Download PTU B-Tech CSE-IT 2020 Dec 3rd Sem 76438 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 76438 Mathematics Iii Previous Question Paper

Roll No.
Total No. of Pages : 03
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
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
Solve the following :
2x y
1.
Show that the limit for the function f (x, y) =
does not exists as (x, y) (0,0).
2x y
x
1
2.
Evaluate the integral
y/ x
e
dydx
0 0
3.
Check the convergence of the following sequences whose nth term is given by
n
an
2
n 1

4.
State Leibnitz test for convergence of an alternating series x
2

5.
Write down the Taylor's series expansion for cos x about x
.
2
dy
6.
Solve by reducing into Clairaut's equation: y = px + p2, where p =
dx
dy
7.
Solve the differential equation
y x
dx
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8.
Determine whether the differential equation is exact, if found exact solve it.
(x2 + y2) dx + 2xydy = 0
2
d y
dy
9.
Solve the differential equation 16
8
5 y 0
2
dx
dx
10. Find Particular solution of the differential equation :
2
d y
dy
3
3
2
x
y e
2
dx
dx
SECTION-B
11. Find the maximum and minimum distance of the point (1, 2, ?1) from the sphere x2 + y2 +
z2 = 24.
2
2
12. Evaluate
(x y )
e
dydx
, where D is the region bounded x2 + y2 = 1
D
13. For what value(s) of x does the series converge (i) conditionally (ii) absolutely?
2
3
x
x
x
to . Also find the interval of convergence.
2
3
14. Solve the differential equation by finding integrating factor
(xy + 1) ydx + x(l + xy + x2y2)dy = 0
2
d y
dy
15. Solve the differential equation
3
3
2
x
y xe
sin 2x
2
dx
dx
SECTION-C
1
16. a) Show that the series
converges for p > 1 and diverges for 0 < p 1.
p
n
n 1
b) Using double integration, find the area bounded between the parabolas y2 = 4ax and
x2 = 4ay.
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dy
y
y
17. a) Solve the Bernoulli's equation
y
2
dx
x
x
dy
b) Solve the differential equation xp2 ? 2yp + x = 0, where p
dx
18. a) Solve by Method of Variation of parameters
2
2x
d y
dy
e
4
4 y
2
dx
dx
x
2
d y
dy
b) Find the complete solution of
2
5
6
x
y e
sin 2x
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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