Download PTU B.Tech 2020 March ME 1st and 2nd Sem Mathematics II Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech ME (Mechanical Engineering) 2020 March 1st and 2nd Sem Mathematics II Previous Question Paper

1 | M-76256 (S1)-2037

Roll No. Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (Mechnical Engg/Automobile Engg./
Civil Engg./CSE/ECE/Electrical & Electronics Engg.) (2018 & onwards)
(Sem.?2)
MATHEMATICS-II
Subject Code : BTAM-203-18
M.Code : 76256
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 & C have FOUR questions each.
3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.

SECTION-A
Answer briefly :
1) Define Bernoulli?s equation with an example.
2) Solve : p
2
? 7p + 12 = 0.
3) Solve : (y cos x + 1) dx + sin xdy = 0.
4) Write Clairaut?s equation with example.
5) What is the significance of integrating factor.
6) Check the analyticity of log z, where z = x + iy.
7) Define conformal mapping.
8) Expand f (z) =
( 1)( 2)
z
z z ? ?
about z = ? 2.
9) State Cauchy Integral formula.
10) Evaluate,
2
( 1)
z
C
e
dz
z ?
? ?
along the circle C : | z ? 3 | = 3.
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1 | M-76256 (S1)-2037

Roll No. Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (Mechnical Engg/Automobile Engg./
Civil Engg./CSE/ECE/Electrical & Electronics Engg.) (2018 & onwards)
(Sem.?2)
MATHEMATICS-II
Subject Code : BTAM-203-18
M.Code : 76256
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 & C have FOUR questions each.
3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.

SECTION-A
Answer briefly :
1) Define Bernoulli?s equation with an example.
2) Solve : p
2
? 7p + 12 = 0.
3) Solve : (y cos x + 1) dx + sin xdy = 0.
4) Write Clairaut?s equation with example.
5) What is the significance of integrating factor.
6) Check the analyticity of log z, where z = x + iy.
7) Define conformal mapping.
8) Expand f (z) =
( 1)( 2)
z
z z ? ?
about z = ? 2.
9) State Cauchy Integral formula.
10) Evaluate,
2
( 1)
z
C
e
dz
z ?
? ?
along the circle C : | z ? 3 | = 3.
2 | M-76256 (S1)-2037

SECTION-B
11) a) Find the power series solution about the origin of the equation
(1 ? x
2
) y ? ? ? 2xy ? + 6y = 0
b) Solve (2x log x ? xy) dy + 2ydx = 0.
12) a) Solve ye
y
dx = (y
3
+ 2xe
y
) dy.
b) Solve : (xy
2
+ 2x
2
y
3
) dx + (x
2
y ? x
3
y
2
)dy = 0.
13) Solve by method of variation of parameters :
(D
2
+ 2D + 1) y = 4e
?x
log x.
14) Solve :
3 2
2 2
3 2
3 log
d y d y dy
x x x x
dx
dx dx
? ? ?

SECTION-C
15) a) Show that function f (z) defined by f (z) =
2 3
6 10
( )
,
x y x iy
x y
?
?
z ? 0, f (0) = 0, is not analytic
at the origin even though it satisfies C-R equations.
b) Find the bilinear transformation that map the points z = 1, i, ?1 into the points w = i,
0, ?i.
16) a) Determine the analytic function whose real part is e
2x
(x cos 2y ? y sin 2y).
b) Prove that u = e
?2xy
sin (x
2
? y
2
) is harmonic. Find a function v such that f (z) = u + iv
is analytic. Also express f (z) in terms of z.
17) a) Use the concept of residues to evaluate
2
0
5 4sin
dx
x
?
?
?
.
b) Evaluate
2
3
( 2 5)
C
z
dz
z z
?
? ?
? ?
along the circle C : | z + 1 ? i | = 2.
18) Expand f (z)
( 2)( 2)
( 1)( 4)
z z
z z
? ?
?
? ?
in the following given regions :
a) | z | < 1, b) 1 < | z | < 4, c) | z | > 4.
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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