Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech CSE/IT (Computer Science And Engineering/ Information Technology) 2020 March 3rd Sem BTAM304 18 Mathematics Iii Previous Question Paper
Roll No. Total No. of Pages : 02
Total No. of Questions : 18
B.Tech.(CSE) (2018 Batch) (Sem.?3)
MATHEMATICS-III
Subject Code : BTAM304-18
M.Code : 76438
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
Solve the following :
1) Evaluate the limit for the function f (x, y) =
2
2
?
?
x y
x y
if exists as (x, y) ? (0, 0)
2) Evaluate the integral
2
1 1 1
0 0
? ?
? ? ?
y x
y
xdzdxdy
3) Check the convergence of the following sequences whose nth term is given by
2
2
1
1
?
?
?
n
n
a
n
.
4) State Leibnitz test for convergence of an alternating series.
5) Write down the Taylor?s series expansion for ln (1 + x) about x = 0.
6) Define Clairaut?s equation and obtain its general solution.
7) Solve the differential equation
sin
tan 3
?
? ?
x
dy
y x e
dx
8) Define Exact differential equation and obtain the necessary condition for M (x, y) dx + N
(x, y) dy = 0 to be exact.
9) Solve the differential equation
2
2
14 49 0 ? ? ?
d y dy
y
dx
dx
10) Find particular integral for
2
2
2
? ?
d y
y x
dx
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1 | M-76438 (S2)- 751
Roll No. Total No. of Pages : 02
Total No. of Questions : 18
B.Tech.(CSE) (2018 Batch) (Sem.?3)
MATHEMATICS-III
Subject Code : BTAM304-18
M.Code : 76438
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
Solve the following :
1) Evaluate the limit for the function f (x, y) =
2
2
?
?
x y
x y
if exists as (x, y) ? (0, 0)
2) Evaluate the integral
2
1 1 1
0 0
? ?
? ? ?
y x
y
xdzdxdy
3) Check the convergence of the following sequences whose nth term is given by
2
2
1
1
?
?
?
n
n
a
n
.
4) State Leibnitz test for convergence of an alternating series.
5) Write down the Taylor?s series expansion for ln (1 + x) about x = 0.
6) Define Clairaut?s equation and obtain its general solution.
7) Solve the differential equation
sin
tan 3
?
? ?
x
dy
y x e
dx
8) Define Exact differential equation and obtain the necessary condition for M (x, y) dx + N
(x, y) dy = 0 to be exact.
9) Solve the differential equation
2
2
14 49 0 ? ? ?
d y dy
y
dx
dx
10) Find particular integral for
2
2
2
? ?
d y
y x
dx
2 | M-76438 (S2)- 751
SECTION-B
11) Find the minimum value of the function x
2
+ y
2
+ z
2
subjected to x + y + z = 3a.
12) Evaluate
2 2
( )
0 0
? ?
? ?
? ?
x y
e dydx , by changing into polar coordinates.
13) Discuss the convergence of the series :
2 2 2 2 2 2
2 2 2 2 2 2
1 1 5 1 5 9
.....
4 4 8 4 8 12
? ? ? to ?
14) Solve the differential equation :
3
1
2 2
( ) 0 ? ? ?
x
xy e dx x ydy
15) Solve the differential equation
2
3
2
6 13 sin 4 ? ? ?
x
d y dy
y e x
dx
dx
SECTION-C
16) a) Find the interval of convergence for the infinite series :
3 5
? .....to
3 5
x x
x ? ? ? .
b) Find the area bounded by the parabola y = x
2
and line y = 2x + 3
17) a) Solve the differential equation
3 2
sin 2 cos ? ?
dy
x y x y
dx
.
b) Solve the differential equation xp
2
? 2yp + x = 0, where ?
dy
p
dx
18) a) Apply method of variation of parameters to solve
2
2
2 2 tan
x
d y dy
y e x
dx
dx
? ? ? ,
b) Solve
2
2
2
3 5 sin (ln ) ? ? ?
d y dy
x x y x
dx
dx
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 21 March 2020