Download PTU B-Tech Industrial Engineering 2020 Dec 1st Sem 61004 Applied Mathematics Question Paper

Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) (IE)- Industrial Engineering 2020 December 1st Sem 61004 Applied Mathematics Previous Question Paper

Roll No.
Total No. of Pages : 02
Total No. of Questions : 16
B.Tech. (Ind. Engg. & Mgt. (TQM) (Sem.?1)
APPLIED MATHEMATICS
Subject Code : IEM-104
M.Code : 61004
Time : 3 Hrs. Max. Marks : 40
INST RUCT IONS T O CAND IDAT ES :
1 .
Attempt a ny EIGHT out of TEN Question s from SECT ION - A ca rryin g THREE
marks eac h.
2 .
Attempt any FOUR out o f SIX question s from SECT ION-B carry in g NINE mark s
each.
SECTION-A
1.
Evaluate sin 225?.
2.
Find the area of the triangle formed by the lines joining the vertex of the parabola x2 ? 12y
to the ends of its latus rectum
3.
Differentiate (log x)cos x w.r.t x.
4.
Find all vectors of magnitude 10 3 that are perpendicular to the plane of i 2 j k and
i 3 j 4 k .
3
2
1
0
5.
If A
and I = A
. Find k so that A2 = kA ? 2I.
4
2
0 1
1 2
6.
If A
is a singular matrix, then find k.
4
k
7.
(a) Evaluate (4x3 ? 9x2 + 7x + 3) e?x dx.
(b) Evaluate (4x3 ? 9x2 + 7x + 3) e?x dx.
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8.
A wheel makes 270 revolutions in one minute. Through how many radians does it turn in
one-second ?
9.
A particle moves along the x-axis. The function x (t) gives the particle's position at anytime
t 0, x (t) = t3 ?3t2 + 7t ? 6. What is the particle's acceleration a (t) at t = 3.
sin 3x
10. Evaluate lim
.
x 0
5x
SECTION-B
11. If three consecutive coefficients in the bionomial expansion of (1 + x)n are in the ratio 6 :
33 : 110, find n and the rth term of this Binomial expansion.
12. The moon's distance from the earth is 385000 kms and its diameter subtends an angle of
31' at the eye of the observer. Find the diameter of the moon.
1
2
2
13. If A
2 1
2
is a matrix satisfying AAT = 9I3, then find the values of a and b.
a
2
b
14. Using vectors, prove that the perpendiculars from the vertices to the opposite sides
(altitudes) of a triangle are concurrent.
1
x sin
x
15. Evaluate
d .
x
2
1 x
16. Find the area of the region bounded by the curves y2 = 4ax and x2 = 4ay, a > 0.
NOTE : Disclosure of Identity by writing Mobile No. or Marking of passing request on any
paper of Answer Sheet will lead to UMC against the Student.
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