Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) Mechanical Engineering 2020 December 2nd Sem 76256 Mathematics Ii Previous Question Paper
Roll No.
Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (Mechnical Engg) (2018 & onwards) (Sem.?2)
MATHEMATICS-II
Subject Code : BTAM-203-18
M.Code : 76256
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 have FOUR questio ns eac h.
3 .
Attempt any FIVE questions from SECT ION B & C carrying EIGHT marks eac h.
4 .
Select atleast T WO que stions from SECT ION - B & C.
SECTION-A
Answer briefly :
1.
Solve y (log y) dx + (x ? log y) dy = 0.
2.
Solve p = log (px ? y).
3.
Find the particular integral of (D2 ? 2D + 4)y = ex cos x.
4.
Solve (D2 + l)3 = 0.
5.
What is the necessary and sufficient condition for a differential equation to be exact?
6.
Define analytic function.
7.
Evaluate
2
2
(x y 2ixy) dz
where C is the contour | z | = 1.
C
8.
State maximum modulus theorem.
9.
Find all zeros of sin z.
10. What is the principal value of ii?
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SECTION-B
11. Solve :
dy
a)
3 6
x
y x y .
dx
b) Solve (xy3 + y) dx + 2(x2y2 + x + y4) dy = 0.
12. Solve y = 2px + y2p3
2
d y
13. a) Using method of variation of parameters, solve
4 y = tan 2x.
2
dx
b) Solve y ? 2y + 5y = 0 if y (0) = ? 3, y (0) = 1.
2
d y
dy
sin (log x) 1
14. Solve 2
x
3x
y log x
.
2
dx
dx
x
SECTION-C
15. Show that the function u = e ?2xy sin (x2 ? y2) is harmonic. Find conjugate function v and
express u + iv as an analytic function of z.
16. Derive Cauchy Riemann equations for analytic functions.
23i
17. a) Evaluate
2
(z z) dz
along the line joining the points (1, ?1) and (2, 3).
1i
2
cos 3
b) By integrating around a unit circle evaluate
d.
0
5 4cos
1
18. Evaluate
in the region.
2
z 3z 2
a) | z | < 1
b) 1 < | z | < 2
c) | z | > 2
d) 0 < | z ? 1 | < 1
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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This post was last modified on 13 February 2021