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Be first-year-fe-engineering semester-2 2022 may engineering-mathematics-ii-pattern-2019
M2 TEXTBOOK NIRALI PUBLICATION
Course
BE IT (2019) (414442)
234 Documents
Students shared 234 documents in this course
University
Savitribai Phule Pune University
Academic year: 2023/2024
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Total No. of Questions : 9]
[5868]-
First Year Engineering
ENGINEERING MATHEMATICS - II
(2019 Pattern) (Semester - I & III) (107008)
Time : 2Ω Hours] [Max. Marks : 70
Instructions to the candidates:
1) Q. 1 is compulsory.
2) Solve Q or Q, Q or Q, Q or Q, Q, or Q.
3) Neat diagrams must be drawn whenever necessary.
4) Figures to the right indicate full marks.
5) Use of electronic pocket calculator is allowed.
6) Assume suitable data if necessary.
P6492 [Total No. of Pages : 4
SEAT No. :
Q1) Write the correct option for the following multiple choice questions.
a)
2
6
0
cos x
[2]
i)
5
16
ii)
5
32
iii)
16
10
iv)
5
48
b) The curve
2 2
y x a x 2 a x is [2]
i) Symmetric about X - axis and net passing through origin
ii) Symmetric about Y - axis and net passing through origin
iii) Symmetric about X - axis and passing through origin
iv) Symmetric about Y - axis and passing through origin
c) The value of double integral
1 1
2 2
0 0
1
is
1 1
dx dy
x y
[2]
i)
2
ii)
2
2
iii)
2
4
iv)
2
16
P.T.
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[5868]-109 2
d) The Centre (C) and radius (r) of the sphere
2 2 2
x y z 2 y 4 z 11 0
are [2]
i) C 0,1, 2 ; r 4 ii) C 0, 1, 2 ; r 2
iii) C 0, 2, 4 ; r 4 iv) C 0,1, 2 ; r 2
e) The number of loops in the rose curve r = a cos 4 θ are [1]
i) 2 ii) 4
iii) 6 iv) 8
f)
R
dxdyrepresents [1]
i) Volume ii) Centre of gravity
iii) Moment of inertia iv) Area of region R
Q2) a) If In
2
4
cot
n
d
prove that 2
1
I I
1
n n
n
. [5]
b) Show that
1
1 2 1
0
1
1 ,
2 2
m n m
x x dx n
. [5]
c) Prove that
1
0
1
log 1 , 0
log
a
x
dx a a
x
. [5]
OR
Q3) a) If In
2
0
sin
n
x x dx
then prove that In
1
1 I 2.
2
n
n n n n
[5]
b) Show that
2 2
0 2
h x
e dx
h
. [5]
c) Show that [5]
2
2
b
x
a
e dx erf b erf a
OR
CEGP
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CEGP
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CEGP
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[5868]-109 4
Q8) a) Change the order of integration and evaluate
0
sin
.
x
y dx dy
y
[5]
b) Find the area of one loop of r asin 2. [5]
c) Find the moment of inertia of one loop of the lemniscate
2 2
r acos2
about initial line. Given that
2
2
,
m m
a
is the mass of loop of lemniscate.
[5]
OR
Q9) a) Evaluate
1
ydxdyover the region enclosed by the parabola x 2 y,and
the line y x 2. [5]
b) Evaluate
2
x yzdxdydz, throughout the volume bounded by the plane
x 0, y 0, z 0 1
x y z
a b c
. [5]
c) Find the y - coordinate of the centre of gravity of the area bounded by
r a sin and r 2 sina . Given that the area bounded by these curves
is
2
3
4
a. [5]
CEGP
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CEGP
49.248.216 11/08/2022 08:31:11 static-
CEGP
49.248.216 11/08/2022 08:31:11 static-
Was this document helpful?
Be first-year-fe-engineering semester-2 2022 may engineering-mathematics-ii-pattern-2019
Course: BE IT (2019) (414442)
234 Documents
Students shared 234 documents in this course
University: Savitribai Phule Pune University
Was this document helpful?
Total No. of Questions : 9]
[5868]-109
First Year Engineering
ENGINEERING MATHEMATICS - II
(2019 Pattern) (Semester - I & III) (107008)
Time : 2½ Hours] [Max. Marks : 70
Instructions to the candidates:
1) Q.No. 1 is compulsory.
2) Solve Q.2 or Q.3, Q.4 or Q.5, Q.6 or Q.7, Q.8, or Q.9.
3) Neat diagrams must be drawn whenever necessary.
4) Figures to the right indicate full marks.
5) Use of electronic pocket calculator is allowed.
6) Assume suitable data if necessary.
P6492 [Total No. of Pages : 4
SEAT No. :
Q1) Write the correct option for the following multiple choice questions.
a)
2
6
0
cos
x
[2]
i) 5
16 ii) 5
32
iii) 16
10
iv) 5
48
b) The curve
2 2 2y x a x a x is [2]
i) Symmetric about X - axis and net passing through origin
ii) Symmetric about Y - axis and net passing through origin
iii) Symmetric about X - axis and passing through origin
iv) Symmetric about Y - axis and passing through origin
c) The value of double integral
1 1
2 2
0 0
1 is
1 1
dx dy
x y
[2]
i) 2
ii)
2
2
iii)
2
4
iv)
2
16
P.T.O.
CEGP013091
49.248.216.238 11/08/2022 08:31:11 static-238
CEGP013091
49.248.216.238 11/08/2022 08:31:11 static-238
CEGP013091
49.248.216.238 11/08/2022 08:31:11 static-238
