2
2
2
2
| f (z)| 4 | f (z) |
2
2
x
y
14. Solve
4x ? 3y ? 9z + 6w = 0
2x + 3y + 3z + 6w = 0
4x ? 21y ? 39z ? 6w = ? 24
15. The following table shows the distribution of digits in numbers chosen at random from a
telephone directory :
Digits
0
1
2
3
4
5
6
7
8
9
Frequency 1026
1107
997
966
1075
933
1107
972
964
853
Test whether the digits may be taken to occur equally frequently in the directory.
SECTION-C
16. Solve (x2 ? 2yz ? y2) p + (xy + zx) q = xy ? zx.
1
1 0
17. Find the eigen values and the corresponding eigen vectors of 0
1
1 .
0
0
1
dy
18. Evaluate y (0.8) using Runge's method of order four, given that
x y; y (0.4) =
dx
0.4 (Take h = 0.2).
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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(S2)-416
This post was last modified on 13 February 2021