Download PTU B-Tech CSE-IT 2020 Dec 3rd Sem 76393 Mathematics Iii Question Paper

Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) (CSE-IT)- Computer Science Engineering -Information Technology 2020 December 3rd Sem 76393 Mathematics Iii Previous Question Paper

Roll No.
Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (IT) (2018 Batch) (Sem.?3)
MATHEMATICS-III
Subject Code : BTAM-304-18
M.Code : 76393
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 ontains F IVE questions c arrying FIVE marks eac h and s tud ents
have to atte mpt any FOUR q ues tions.
3 .
SECT ION-C contains THREE questions carrying T EN marks e ach and s tudents
have to atte mpt any T WO questio ns.
SECTION-A
Write briefly :
2
2
x y
1.
Find the first order derivative of f (x, y) =
1
tan
.
w r.t. x
x y
x
2
dydx
2.
Evaluate the integral
2
2
1
x y
0
3.
Give examples of the convergent and divergent sequences.
4.
State Cauchy Root test for convergence of a positive term infinite series.
5.
Write down the Taylor's series expansion for sinh x about x = 0.
6.
Write down the Clairaut's equation and find its solution.
7.
Solve the differential equation : 3ex tan ydx + (1 + ex) sec2 ydy = 0
8.
Check whether the given equation is exact or not, if yes then find solution 2xydx + x2dy = 0
3
2
d y
d y
dy
9.
Solve the differential equation
6
11
6 y 0
3
2
dx
dx
dx
2
d y
dy
10. Find Particular integral for
3
6
9
x
y e .
2
dx
dx
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SECTION-B
11. Find the dimensions of the rectangular box, open at the top of maximum capacity whose
surface is 432 sq. cm.
12. Find the area bounded by the parabola y = x2 and the line y = 2x + 3.
13. For what value(s) of x does the series converge (i) conditionally (ii) absolutely?
( 1
)n(x 2)n
.
Also find the interval of convergence
n
n 1
n2
14. Solve the differential equation :
(x2 + y2 + 3) dx ? 2xydy = 0
2
d y
dy
15. Solve the differential equation
3
3
2
x
y xe
sin 2x
2
dx
dx
SECTION-C
n!2n
16. a) Check the convergence of the series
n
n
n2
2
2
2
x
y
z
b) Find the volume of the ellipsoid
1
2
2
2
a
b
c
dy
17. a) Solve the differential equation
3
2
xsin 2 y x cos y
dx
dy
b) Solve the differential equation p2 + xp + py + xy = 0, where p
dx
2
d y
dy
18. a) Solve by Method of Variation of parameters
2
x
y e
cos x
2
dx
dx
2
d y
dy
b) Solve 2
x
x
y sin (ln x)
2
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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