Download PTU B.Tech 2020 March CSE-IT 3rd Sem BTAM 301 18 Mathematics Iii Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech CSE/IT (Computer Science And Engineering/ Information Technology) 2020 March 3rd Sem BTAM 301 18 Mathematics Iii Previous Question Paper

1 | M-76393 (S2)- 748
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(IT) (2018 Batch) (Sem.?3)
MATHEMATICS-III
Subject Code : BTAM-301-18
M.Code : 76393
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 contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
1. Write briefly :
a) Show that the function f (x, y) =
2
4 2
2
?
x y
x y
has no limit as (x, y) approaches (0, 0).
b) Find the local extreme values of the function f (x, y) = x
3
? y
3
? 2xy + 6.
c) Sketch the region of integration for the integral
sin
0 0
?
? ?
x
y dydx
and write an integral with the order of integration reversed.
d) Define convergence of a series and give an example of a convergent series.
e) Explain the limit comparison test.
f) By inspection obtain the integrating factor and solve the differential equation :
xdx = ydy + 2 (x
2
+ y
2
) dx = 0
g) Check whether the following differential equation exact.
(2x + e
y
) dx + xe
y
dy = 0
h) Find the general solution of the differential equation y ? ? + 2y ? + y = 0
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1 | M-76393 (S2)- 748
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(IT) (2018 Batch) (Sem.?3)
MATHEMATICS-III
Subject Code : BTAM-301-18
M.Code : 76393
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 contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
1. Write briefly :
a) Show that the function f (x, y) =
2
4 2
2
?
x y
x y
has no limit as (x, y) approaches (0, 0).
b) Find the local extreme values of the function f (x, y) = x
3
? y
3
? 2xy + 6.
c) Sketch the region of integration for the integral
sin
0 0
?
? ?
x
y dydx
and write an integral with the order of integration reversed.
d) Define convergence of a series and give an example of a convergent series.
e) Explain the limit comparison test.
f) By inspection obtain the integrating factor and solve the differential equation :
xdx = ydy + 2 (x
2
+ y
2
) dx = 0
g) Check whether the following differential equation exact.
(2x + e
y
) dx + xe
y
dy = 0
h) Find the general solution of the differential equation y ? ? + 2y ? + y = 0
2 | M-76393 (S2)- 748
i) Verify whether the linear combination of e
x
and e
?2x
is a solution of the differential
equation
y ? ? + y ? ? 2y = 0
j) Find the Wronskian of the functions x, x
2
and x
3
.

SECTION-B
2. Solve the following integral
2 2
2 2
ln 2 (ln 2)
0 0
?
?
? ?
y
x y
e dxdy
by converting it into an equivalent polar integral.
3. For what values of x does the following power series converge ?
1
1
( 1)
?
?
?
?
?
n
n
n
x
n

4. Solve the differential equation (3x
2
y
3
e
y
+ y
3
+ y
2
) dx + (x
3
y
3
e
y
? xy) dy = 0.
5. Solve the differential equation y ? ? + 4y ? + 4y = e
?2x
sin x by using method of variation of
parameters.
6. Check the convergence of the following series
(i)
1
(2 )!
! !
?
?
?
n
n
n n
(ii)
2
1
ln
?
?
?
n
n n


SECTION-C
7. a) Find the maximum and minimum values of the function f (x, y) = 3x + 4y on the circle
x
2
+ y
2
= 1.
b) Find the volume in the first octant bounded by the coordinate planes and the surface
z = 4 ? x
2
? y.
8. State and prove Leibniz?s test for alternating series.
9. Find the general solution of the equation x
3
y ? ? ? ? 3xy ? + 3y = 16x + 9x
2
ln x.


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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