Download PTU B-Tech CE 2020 Dec 2nd Sem 76254 Mathematics Ii Question Paper

Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) (CE)- Civil Engineering 2020 December 2nd Sem 76254 Mathematics Ii Previous Question Paper

Roll No.
Total No. of Pages : 02
Total No. of Questions : 18
B.Tech (Civil Engg.) (2018 & Onwards) (Sem.?2)
MATHEMATICS-II
Subject Code : BTAM-201-18
M.Code : 76254
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 :
2
d y
1)
Is this differential equation
2
a x 0 linear?
2
dx
2)
Is this differential equation x2 ydx ? (x3 + y3) dy = 0 exact?
3)
Write the solution of the Clairaut's equation y = px + sin?1 p.
2
d y
4)
Find the wronskian from
4 y tan 2 .
x
2
dx
2
2
2
z
z
z
5)
Find complementary function of
2
sin .
x
2
2
x
x
y
y
2
2
z
z
6)
Find particular integral of
2
a
E sin pt.
2
2
t
x
7)
Write one dimensional wave equation.
8)
Classify the equation (x + 1) uxx ? 2(x + 2)uxy + (x + 3) yyy = 0.
9)
What is a boundary value problem?
10) Write Laplace equation in cylindrical coordinates.
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SECTION-B
x
11) Solve a) [1 log (xy)]dx 1
dy 0.
y
dx
b) x
y
1
.
y
dy
12) a) Solve (D2 ? 6D + 9) y = 6e3x + 7e?2x ? log 2.
b) Find the power series solution of the differential equation (4x D2 + 2D + 1) y = 0.
13) Solve a) p x q y
z.
b) x2p + y2q = z (x + y).
14) a) Solve the PDE (D2 ? 2DD + D2) z = ex+y.
b) Solve the PDE (D + D) (D ? 2D + 2) z = sin (2x + y).
SECTION-C
u
u
15) Solve 4
3u by method of separation of variables. Given that u = 3e?y ? e?5y
x
y
when x = 0.
2
2
u
u
16) Solve the BVP
2
c
using D Alembert's technique subject to the conditions
2
2
t
x
u = P0 cos pt when x = l and u = 0 when x = 0.
2
u
u
17) Solve the BVP
2
c
using separation of variables method subject to the
2
t
x
conditions u (0, t) = u (l, t) = 0, u (x, 0) = x where l > 0.
18) The diameter of a semi-circular plate of radius a is kept at 0?C and the temperature at the
semicircular boundary is T?C. Estimate the steady state temperature in the plate using the
2
2
u
u
u
Laplace equation 2
r
r
0.
2
2
r
r

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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