Download PTU B.Tech 2020 March IE 1st Sem Applied Mathematics Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech IE (Industrial Engineering and Management) 2020 March 1st Sem Applied Mathematics Previous Question Paper

1 | M-61004 (S109)-2514

Roll No. Total No. of Pages : 02
Total No. of Questions : 07
B.Tech. (Ind. Engg. & Mgt. (Spl. in TQM)) PT (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 SECTION-A carrying TWO marks each.
2. Attempt any FOUR questions out of SIX questions from SECTION-B carrying SIX
marks each.

SECTION-A
l. Attempt the following :
a) Solve the quadratic equation
2
2 12 0 x ix ? ? ? .
b) Prove that 2 sin
2

2 2
7 3
cos cos
6 6 3 2
ec
? ? ?
? ? .
c) Two lines passing through point (2, 3) intersect each other at an angle of 60?. If the
slope of one line is 2, find the equation of other line.
d) Find the equation of ellipse whose directrix is x ? y + 3 = 0, focus (?1, 1) and
eccentricity is 1/2.
e) Define scalar matrix.
f) If 2 2 , a i j k
? ? ? ?
? ? ? 6 3 2 b i j k
? ? ? ?
? ? ? find a b
? ?
? and a vector ? to both and a b
? ?
. Also
determine sine of angle between and a b
? ?
.
g) Differentiate
1 tan
1 tan
x
x
? ? ?
? ?
?
? ?
w.r.t. x.
h) Find gradient of a curve.
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1 | M-61004 (S109)-2514

Roll No. Total No. of Pages : 02
Total No. of Questions : 07
B.Tech. (Ind. Engg. & Mgt. (Spl. in TQM)) PT (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 SECTION-A carrying TWO marks each.
2. Attempt any FOUR questions out of SIX questions from SECTION-B carrying SIX
marks each.

SECTION-A
l. Attempt the following :
a) Solve the quadratic equation
2
2 12 0 x ix ? ? ? .
b) Prove that 2 sin
2

2 2
7 3
cos cos
6 6 3 2
ec
? ? ?
? ? .
c) Two lines passing through point (2, 3) intersect each other at an angle of 60?. If the
slope of one line is 2, find the equation of other line.
d) Find the equation of ellipse whose directrix is x ? y + 3 = 0, focus (?1, 1) and
eccentricity is 1/2.
e) Define scalar matrix.
f) If 2 2 , a i j k
? ? ? ?
? ? ? 6 3 2 b i j k
? ? ? ?
? ? ? find a b
? ?
? and a vector ? to both and a b
? ?
. Also
determine sine of angle between and a b
? ?
.
g) Differentiate
1 tan
1 tan
x
x
? ? ?
? ?
?
? ?
w.r.t. x.
h) Find gradient of a curve.
2 | M-61004 (S109)-2514

i) Evaluate
2
2
0
(2 3 1) x x ? ?
?
by second fundamental theorem.
j) Find the maximum and minimum value of the function f (x) = sin 2x + 5

SECTION-B
2. Prove that tan ? + 2 tan 2 ? + 4 tan 4 ? + 8 cot 8 ? = cot ?.
3. Using matrices solve the system of equations for x, y and z
x + 2y ? 3z = 6
3x + 2y ? 2z = 3
2x ? y + z = 2
4. In binomial expansion of (1 + x)
n
, coefficients of fifth, sixth and seventh terms are in A.P.
Find all possible values of n.
5. Differentiate (x
tanx
+ (sinx)
cosx
) w.r.t. x.
6. Evaluate
0
cos 2 log sin x xdx
?
?
.
7. Solve y ? ? 2y = cos3x.




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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