PTU B.Tech Industry Engineering 1st Semester May 2019 61004 APPLIED MATHEMATICS Question Papers

PTU Punjab Technical University B-Tech May? 2019 Question Papers 1st Semester May Industry Engineering

Roll No.
Total No. of Pages : 02
Total No. of Questions : 07
B.Tech. Ind. Engg. & Mgt. (Spl. in TQM) (Sem.?1)
APPLIED MATHEMATICS
Subject Code : IEM-104
M.Code : 61004
Time : 3 Hrs. Max. Marks : 40

INSTRUCTIONS TO CANDIDATES :
1.
Attempt Any EIGHT questions from SECT ION-A carrying T WO marks each.
2.
Attempt any FOUR questions out of SIX questions from SECTION-B carrying SIX
marks each.





SECTION-A
1.
Answer briefly :

a) If 10x = 3 find the value of x.
1

b) Find sin75?, if sin 45? =
, and sin30? = ?.
2

c) Find the coordinates of the point which divides the join of points (1, 2) and (3, 5) in

ratio 1:2 internally.
1

4
2

d) Find the value of the determinant 2
2

3

.
1

6

2


e) Find the angle between the vectors v = i - j + k and w = ? i + 2k.
dy

f) Find
2
2
, if y (x 1) x
e .
dx
2

g) Evaluate the integral
x
e x
.
dx


dy

h) Solve the differential equation
3
y
x e .
dx

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i) Expand(x2+2a)4 using Binomial Theorem.


j) Write down the Polar equivalent of 1?i.

SECTION-B
1
2.
Prove that : sin sin(60? ? ) sin(60? + ) =
sin 3 .
4
3.
Find the length of major and minor axis, coordinate of the vertices and the foci, eccentricity
and length of latus rectum of the ellipse : y2 + 36x2 = 36.
4.
The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs. 60. The cost of 2 kg onion, 4 kg
wheat and 6 kg rice is Rs. 90. The cost 6 kg onion, 2 kg wheat and 3 kg rice is Rs. 70. Find
the cost of each item by matrix or determinant method.
5.
A circular disc of radius 4 cm is being heated. Due to thermal expansion, its area increases
at a rate of 12cm2/s. Find the rate at which radius is increasing.
2x
6.
Find the value of integral
d .
x


2
x 3x 2
7.
Find the area of the region bounded by the curve y = x2 and the lines x = l, x = 4 and
x ? axis.




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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