Download VTU BE 2020 Jan CSE Question Paper 17 Scheme 3rd Sem 17MATDIP31 Additional Mathematics I

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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

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3+i
2+i
x
i lf x = cos? + sinO, then show that = tan nO .
xr + 1

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(cos30 + i sin 30)
4
(cos40 + i sin 40)
5

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C. Simplify
(cos40 + i sin 40)
3
(cos50 + i sin 50)
-4

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OR
(07 Marks)
(07 Marks)
(06 Marks)

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a.
b.
c.
a.
b.

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c.
a.
b.
C.
Find the sine

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Find the value
are coplanar.
Prove that
Find the n
th

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If y = a cos(log
If u = sin
-1

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Find the pedal
Expand log
e
(
If x = r cos0,

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of the angle
of X. , so
a x (f) x c)
derivative
x) +

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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 .

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Module-2
(07 Marks)
= i +
(07 Marks)
(06 Marks)

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(07 Marks)
= 0.
(07 Marks)
(06 Marks)
(07 Marks)

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(07 Marks)
(06 Marks)
of e" cos(bx + c).
b sin(log x) prove that x
2

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y?,
2
+ (2n +1)xy,,_,. + (n
2
+1)y.,

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a
u
a
u

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, prove that x ? + y? = tan u.
ox ay
OR
of r= cos nO.
ascending powers of x as for as the term containing x

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4
.
3(x,y)
find
x + y

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equation
I + x) in
y = r sin?,
?(r, 0)
Module-3

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y
5 a. Evaluate 1(1+ xy
2
)dx dy
b. Evaluate J sin

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4
X cos
`'
x dx
c. Evaluate .\,

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4
f
2
dx
(07 Marks)

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(07 Marks)
(06 Marks)
USN
1 of 2
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2
3
4
17MATDIP31
Third Semester B.E. Degree Examination, Dec.2019/Jan.2020

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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

--- Content provided by‍ FirstRanker.com ---

3+i
2+i
x
i lf x = cos? + sinO, then show that = tan nO .
xr + 1

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(cos30 + i sin 30)
4
(cos40 + i sin 40)
5

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C. Simplify
(cos40 + i sin 40)
3
(cos50 + i sin 50)
-4

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OR
(07 Marks)
(07 Marks)
(06 Marks)

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a.
b.
c.
a.
b.

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c.
a.
b.
C.
Find the sine

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Find the value
are coplanar.
Prove that
Find the n
th

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If y = a cos(log
If u = sin
-1

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Find the pedal
Expand log
e
(
If x = r cos0,

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of the angle
of X. , so
a x (f) x c)
derivative
x) +

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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 .

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Module-2
(07 Marks)
= i +
(07 Marks)
(06 Marks)

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(07 Marks)
= 0.
(07 Marks)
(06 Marks)
(07 Marks)

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(07 Marks)
(06 Marks)
of e" cos(bx + c).
b sin(log x) prove that x
2

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y?,
2
+ (2n +1)xy,,_,. + (n
2
+1)y.,

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a
u
a
u

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, prove that x ? + y? = tan u.
ox ay
OR
of r= cos nO.
ascending powers of x as for as the term containing x

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4
.
3(x,y)
find
x + y

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equation
I + x) in
y = r sin?,
?(r, 0)
Module-3

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y
5 a. Evaluate 1(1+ xy
2
)dx dy
b. Evaluate J sin

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4
X cos
`'
x dx
c. Evaluate .\,

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4
f
2
dx
(07 Marks)

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(07 Marks)
(06 Marks)
USN
1 of 2
1 7 M ATD1 P31

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OR
24
6 a. Evaluate J Sky + eY dydx
L 3
b. Evaluate fx sin

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s
x dx
2 1 1
c. Evaluate (x
2

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+ y
2
+ z
2
)dxdydz

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(07 Marks)
(07 Marks)
(06 Marks)
Module-4
7 a. If particle moves on the curve x = 2t

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-
, y = t
2
- 4t, z = 3t ? 5 where t is the time. Find the
velocity and acceleration at t = 1. (07 Marks)

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b. Find the angle between the tangents to the curve r = t
2
2t j ? t
3
k at the point t = ? 1.

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(07 Marks)
c.
If /'=(3x
2
y ? z)i+(xz

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3
+ y
4
)] ?2x
3

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z
2
k find grad(div ) at (2, ?1, 0). (06 Marks'
OR
8 a.

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Find the directional derivative of (I) = 4xz
3
3x
2
y

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2
z at (2, ?1, 2) along 21? 3 3+ 6IC
b.
c.
9 a.

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b.
c.
10 a.
b.
c.

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Find the unit normal to the surface x
2
y + 2xz = 4 at (2, ?2, 3).
Show that fs = (2xy
2

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+ yz)i + (2x
2
y + xz + 2yz
2
)] + (2y

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2
z + xy)k is irrotational.
(07 Marks)
(07 Marks)
(06 Marks)

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NIoduie-5
Solve ?
dy
= sin( x + y)
dx

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(07 Marks)
Solve
dy
? + y cot x = cos x
dx

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(07 Marks)
Solve (x ? y + 1)dy ? (x + y 1)dx = 0 (06 Marks)
(
x
OR

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Solve + e'
4
)dx + e" 1 dy = 0 . (07 Marks)
Y.
Solve (x

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3
cos
2
y ? x sin 2y) dx = dy . (07 Marks)
Solve (3x

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2
y
4
+ 2xy)dx + (2x
3

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y
3
? x
2
)dy = 0 (06 Marks)

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