Download GTU B.Tech 2020 Summer 1st and 2nd Sem 3110015 Mathematics Ii Question Paper

Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Summer 1st and 2nd Sem 3110015 Mathematics Ii Previous Question Paper

Seat No.: ________
Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE ? SEMESTER 1&2 EXAMINATION ? SUMMER 2020
Subject Code: 3110015 Date:09/11/2020
Subject Name: Mathematics II
Time: 10:30 AM TO 01:30 PM
Total Marks: 70
Instructions:
1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.


Marks
Q.1 (a) Evaluate F d r
along the parabola 2
y x between the points (0, 0)
03
c
and (1, 1) where
2
F x ^i xy ^j

(b) Find the work done in moving particle from A (1, 0, 1) to B (2,1,2)
04
along the straight-line AB in the force field
2
F x ^i x y ^j y z ^k

(c)
Verify green`s theorem for
2
2xydx y dy where C is the boundary
07
c
of the region bounded by the ellipse
2
2
3x 4y 12


Q.2 (a) Find the Laplace transform of 4t
te
sin 3t .
03

(b)
5s 3
04
Find the inverse Laplace transform of
.
s
1 2
s 2s 5

(c)
Show that the vector field
07
F ysin z sin x ^i xsin z 2yz ^j
2
xy cos z y ^k is
conservative and find the corresponding scalar potential.


OR


(c)
Show that F 2xyz ^i 2
x z 2y
2
^
^
j x y k is irrotational and find a
07
scalar func
Q.3 (a) Find the
tion such that F
grad .
directional derivative of ,
y
f x y xy xe cosxy at the
03
point P(1,0) in the direction of u 3^i 4 ^j .

(b)
1
04
Find the inverse Laplace transform of log 1
.
2
s

(c)
Find the singular solution and general solution of
4
2
y px x p
07


OR

Q.3 (a)
cos at cosbt
03
Find the Laplace transform of
.
t

(b)
3
sinx
04
Show that
x
d
e cos ;
x x 0.
4
4
2
0

(c)
Find the power series solution of y 2xy 0; y(0) 1 near x 0.
07
1

---

Q.4 (a) Find the Laplace transform of t
e 1ut 2
.
03


(b)
2
d x
dx
dx
04
Solve
2
t
x e with x 2,
1
at t 0.
2
dt
dt
dt

(c)
Solve 2
1
x
D
y xe sin x
07

OR

Q.4 (a)
dy
03
Solve
3
2
xsin 2y x cos y
dx

(b)
2
d y
04
Using method of variation of parameter, solve
4y tan 2x .
2
dx

(c)
Using method of undetermined coefficients solve
07
2
d y
dy
2
2
x
y x e .
2
dx
dx
Q.5 (a) Classify the singular points of 2
x y xy 2y 0 .
03

(b)
2
d y
04
Solve
9y sin 2xsin .
x
2
dx

(c)
Solve (i) 3
2
x xy dx 2
3
3
3x y y dy 0.
07
dy
(ii)
y cot x 2cos .
x
dx


OR
Q.5 (a)
2
2
dy
y x y
03
Solve
.
dx
x
(b)
2
d y
dy
04
Solve 2
x
2x
y cos ln x .
2
dx
dx
(c)
Using Frobenius method solve
2
2x y xy x
1 y 0.
07


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