Download PTU B.Tech 2021 Jan IT 3rd Sem 76393 Mathematics Iii Question Paper

Download PTU (Punjab Technical University) B.Tech (Bachelor of Technology) / BE (Bachelor of Engineering) 2021 January IT 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 brief :
1.
Express w/r and w/s in terms of r and s if
w = x + 2y + z2, x = r , y = r2 + ln s, z = 2r
s
2.
Show that the function
2 xy
( x , y ) ( 0, 0)
2
2
f ( x , y ) x y
0
( x, y ) ( 0, 0)
is not continuous at origin.
3.
Find the local extreme values of the function f (x, y) = x3 + y3 + 3x2 ? 3y2 ? 8
4.
Define convergence of a sequence and give an example of a convergent sequence.
5.
State Leibniz's test for alternating series.
6.
Determine for what values of a and b, the following differential equation is exact.
(y + x3)dx + (ax + by3)dy = 0
7.
Find the integrating factor for the following differential equation
(5x3 + 12x2 + 6y2)dx + 6xydy = 0
1 | M-76393
(S2)- 540

---

8.
Give an example of a fourth order linear differential equation.
9.
Find the solution of the differential equation y ? 4y ? 12y = 0
10. If y1 and y2 are two linearly independent solutions of a second order linear differential
equation, then what can you say about the general solution of this equation. Justify your
answer.
SECTION-B
11. Find the volume of the region in the first octant bounded by the coordinate planes and the
planes x + z ? 1 and y + 2z = 2.
12. For what values of x does the following power series converge ?
2 n 1
n 1
x
( 1)
2 n 1
n 1
13. Obtain the general solution and singular solution of the non-linear equation
y = xy ? (y)3.
14. Solve the differential equation y + 16y = 32 sec 2x by using method of variation of
parameters.
15. If
| a |
n converges, then show that
a
n also converges. Is the converse also true?
n 1
n 1
Justify your answer.
SECTION-C
16. Find the extreme, values of the function f (x, y, z) = x2 + y2 + z2 subject to the constraints
x2 + y2 ? 1 = 0 and x + y + z = 1.
ln n
1
8 tan
n
17. Test the convergence of the series (i)
( 1) n
(ii)
n ln n
2
n 1
1 1
n
n
18. Find the general solution of the equation y ? 4y + 13y = 18e2x sin 3x.
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.
2 | M-76393
(S2)- 540

---