Download PTU B.Tech 2020 March Civil 1st and 2nd Sem AM 101 Applied Mathematics I Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech Civil Engineering (CE) 2020 March 1st and 2nd Sem AM 101 Applied Mathematics I Previous Question Paper

1 | M-54001 (S1)-2724

Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech (CSE/CE/IT/ECE/Civil/ME/EIE/EEE/EE) (Sem.?1)
ENGG. MATHEMATICS/ENGG. MATHEMATICS-I/APPLIED
MATHEMATICS-I
Subject Code : AM-101
M.Code : 54001
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION - B & C. have FOUR questions each.
3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.

SECTION-A
l. Write short notes on :
a) Give the formula for curvature of parametric curves.
b) Give the formula for centre of gravity.
c) If u = e
xyz
, then find
u
x
?
?
.
d) If u = yx
2
, x = at
2
, y = 2at, then find
dz
dt
.
e) Write Taylor?s series for a function of two variables.
f) Give the standard equation of paraboloid.
g) Give the expression of Beta function.
h) Write the formula for integral test for convergence of infinite series.
i) Find the modulus of ( 1 3)(1 ) i i ? ? ? .
j) Find the value of u, if u + iv = cos
4
i
? ? ?
? ?
? ?
? ?
.

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1 | M-54001 (S1)-2724

Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech (CSE/CE/IT/ECE/Civil/ME/EIE/EEE/EE) (Sem.?1)
ENGG. MATHEMATICS/ENGG. MATHEMATICS-I/APPLIED
MATHEMATICS-I
Subject Code : AM-101
M.Code : 54001
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION - B & C. have FOUR questions each.
3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.

SECTION-A
l. Write short notes on :
a) Give the formula for curvature of parametric curves.
b) Give the formula for centre of gravity.
c) If u = e
xyz
, then find
u
x
?
?
.
d) If u = yx
2
, x = at
2
, y = 2at, then find
dz
dt
.
e) Write Taylor?s series for a function of two variables.
f) Give the standard equation of paraboloid.
g) Give the expression of Beta function.
h) Write the formula for integral test for convergence of infinite series.
i) Find the modulus of ( 1 3)(1 ) i i ? ? ? .
j) Find the value of u, if u + iv = cos
4
i
? ? ?
? ?
? ?
? ?
.

2 | M-54001 (S1)-2724

SECTION-B
2. Write complete steps for the tracing of any Cartesian curve.
3. Find the area bounded by the curve a
4
y
2
= x
4
(a
2
? x
2
).
4. If u = sin
?1

2 2
x y
x y
? ?
? ?
? ?
?
? ?
, the using Euler?s theorem prove that 3tan
u u
x y u
x y
? ?
? ?
? ?
.
5. Find the equations of tangent and normal to the curve y = 2x
2
? 4x + 5 at (3, 11).

SECTION-C
6. Find the equation of sphere through the points (2, 0, 1), (1, ?5, ?1), (0, ?2, 3) and (4, ?1,
2).
7. Evaluate the integral
2
2
2 2
1 2
2
y
y
x y dxdy
?
? ?
? ?
.
8. Test the convergence of the series
( 1)!
3
n
n ?
?
.
9. Simplify
8
1 sin cos . 1 sin cos
8 8 8 8
i i
? ?
? ? ? ? ? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
using De-Moivre?s theorem.






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page of Answer Sheet will lead to UMC against the Student.
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