Download Visvesvaraya Technological University (VTU) BE ( Bachelor of Engineering) Civil Engineering 17 Scheme 2020 January Previous Question Paper 3rd Sem 17MATDIP31 Additional Mathematics I
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17MATDIP31
Third Semester B.E. Degree Examination, Dec.2019/Jan.2020
Additional Mathematics - I
Time: 3 hrs. Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.
Module-1
1 a. Find the modulus and amplitude of
3+i
2+i
x
i lf x = cos? + sinO, then show that = tan nO .
xr + 1
(cos30 + i sin 30)
4
(cos40 + i sin 40)
5
C. Simplify
(cos40 + i sin 40)
3
(cos50 + i sin 50)
-4
OR
(07 Marks)
(07 Marks)
(06 Marks)
a.
b.
c.
a.
b.
c.
a.
b.
C.
Find the sine
Find the value
are coplanar.
Prove that
Find the n
th
If y = a cos(log
If u = sin
-1
Find the pedal
Expand log
e
(
If x = r cos0,
of the angle
of X. , so
a x (f) x c)
derivative
x) +
1 _
X - y
between A = 21+ 2j ? k and B = 6i ?33+ 2k .
that the vectors a = 2i ?3j+ k , o = i + 2] ?3K and c
+ b x (c x + c x (a x = 0 .
Module-2
(07 Marks)
= i +
(07 Marks)
(06 Marks)
(07 Marks)
= 0.
(07 Marks)
(06 Marks)
(07 Marks)
(07 Marks)
(06 Marks)
of e" cos(bx + c).
b sin(log x) prove that x
2
y?,
2
+ (2n +1)xy,,_,. + (n
2
+1)y.,
a
u
a
u
, prove that x ? + y? = tan u.
ox ay
OR
of r= cos nO.
ascending powers of x as for as the term containing x
4
.
3(x,y)
find
x + y
equation
I + x) in
y = r sin?,
?(r, 0)
Module-3
y
5 a. Evaluate 1(1+ xy
2
)dx dy
b. Evaluate J sin
4
X cos
`'
x dx
c. Evaluate .\,
4
f
2
dx
(07 Marks)
(07 Marks)
(06 Marks)
USN
1 of 2
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17MATDIP31
Third Semester B.E. Degree Examination, Dec.2019/Jan.2020
Additional Mathematics - I
Time: 3 hrs. Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.
Module-1
1 a. Find the modulus and amplitude of
3+i
2+i
x
i lf x = cos? + sinO, then show that = tan nO .
xr + 1
(cos30 + i sin 30)
4
(cos40 + i sin 40)
5
C. Simplify
(cos40 + i sin 40)
3
(cos50 + i sin 50)
-4
OR
(07 Marks)
(07 Marks)
(06 Marks)
a.
b.
c.
a.
b.
c.
a.
b.
C.
Find the sine
Find the value
are coplanar.
Prove that
Find the n
th
If y = a cos(log
If u = sin
-1
Find the pedal
Expand log
e
(
If x = r cos0,
of the angle
of X. , so
a x (f) x c)
derivative
x) +
1 _
X - y
between A = 21+ 2j ? k and B = 6i ?33+ 2k .
that the vectors a = 2i ?3j+ k , o = i + 2] ?3K and c
+ b x (c x + c x (a x = 0 .
Module-2
(07 Marks)
= i +
(07 Marks)
(06 Marks)
(07 Marks)
= 0.
(07 Marks)
(06 Marks)
(07 Marks)
(07 Marks)
(06 Marks)
of e" cos(bx + c).
b sin(log x) prove that x
2
y?,
2
+ (2n +1)xy,,_,. + (n
2
+1)y.,
a
u
a
u
, prove that x ? + y? = tan u.
ox ay
OR
of r= cos nO.
ascending powers of x as for as the term containing x
4
.
3(x,y)
find
x + y
equation
I + x) in
y = r sin?,
?(r, 0)
Module-3
y
5 a. Evaluate 1(1+ xy
2
)dx dy
b. Evaluate J sin
4
X cos
`'
x dx
c. Evaluate .\,
4
f
2
dx
(07 Marks)
(07 Marks)
(06 Marks)
USN
1 of 2
1 7 M ATD1 P31
OR
24
6 a. Evaluate J Sky + eY dydx
L 3
b. Evaluate fx sin
s
x dx
2 1 1
c. Evaluate (x
2
+ y
2
+ z
2
)dxdydz
(07 Marks)
(07 Marks)
(06 Marks)
Module-4
7 a. If particle moves on the curve x = 2t
-
, y = t
2
- 4t, z = 3t ? 5 where t is the time. Find the
velocity and acceleration at t = 1. (07 Marks)
b. Find the angle between the tangents to the curve r = t
2
2t j ? t
3
k at the point t = ? 1.
(07 Marks)
c.
If /'=(3x
2
y ? z)i+(xz
3
+ y
4
)] ?2x
3
z
2
k find grad(div ) at (2, ?1, 0). (06 Marks'
OR
8 a.
Find the directional derivative of (I) = 4xz
3
3x
2
y
2
z at (2, ?1, 2) along 21? 3 3+ 6IC
b.
c.
9 a.
b.
c.
10 a.
b.
c.
Find the unit normal to the surface x
2
y + 2xz = 4 at (2, ?2, 3).
Show that fs = (2xy
2
+ yz)i + (2x
2
y + xz + 2yz
2
)] + (2y
2
z + xy)k is irrotational.
(07 Marks)
(07 Marks)
(06 Marks)
NIoduie-5
Solve ?
dy
= sin( x + y)
dx
(07 Marks)
Solve
dy
? + y cot x = cos x
dx
(07 Marks)
Solve (x ? y + 1)dy ? (x + y 1)dx = 0 (06 Marks)
(
x
OR
Solve + e'
4
)dx + e" 1 dy = 0 . (07 Marks)
Y.
Solve (x
3
cos
2
y ? x sin 2y) dx = dy . (07 Marks)
Solve (3x
2
y
4
+ 2xy)dx + (2x
3
y
3
? x
2
)dy = 0 (06 Marks)
2 oft
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This post was last modified on 02 March 2020