Download PTU B.Tech 2021 Jan CSE 3rd Sem 76438 Mathematics Iii Question Paper

Download PTU (Punjab Technical University) B.Tech (Bachelor of Technology) / BE (Bachelor of Engineering) 2021 January CSE 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 :
2
2
x y
1.
Show that the limit for the function f ( x, y )
does not exists as (x, y) (0, 0).
2
2
x y
1
z
x z
2.
Evaluate the integral
dydxdz.
1
0
x z
3.
Check the convergence of the following sequences whose nth term is given by
n
3n 1
an =
.
3n 1
4.
State Cauchy Integral test for convergence of a positive term infinite series.
5.
Write down the Taylor's series expansion for sin x about
x
.
2
dy
6.
Solve by reducing into Clairaut's equation : p = log(px ? y), where p
.
dx
dy
7.
Solve the differential equation
y cot x x cosec x
dx
8.
Determine whether the differential equation is exact
(x2 + y2 + 2x)dx + 2ydy = 0
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2
d y
dy
9.
Solve the differential equation
y 0
2
dx
dx
2
d y
dy
10. Find Particular integral for
2
x
y e
2
dx
dx
SECTION-B
11. Using Method of Lagrange Multipliers, find the maximum and minimum distance of the
point (3, 4, 12) from the sphere x2 + y2 + z2 = 1.
a
a
x
12. Solve by changing order of integration :
dxdy
, a is any positive constant.
0
y
2
2
x y
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 :
(xy3 + y)dx + 2 (x2y2 + x + y4)dy = 0
2
d y
dy
15. Solve the differential equation
3
3
2
x
y xe
sin 2 x.
2
dx
dx
SECTION-C
n 1 n
16. a) Check the convergence of the series
.
3/2
n2
n
b) Find by double integration, the area lying inside the circle r = a sin and outside the
cardiode r = a (1 ? cos ).
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dy
x
17. a) Solve the differential equation
y x y .
dx
2
1 x
dy
b) Solve the differential xyp2 ? (x2 + y2) p + xy = 0, where p =
.
dx
2
d y
18. a) Solve by Method of Variation of parameters
y sec x.
2
dx
2
d y
dy
b) Solve (1 + x)2
(1 x )
y cos ln(1 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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